QSVT Lab.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9accaaf0-1343-47b0-a609-229af4ee3f9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "from pennylane import numpy as np \n",
    "\n",
    "st = time.time()\n",
    "np.random.seed(12345678)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "111f0a27-bbb0-42e4-8069-f9c7a0cdbb04",
   "metadata": {},
   "source": [
    "# Technology Laboratory: Exploring Quantum Signal Processing and the Quantum Singular Value Transformation\n",
    "\n",
    "**Jay Soni**  \n",
    "Quantum Software Developer  \n",
    "XanaduAI\n",
    "\n",
    "**James D Whitfield**  \n",
    "Amazon Visiting Academic  \n",
    "Dartmouth College\n",
    "\n",
    "Instructor: James Whitfield (james.d.whitfield@dartmouth.edu), Amazon Visiting Academic;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ecd6d5c-381d-413b-a850-fa1605ebffc4",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## Introduction \n",
    "\n",
    "The Quantum Singular Value Transformation (QSVT) algorithm$^{[1]}$ allows us to transform the singular values of a matrix **without** the need for explicit diagonalization. It's a very versatile framework that can be used to recover some of the most well-known algorithms in quantum computing (search, hamiltonian simulation, factoring)$^{[2]}$. In this laboratory we will explore the concept of Quantum Signal Processing (QSP) that underpins QSVT then, we will use this concept to build a polynomial function approximator. Finally, we will learn about qubitization and use it to generalize the QSP theorem to QSVT! \n",
    "\n",
    "Additionally, this lab will be using PennyLane to generate and execute quantum circuits. If you don't have PennyLane installed on your machine, please follow the installation instructions [here](https://pennylane.ai/install/).\n",
    "\n",
    "## Outline\n",
    "1. **Reflections, Rotations and ... Polynomials?**\n",
    "    - A. Build Intuition\n",
    "    - B. Quantum Signal Processing Theorem \n",
    "    - C. Code Example\n",
    "2. **Its Fun Fitting Functions!**\n",
    "    - A. Learning phase angles on the Fly \n",
    "    - B. QSP as a polynomial function approximator\n",
    "    - C. Recovering the right Unitary \n",
    "3. **Qubitized, Factorized and Generalized:**\n",
    "    - A. Qubitization as an Elevator of QSP\n",
    "    - B. Quantum Singular Value Transformation Theorem\n",
    "    - C. Code Example\n",
    "4. **Conclusions and Further Readings**\n",
    "5. **References**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5de1e2b6-a849-4a9a-9dfe-854dd9742f7d",
   "metadata": {},
   "source": [
    "## 1. Reflections, Rotations and ... Polynomials? \n",
    "\n",
    "Whether we are calculating the minimum grade we need to pass a course, using Google's search engine optimization algorithm to find the nearest coffee shop, or using ChatGPT to write sections in a lab: a standard computational task that one performs is taking \"$a$\" as input and producing \"$f(a)$\" as the output of some function. Suppose you have a fully functional, single-qubit quantum computer: \n",
    "\n",
    "**How would you deterministically transform a given input by some arbitrary function?**\n",
    "\n",
    "Applying an arbitrary function is a rather general task; but recall that we can (*almost*) always approximate it with an appropriate Taylor Polynomial upto $\\epsilon$-precision. Therefore it is sufficient if we are able to transform the input by any polynomial function, because we can then build arbitrary functions from the polynomials. It turns out that the Quantum Signal Processing (QSP) technique holds the key to this problem. In this section we will build an understanding for what QSP is, and how it helps us answer this question. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05f7a61a-76fa-492b-9929-5458833bab9b",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 1A) Building Intuition \n",
    "\n",
    "The best way to build intuition about something is to dive in and get our hands dirty. Consider the following single-qubit operator parameterized by $a \\in [-1, 1]$:\n",
    "\n",
    "$$\\hat{W}(a) = \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix}$$\n",
    "\n",
    "We need to restrict \"$a$\" to this domain to ensure the operator is unitary (verify for yourself that it is unitary). Let's consider what happens if we repeatedly multiply this operator:\n",
    "<br> <br>\n",
    "\n",
    "$$\\hat{W}^2(a) = \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} \\circ \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix}$$\n",
    "$$\\hat{W}^2(a) = \\begin{bmatrix} 2a^2 - 1 & -2a \\sqrt{1 - a^{2}} \\\\ 2a\\sqrt{1 - a^{2}} & 2a^2 - 1 \\end{bmatrix}$$\n",
    "\n",
    "<br>\n",
    "Consider the top-left entry of this matrix, this entry corresponds to computing the expectation value $\\langle 0|\\hat{W}(a)|0\\rangle$. Notice that this quantity is a polynomial in \"$a$\". Equivalently, suppose we wanted to create a map $S: a \\to 2a^2 - 1$.\n",
    "This expectation value would give us the means to perform such a mapping. This may seem oddly specific at first, let's try multiplying it again, only focusing on the upper left corner: \n",
    "<br> <br>\n",
    "\n",
    "$$\\hat{W}^3(a) = \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} \\circ \\hat{W}^2(a)$$\n",
    "$$\\hat{W}^3(a) = \\begin{bmatrix} 4a^3 - 3a & * \\\\ * & * \\end{bmatrix}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Once again, we recover a polynomial in \"$a$\". Additionally, we notice that these polynomials look familiar, infact they are the [Chebyshev polynomials](https://en.wikipedia.org/wiki/Chebyshev_polynomials) of the first kind. It turns out that this pattern continues in general: \n",
    "\n",
    "$$\\langle 0|\\hat{W}^k(a)|0\\rangle = T_{k}(a)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "-------------\n",
    "<br>\n",
    "\n",
    "\n",
    "**Why does it matter if we can generate all of the Chebyshev polynomials?** \n",
    "\n",
    "Recall that our goal is to apply an arbitrary polynomial transformation of our input. The Chebyshev Polynomials form a basis for the set of all polynomials, if we could generate each Chebyshev Polynomial individually, then all that would be left to do is take linear combinations of them to prepare any polynomial. \n",
    "\n",
    "**Where does this pattern come from?**\n",
    "\n",
    "I offer two independant approaches for understanding where this pattern comes from. The first, and my personal favorite, is the \"because math\" explanation. The second is the geometric interpretation (courtesy of my colleague and friend Guillermo Alonso).\n",
    "\n",
    "#### The \"Mechanical\" Explanation: \n",
    "\n",
    "In order to demystify this pattern, let's examine each term in the sequence. \n",
    "\n",
    "$$\\begin{align*}\n",
    "\\hat{W}(a) = \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} &\\equiv \\begin{bmatrix} P_1(a) & -Q_1(a)\\sqrt{1 - a^{2}} \\\\ Q_1(a)\\sqrt{1 - a^{2}} & P_1(a) \\end{bmatrix} \\\\\n",
    "\\hat{W}^2(a) = \\begin{bmatrix} 2a^2 - 1 & -2a \\sqrt{1 - a^{2}} \\\\ 2a\\sqrt{1 - a^{2}} & 2a^2 - 1 \\end{bmatrix} &\\equiv \\begin{bmatrix} P_2(a) & -Q_2(a)\\sqrt{1 - a^{2}} \\\\ Q_2(a)\\sqrt{1 - a^{2}} & P_2(a) \\end{bmatrix} \\\\ \n",
    "&\\ \\ \\vdots \\\\\n",
    "\\hat{W}^k(a) &\\equiv \\begin{bmatrix} P_k(a) & -Q_k(a)\\sqrt{1 - a^{2}} \\\\ Q_k(a)\\sqrt{1 - a^{2}} & P_k(a) \\end{bmatrix}\n",
    "\\end{align*}$$\n",
    "\n",
    "But, we can also express the $k^{th}$-power of our operator recurrsively as $\\hat{W}^k(a) = \\hat{W}(a) \\circ \\hat{W}^{k-1}(a)$. We can use this to come up with a recurrsive expression that describes the sequence:\n",
    "<br><br>\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\hat{W}^k(a) &= \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} \\circ \\begin{bmatrix} P_{k-1}(a) & -Q_{k-1}(a)\\sqrt{1 - a^{2}} \\\\ Q_{k-1}(a)\\sqrt{1 - a^{2}} & P_{k-1}(a) \\end{bmatrix} \\\\\n",
    "\\begin{bmatrix} P_k(a) & -Q_k(a)\\sqrt{1 - a^{2}} \\\\ Q_k(a)\\sqrt{1 - a^{2}} & P_k(a) \\end{bmatrix} &= \\begin{bmatrix} a \\cdot P_{k-1}(a) + (a^2 - 1) \\cdot Q_{k-1}(a)  & -(a \\cdot Q_{k-1}(a) + P_{k-1}(a)) \\sqrt{1 - a^{2}} \\\\ (a \\cdot Q_{k-1}(a) + P_{k-1}(a))\\sqrt{1 - a^{2}} & a \\cdot P_{k-1}(a) + (a^2 - 1) \\cdot Q_{k-1}(a) \\end{bmatrix}\n",
    "\\end{align*}$$\n",
    "\n",
    "<br>\n",
    "Which gives us the coupled recurrsive expressions, \n",
    "<br>\n",
    "\n",
    "$$\\begin{align*}\n",
    "P_k(a) &= a \\cdot P_{k-1}(a) + (a^2 - 1) \\cdot Q_{k-1}(a) \\\\\n",
    "Q_k(a) &= a \\cdot Q_{k-1}(a) + P_{k-1}(a)\n",
    "\\end{align*}$$\n",
    "\n",
    "We can decouple the equations by eliminating the dependance on $Q_{k-1}$ and deriving an expression for $Q_k$ only in terms of $P_k$ and $P_{k-1}$: \n",
    "<br> <br>\n",
    "\n",
    "$$\\begin{align*}\n",
    "a \\cdot P_k(a) - (a^2 - 1) \\cdot Q_k(a) &= a \\cdot (a \\cdot P_{k-1}(a) + (a^2 - 1) \\cdot Q_{k-1}(a)) \\\\ \n",
    "                                        &\\ \\ - (a^2 - 1) \\cdot (a \\cdot Q_{k-1}(a) + P_{k-1}(a)) \\\\\n",
    "                                        &= a^2 \\cdot P_{k-1}(a) + a(a^2 - 1) \\cdot Q_{k-1}(a) \\\\ \n",
    "                                        &\\ \\ - (a^2 - 1) \\cdot P_{k-1}(a) - a(a^2 - 1) \\cdot Q_{k-1}(a) \\\\ \\\\\n",
    "        \\implies (a^2 - 1) \\cdot Q_k(a) &= a \\cdot P_k(a) - P_{k-1}(a)\n",
    "\\end{align*}$$\n",
    "\n",
    "Finally, we can take this expression for $Q_k(a)$ (setting $k \\rightarrow k-1$) and substitute it back into the first recurrence relation for $P_k(a)$. This decouples the expressions and gives us a final recurrence relation for the polynomial we are generating in the top-left corner: \n",
    "\n",
    "$$\\begin{align*}\n",
    "P_k(a) &= a \\cdot P_{k-1}(a) + (a \\cdot P_{k-1}(a) - P_{k-2}(a)) \\\\\n",
    "P_k(a) &= 2a \\cdot P_{k-1}(a) - P_{k-2}(a)\n",
    "\\end{align*}$$\n",
    "\n",
    "This is exactly the recurrsive definition of the Chebyshev Polynomials of the first kind $T(a)_n$. Thus we have shown, due to the structure of the matrix, taking repeated powers of the matrix will give you higher order Chebyshev Polynomials. \n",
    "\n",
    "\n",
    "#### The \"Geometric\" Explanation: \n",
    "\n",
    "Another way to understand this behaviour is to look at it from the prespective of reflections and rotations. $\\hat{W}(a)$ for $a \\in [-1, 1]$ can itself be interpreted as a rotation matrix with an angle $\\theta = cos^{-1}(a)$ (in the block sphere representation, this corresponds to an $\\hat{R}_y(2\\theta)$ rotation). The figure below highlights this interpretation: \n",
    "\n",
    "<br>\n",
    "\n",
    "<div>\n",
    "<img src=\"https://raw.githubusercontent.com/Jaybsoni/QSVT_Lab/17c65fa13b1bfffc22bc311dcf028e56ff521eb4/imgs/qsp1.png\" width=\"750\"/>\n",
    "<!-- <img src=\"imgs/qsp1.png\" width=\"750\"/> -->\n",
    "</div>\n",
    "\n",
    "<br>\n",
    "\n",
    "After rotating the $|0\\rangle$ state, we obtain the state $|\\psi\\rangle \\coloneqq \\hat{W}(a)|0\\rangle = \\begin{bmatrix} cos(\\theta) \\\\ sin(\\theta) \\end{bmatrix}$. Looking at the $|0\\rangle$ component of this transformation gives us the top-left entry. Now, let's consider what happens when we reflect across these two states. Starting in the rotated state $|\\psi\\rangle$, we first reflect across the $|0\\rangle$ state, then we reflect across $|\\psi\\rangle$:  \n",
    "\n",
    "<br>\n",
    "\n",
    "<div>\n",
    "<img src=\"https://raw.githubusercontent.com/Jaybsoni/QSVT_Lab/17c65fa13b1bfffc22bc311dcf028e56ff521eb4/imgs/qsp2.png\" width=\"750\"/>\n",
    "<!-- <img src=\"imgs/qsp2.png\" width=\"750\"/> -->\n",
    "</div>\n",
    "\n",
    "<br>\n",
    "\n",
    "This should look very familiar, infact this is just a Grover type iteration operator. **We are using the pair of reflections to rotate our state.** This concept is very important and will re-surface when we generalize QSP to QSVT using qubitization. Let's analyze what happens after we have applied both of these operators in sequence. The final state (denoted in red), makes an angle of $3\\theta$. Thus, the top-left entry of the resulting operator is $cos(3\\theta)$: \n",
    "\n",
    "$$\\hat{R}_{|\\psi\\rangle} \\circ \\hat{R}_{|0\\rangle} \\circ \\hat{W}(a) |0\\rangle = \\begin{bmatrix} cos(3\\theta) & * \\\\ * & * \\end{bmatrix} |0\\rangle $$\n",
    "\n",
    "Where $\\hat{R}_{|0\\rangle} \\coloneqq 2|0\\rangle \\langle 0| - \\mathbb{I}$ denotes the reflection over the $|0\\rangle$ state and $\\hat{R}_{|\\psi\\rangle} \\coloneqq 2|\\psi\\rangle \\langle \\psi| - \\mathbb{I}$ denotes the reflection over $|\\psi\\rangle$. Repeating this Grover iterator rotates our state in increments of $2\\theta$. Let's expand the $\\hat{R}_{|\\psi\\rangle}$ operator further: \n",
    "\n",
    "$$\\begin{align*}\n",
    "\\hat{R}_{|\\psi\\rangle} &= 2|\\psi\\rangle \\langle \\psi| - \\mathbb{I} \\\\\n",
    "&= 2(\\hat{W}(a)|0\\rangle \\langle 0|\\hat{W}^\\dagger(a)) - \\mathbb{I} \\\\\n",
    "&= 2(\\hat{W}(a)|0\\rangle \\langle 0|\\hat{W}^\\dagger(a)) - \\hat{W}(a)\\hat{W}^\\dagger(a) \\\\\n",
    "&= \\hat{W}(a)(2|0\\rangle \\langle 0| - \\mathbb{I})\\hat{W}^\\dagger(a) \\\\\n",
    "\\hat{R}_{|\\psi\\rangle} &= \\hat{W}(a) \\circ \\hat{R}_{|0\\rangle} \\circ \\hat{W}^\\dagger(a)\n",
    "\\end{align*}$$ \n",
    "\n",
    "Additionally, it can be shown (rather straightforwardly) that $\\hat{R}_{|0\\rangle} \\circ \\hat{W}^\\dagger(a) \\circ \\hat{R}_{|0\\rangle} = \\hat{W}(a)$. Substituting these two results back into our expression above we see something remarkable: \n",
    "\n",
    "$$\\begin{align*}\n",
    "\\begin{bmatrix} cos(3\\theta) & * \\\\ * & * \\end{bmatrix} &= \\hat{R}_{|\\psi\\rangle} \\circ \\hat{R}_{|0\\rangle} \\circ \\hat{W}(a)  \\\\ \n",
    " &= (\\hat{W}(a) \\circ \\hat{R}_{|0\\rangle} \\circ \\hat{W}^\\dagger(a)) \\circ \\hat{R}_{|0\\rangle} \\circ \\hat{W}(a) \\\\ \n",
    " &= \\hat{W}(a) \\circ (\\hat{R}_{|0\\rangle} \\circ \\hat{W}^\\dagger(a) \\circ \\hat{R}_{|0\\rangle}) \\circ \\hat{W}(a) \\\\\n",
    " &= \\hat{W}(a) \\circ \\hat{W}(a) \\circ \\hat{W}(a)  \\\\\n",
    "\\begin{bmatrix} cos(3\\theta) & * \\\\ * & * \\end{bmatrix} &= \\hat{W}^3(a)  \\\\\n",
    "\\end{align*}$$\n",
    "\n",
    "Recall that the Chebyshev Polynomials of the first kind are also defined as $T_n(cos(\\theta)) = cos(n\\theta)$, thus we have shown that repeated products of $\\hat{W}(a)$ produce the Chebyshev polynomials. The product of **repeated reflections** along these two states **generates rotations in increments ~ $\\theta$** which, when **represented in terms of $a$ produce Chebyshev Polynomials** for the transformation.  \n",
    "\n",
    "<br>\n",
    "\n",
    "--------------\n",
    "<br>\n",
    "\n",
    "This method of repeatedly applying $\\hat{W}(a)$ allows us to prepare the associated Chebyshev Polynomial, but what about arbitrary polynomials? It still isn't clear, for example, how I would prepare the polynomial $f(a) = a^2$. We need some way of tuning the coefficients of the polynomials to get more flexability over the types of polynomials we can generate. Let's modify our previous workflow by introducing a complex phase via a $z$-axis rotation: \n",
    "<br> <br>\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\hat{W}(a) \\circ e^{i\\phi\\hat{Z}} \\circ \\hat{W}(a) &= \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} \\circ \\begin{bmatrix} e^{i\\phi} & 0 \\\\ 0 & e^{-i\\phi} \\end{bmatrix} \\circ \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix} a & -\\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & a \\end{bmatrix} \\circ \\begin{bmatrix} e^{i\\phi} \\cdot a & - e^{i\\phi} \\cdot \\sqrt{1 - a^{2}} \\\\ e^{-i\\phi} \\cdot \\sqrt{1 - a^{2}} & e^{-i\\phi} \\cdot a \\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix} e^{i\\phi} \\cdot a^2 + e^{-i\\phi} \\cdot (a^2 - 1) & * \\\\ * & * \\end{bmatrix}\n",
    "\\end{align*}$$\n",
    "\n",
    "<br>\n",
    "Notice that we can tune our polynomial by choosing an appropriate $\\phi$. Setting $\\phi = 0$ recovers the standard $f(a) = 2a^2 - 1$, but we could set $\\phi = \\pi$ to produce $f(a) = 1 - 2a^2$. We can generalize this idea by inserting rotations inbetween every product:\n",
    "\n",
    "$$\\hat{U}_{qsp} = e^{i\\phi_{0}\\hat{Z}} \\circ \\hat{W}(a) \\circ e^{i\\phi_{1}\\hat{Z}} \\circ \\hat{W}(a) \\circ e^{i\\phi_{2}\\hat{Z}} \\dots$$\n",
    "\n",
    "**We have just postulated the QSP unitary!** All of the ideas we discussed in this section are expressed mathematically by the following theorem: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f936dca2-a19e-4666-9549-a13b3e940664",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 1B) Quantum Signal Processing Theorem\n",
    "\n",
    "Let the *Quantum Signal Processing Operator* $\\hat{U}_{qsp}(\\vec{\\phi}, a)$  be defined as follows$^{[2]}$: \n",
    "\n",
    "$$ \\hat{U}_{qsp}(\\vec{\\phi}, a) = e^{i\\phi_{0}\\hat{Z}} \\prod_{k=1}^{d} \\hat{U}(a) e^{i\\phi_{k}\\hat{Z}} $$ \n",
    "\n",
    "Where $d$ represents the number of repetitions and the *Signal Rotation Operator* $\\hat{U}(a)$ is given by:   $\\ \\ \\ \\hat{U}(a) = \\begin{bmatrix} a & i\\sqrt{1 - a^{2}} \\\\ i\\sqrt{1 - a^{2}} & a \\end{bmatrix}$\n",
    "\n",
    "Given a vector $\\vec{\\phi} \\in \\mathbb{R}^{d+1}$, there exist complex polynomials $P(a)$ and $Q(a)$ such that the QSP operator can be expressed in matrix form as:\n",
    "\n",
    "$$\\hat{U}_{qsp}(\\vec{\\phi}, a) = \\begin{bmatrix} P(a) & iQ(a)\\sqrt{1 - a^{2}} \\\\ iQ^{*}(a)\\sqrt{1 - a^{2}} & P^{*}(a) \\end{bmatrix}$$\n",
    "\n",
    "where $a \\in [-1, 1]$ and the polynomials $P(a)$, $Q(a)$ satisfy the following constraints:\n",
    "\n",
    "-  $deg(P(a)) \\leq d \\ $ and $deg(Q(a)) \\leq d - 1$,\n",
    "-  $P(a)$ has parity $d$ mod $2$ and $Q(a)$ has parity $(d - 1)$ mod $2$,\n",
    "-  $|P(a)|^{2} + (1 - a^{2})|Q(a)|^{2} = 1$.\n",
    "\n",
    "<br>\n",
    "\n",
    "#### Some Subtleties: \n",
    "\n",
    "You may have noticed that the form of the signal rotation operator $\\hat{U}(a)$ is different from the one we worked with so far ($\\hat{W}(a)$). This may seem like a significant difference at first, but it is purely a matter for convention. They only differ by some fixed rotations $e^{i\\frac{\\pi}{4}\\hat{z}} \\circ \\hat{U}(a) \\circ e^{-i\\frac{\\pi}{4}\\hat{z}} = \\hat{W}(a)$. These extra $z$-axis rotations can be absorbed into the definition of the $\\phi_{k}$'s. Ultimately, it doesn't matter which convention is used, just that we are consistent in our choice of the convention throughout the quantum workflow. In fact, PennyLane uses a slightly different convention for the signal rotation operator: \n",
    "<br><br>\n",
    "\n",
    "$$\\hat{U}_{pl}(a) = \\begin{bmatrix} a & \\sqrt{1 - a^{2}} \\\\ \\sqrt{1 - a^{2}} & -a \\end{bmatrix}$$ \n",
    "\n",
    "\n",
    "Additionally, notice that we don't have complete freedom over the polynomials we can produce. There are a set of constraints that the polynomials must satisfy. The first constraint states that the degree of the polynomial we generate can't be more than the number of repetitions $d$. This follows naturally because each time we apply $\\hat{U}(a)$ we increment the degree by 1. The second constraint tells us the parity of our polynomial, this arises from the product of Chebyshev polynomials which form the basis of $P(a)$. Finally, the third constriant is a statement about the normalization of the polynomial we generate. We can typically work around this constraint by re-defining our polynomial as $$\\tilde{P}(a) \\coloneqq \\langle +|\\hat{U}_{qsp}|+\\rangle \\equiv Re(P(a)) + iRe(Q(a))\\sqrt{1-a^2}$$. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7583aaa1-2317-491b-b5e8-faf83b64dd04",
   "metadata": {},
   "source": [
    "### 1C) Code Example\n",
    "\n",
    "In this section we will test the theorem by randomly generating parameters $\\vec{\\phi}$ and plotting the expectation value $\\langle 0 |\\hat{U}_{qsp}(\\vec{\\phi},a)|0\\rangle$ for $a \\in [-1, 1]$. We can verify that the theorem holds qualitatively, by checking that the graphs we plot are polynomials which satisfy the constraints listed above. Since we are randomly sampling the phase angles, we can re-running the code will generate a new polynomial each time!\n",
    "\n",
    "I encourage you to play around with the degree variable `degree` and the phase angles `phi_vals` to tune the types of polynomials that are generated! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b1be573d-4772-44f2-a1f8-af6093e14ac3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Code example: \n",
    "import pennylane as qml\n",
    "from pennylane import numpy as np\n",
    "\n",
    "def W(a):\n",
    "    diag, off_diag = (a, (1 - a**2) ** (1 / 2) * 1j)\n",
    "    W_a = [[diag,     off_diag], \n",
    "           [off_diag,     diag]]\n",
    "\n",
    "    return np.array(W_a)\n",
    "\n",
    "\n",
    "def U_qsp(a, phase_angles):\n",
    "    phi_0, W_mat = (phase_angles[0], W(a))    \n",
    "    res = np.diag([np.exp(1j*phi_0), np.exp(-1j*phi_0)])\n",
    "    \n",
    "    for phi_i in phase_angles[1:]:    \n",
    "        res = res @ W_mat @ np.diag([np.exp(1j*phi_i), np.exp(-1j*phi_i)])\n",
    "    \n",
    "    return res\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e6c3606a-ec0f-40ee-8148-aacab203dc53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "degree = 2                                             # This is also the number of repetitions \"d\"\n",
    "a_vals = np.linspace(-1, 1, 50)\n",
    "\n",
    "phi_vals = (2*np.random.rand(degree + 1) - 1) * np.pi  # Sample \"degree+1\"-many phase angles from (-pi, pi)\n",
    "# phi_vals = list(0 for _ in range(degree))            # Set all phase angles to 0 \n",
    "\n",
    "poly_0_a = np.array([U_qsp(a, phi_vals)[0,0] for a in a_vals])\n",
    "\n",
    "plt.plot(a_vals, np.real(poly_0_a), label=\"Re(<0|Uqsp|0>)\")\n",
    "plt.plot(a_vals, np.imag(poly_0_a), label=\"Im(<0|Uqsp|0>)\")\n",
    "\n",
    "plt.vlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "plt.hlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b45acd4e-c30f-40a1-ba82-409826dc5eec",
   "metadata": {},
   "source": [
    "### Exercises: \n",
    "For each exercise, use the convention from the QSP theorem for the signal rotation operator.\n",
    "\n",
    "- ***Exercise 1.1:*** What is the polynomial $P(a)$ constructed for a QSP circuit with phase angles $\\vec{\\phi} = (\\frac{\\pi}{4}, -\\frac{\\pi}{2}, 0)$?\n",
    "- ***Exercise 1.2:*** Solve for the phase angles $(\\vec{\\phi} \\in \\mathbb{R}^3)$ that would generate a polynomial $P(a) = 1 - 2a^2$?\n",
    "- ***Exercise 1.3:*** For both of the questions above, verify your solution by using the code above to plot the theoretical polynomial against the one generated using QSP."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cf47c52-123b-4048-ab60-44106746f9f1",
   "metadata": {},
   "source": [
    "## 2. Its Fun Fitting Functions!\n",
    "\n",
    "As we learned in the previous section, the phase angles $\\vec{\\phi}$ fully determine the polynomial $P(a)$ that will be generated by a given QSP sequence. The next step is to find a way to compute the phase angles for a given polynomial so that we can construct it on our quantum computer, however, this is a non-trivial task. This topic has been heavily studied in literature (see [3] - [5]), with methods ranging from analytical formulas to hybrid optimization based workflows. In this section we will explore how to compute the phase angles for a target polynomial transformation by relying on gradient descent based optimization. \n",
    "\n",
    "This turns out to be a very powerful idea because it will ultimately allow us to approximate QSP transformations for functions which are *NOT* polynomials! "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0995f41e-b198-4916-b8de-63779ae1545a",
   "metadata": {},
   "source": [
    "### 2A) Learning Phase Angles on the Fly\n",
    "\n",
    "The QSP theorem is a direct result of the matrix multiplication of certain key unitary matrices. This means that it is *differentiable*! One simple way to obtain the polynomial transformation we want is through optimization. The general idea is as follows: \n",
    "\n",
    "- Select a set of random initial phase angles $\\vec{\\phi}$ and a target polynomail (eg. $T(x) = x^5 - 3x^3 + x$),\n",
    "- Prepare a quantum circuit which measures the expectation value $\\langle 0| \\hat{U}_{qsp}(a) |0 \\rangle = P(a)$,\n",
    "- Prepare a classical loss function, in this case we use Mean Squared Error (MSE),\n",
    "- Run a standard optimization loop, where we update the phase angles based on the gradient of the loss function,\n",
    "- Return the trained phase angles!\n",
    "\n",
    "Here we rely on Pennylane to prepare and execute our quantum circuit `qsp_circ`, using the state vector simulator `defaul.qubit`. We use the builtin `qml.qsvt(a, phi_vals)` function to prepare the QSP operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "538e90a1-7c86-47bd-b536-569ff2fa5a4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Train a QSP circuit to fit a given polynomial function \n",
    "\n",
    "@qml.qnode(qml.device(\"default.qubit\"))\n",
    "def qsp_circ(a, phi_vals):  # We use the Hadamard test to extract Re(<0|U_qsp|>)\n",
    "    qml.Hadamard(\"aux\")\n",
    "    qml.ctrl(qml.qsvt, control=(\"aux\",), control_values=(1,))(a, phi_vals, wires=[0])\n",
    "    qml.Hadamard(\"aux\")\n",
    "    return qml.expval(qml.Z(\"aux\"))\n",
    "\n",
    "\n",
    "qml.draw_mpl(qsp_circ)(0.5, [1, 2, 3])  # draw the quantum circuit! \n",
    "\n",
    "\n",
    "def target_func(x): \n",
    "    return x**5 - 3*x**3 + x  \n",
    "\n",
    "\n",
    "def loss_func(phi_vals):  # Mean Squared Error (MSE) loss function for the Real value of P(a) \n",
    "    num_samples = 25\n",
    "    \n",
    "    loss = 0\n",
    "    for a in np.linspace(-1, 1, num_samples):\n",
    "        qsp_poly_a = qsp_circ(a, phi_vals)\n",
    "        loss += (qsp_poly_a - target_func(a))**2\n",
    "\n",
    "    return loss / num_samples "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fa6b8d1e-d79a-4f1c-9ae1-35ceb51eeba1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter: 1, cost: 0.6534436355536181\n",
      "iter: 10, cost: 0.014914791014946548\n",
      "iter: 20, cost: 0.005438123003383516\n",
      "iter: 30, cost: 0.0038412295717066116\n",
      "iter: 40, cost: 0.0031688512692195614\n",
      "iter: 50, cost: 0.002731651756486486\n",
      "iter: 60, cost: 0.0023782362292458356\n",
      "iter: 70, cost: 0.002063591919334682\n",
      "iter: 80, cost: 0.0017741721779074892\n",
      "iter: 90, cost: 0.0015079399097070463\n",
      "iter: 100, cost: 0.0012669659969271121\n",
      "Iteration limit reached!\n",
      "Completed Optimization! (final cost: 0.0012443665729229738)\n"
     ]
    }
   ],
   "source": [
    "# Optimization:\n",
    "cost = 1\n",
    "iteration = 0\n",
    "opt = qml.AdagradOptimizer(0.1)\n",
    "\n",
    "phi_vals = (2*np.random.rand(6) - 1) * np.pi/2\n",
    "initial_phi = phi_vals\n",
    "\n",
    "while cost > 1e-5:\n",
    "    iteration += 1\n",
    "    phi_vals, cost = opt.step_and_cost(loss_func, phi_vals)\n",
    "\n",
    "    if iteration % 10 == 0 or iteration == 1:\n",
    "        print(f\"iter: {iteration}, cost: {cost}\")\n",
    "\n",
    "    if iteration > 100:\n",
    "        print(\"Iteration limit reached!\")\n",
    "        break\n",
    "\n",
    "print(f\"Completed Optimization! (final cost: {cost})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41463ca4-2417-44dc-b95e-ee90f190bc01",
   "metadata": {},
   "source": [
    "Now that we have successfully trained the phase angles, lets plot the resulting polynomial and compare it with the target polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "276b3ef9-a895-419a-834b-d8d59074865f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_vals = np.linspace(-1, 1, 25)\n",
    "\n",
    "trained_poly = [qml.matrix(qml.qsvt(a, phi_vals, wires=[0]))[0,0] for a in a_vals]\n",
    "initial_poly = [qml.matrix(qml.qsvt(a, initial_phi, wires=[0]))[0,0] for a in a_vals]\n",
    "targeted_poly = [target_func(a) for a in a_vals]\n",
    "\n",
    "plt.plot(a_vals, np.real(trained_poly), \"*\", label=\"trained\")\n",
    "plt.plot(a_vals, np.real(initial_poly), \"*\", label=\"initial\")\n",
    "plt.plot(a_vals, targeted_poly, label=\"target\")\n",
    "\n",
    "plt.vlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "plt.hlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb50b2c2-b141-4292-bbd3-2ed5fb6068b5",
   "metadata": {},
   "source": [
    "We were successfully able to learn the phase angles for the target polynomial! "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cefe365-66aa-426e-97c6-3612fc58f81c",
   "metadata": {},
   "source": [
    "### 2B) QSP as a Polynomial Function Approximator\n",
    "\n",
    "Notice that all we did in the previous section was *\"optimize some parameters according to some loss function\"*. Nowhere did we enforce the restriction that our target must also be a polynomial, this begs the question:\n",
    "\n",
    "**What happens if our target function isn't a polynomial?**\n",
    "\n",
    "Since the QSP circuit can only generate polynomials $P(a)$, the optimization produces a polynomial approximation to our target function. If we can choose (or transform) our target function to have the same parity/symmetry as the QSP circuit, we can generate even more accurate polynomial approximations. In the next section, let's try and fit the Heaviside Step function using QSP!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "10971900-6fe9-49e5-921d-6db922c7540a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter: 1, cost: 0.18459082919235456\n",
      "iter: 10, cost: 0.08633315849768045\n",
      "iter: 20, cost: 0.08508985764307513\n",
      "iter: 30, cost: 0.08418448297684451\n",
      "iter: 40, cost: 0.08346049659816998\n",
      "iter: 50, cost: 0.08286477599226139\n",
      "iter: 60, cost: 0.08236682752289873\n",
      "iter: 70, cost: 0.08194595358316356\n",
      "iter: 80, cost: 0.08158696485784764\n",
      "iter: 90, cost: 0.08127827354403719\n",
      "iter: 100, cost: 0.0810108481401223\n",
      "Iteration limit reached!\n",
      "Completed Optimization! (final cost: 0.08098608669982857)\n"
     ]
    }
   ],
   "source": [
    "def target_func(x): \n",
    "    return 1 if x>0 else -1  # Step function, notice it has odd parity\n",
    "\n",
    "def loss_func(phi_vals):\n",
    "    num_samples = 50  \n",
    "    \n",
    "    loss = 0\n",
    "    for a in np.linspace(-1, 1, num_samples):\n",
    "        qsp_poly_a = qsp_circ(a, phi_vals)\n",
    "        loss += (qsp_poly_a - target_func(a))**2\n",
    "\n",
    "    return loss / num_samples \n",
    "\n",
    "\n",
    "# Optimization:\n",
    "cost = 1\n",
    "iteration = 0\n",
    "opt = qml.AdagradOptimizer(0.1)\n",
    "\n",
    "phi_vals = np.random.rand(16)  # (d+1) has to be even since P(a) must be odd to match the parity \n",
    "initial_phi = phi_vals         #     of the step function.\n",
    "\n",
    "while cost > 1e-5:\n",
    "    iteration += 1\n",
    "    phi_vals, cost = opt.step_and_cost(loss_func, phi_vals)\n",
    "\n",
    "    if iteration % 10 == 0 or iteration == 1:\n",
    "        print(f\"iter: {iteration}, cost: {cost}\")\n",
    "\n",
    "    if iteration > 100:\n",
    "        print(\"Iteration limit reached!\")\n",
    "        break\n",
    "\n",
    "print(f\"Completed Optimization! (final cost: {cost})\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b049c363-ef7a-4623-b75a-e948367c307c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_vals = np.linspace(-1, 1, 50)\n",
    "trained_phase_angles = phi_vals\n",
    "\n",
    "trained_poly = np.array([qml.matrix(qml.qsvt(a, trained_phase_angles, wires=[0]))[0,0] for a in a_vals])\n",
    "initial_poly = np.array([qml.matrix(qml.qsvt(a, initial_phi, wires=[0]))[0,0] for a in a_vals])\n",
    "targeted_poly = np.array([target_func(a) for a in a_vals])\n",
    "\n",
    "plt.plot(a_vals, np.real(trained_poly), \"*\", label=\"trained\")\n",
    "plt.plot(a_vals, np.real(initial_poly), \"*\", label=\"initial\")\n",
    "plt.plot(a_vals, targeted_poly, label=\"target\")\n",
    "\n",
    "plt.vlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "plt.hlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fddc17d8-6e82-4ad6-8fce-467325cdc87b",
   "metadata": {},
   "source": [
    "We were successfully able to train the phase angles to approximate the heaviside function with a polynomial of degree 15! Try experimenting with the degree of the QSP polynomial (i.e number of phase angles) to see how it affects the fit and optimization process. We will see that the phase angles computed from QSP can be directly used with QSVT."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31d57057-fdf4-4524-bdcf-33f6a4d4f8b6",
   "metadata": {},
   "source": [
    "### 2C) Recovering the Right Unitary\n",
    "\n",
    "\n",
    "Another subtle, yet important point to address is that of the unitary we produce. As you may have noticed, our phase angle training protocol was fitting the real component $Re(P(a))$ of the polynomial generated from QSP. However, suppose we wanted to apply this polynomial transformation in the quantum circuit directly, the QSP unitary would not perform this transformation due to the non-zero imaginary component of $P(a)$. \n",
    "\n",
    "In general, the imaginary part of this transformation will not be zero. We need an operator which only applies the real component. Recall that we can express the real part of a complex number $z$ as: $$Re[z] = \\frac{1}{2}(z + z^{*})$$ \n",
    "\n",
    "Similarly, for operators this is given by:\n",
    "\n",
    "$$ \\hat{U}_{real}(\\vec{\\phi}) = \\frac{1}{2} \\ ( \\hat{U}_{qsp}(\\vec{\\phi}) + \\hat{U}^{*}_{qsp}(\\vec{\\phi}) )$$\n",
    "\n",
    "Where $A^*$ denotes the complex conjugate. We use the well known algorithm of \"Linear Combinations of Unitaries\" to get the real unitary transformation. We will not be explaining this algorithm in this lab, but you can reference [this demo](https://pennylane.ai/qml/demos/tutorial_lcu_blockencoding/) for more information. We obtain the complex conjugate $\\hat{U}^{*}_{qsp}$ by setting $\\vec{\\phi} \\rightarrow - \\vec{\\phi}$. \n",
    "\n",
    "By running the following circuit, if we measure the $|0\\rangle$ state in the `\"aux\"` qubit, then we will have applied the the real unitary in the other register:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b773a797-8784-4ff7-ac45-1a7ca0e4d6f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 700x300 with 1 Axes>, <Axes: >)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Show how to recover the \"real\" unitary\n",
    "dev = qml.device(\"default.qubit\")\n",
    "\n",
    "@qml.qnode(dev)\n",
    "def real_u_circuit(a, phi):\n",
    "    qml.Hadamard(wires=\"aux\")\n",
    "\n",
    "    qml.ctrl(qml.qsvt, control=(\"aux\",), control_values=(0,))(a, phi, wires=[0])\n",
    "    qml.ctrl(qml.qsvt, control=(\"aux\",), control_values=(1,))(a, -1*phi, wires=[0])\n",
    "\n",
    "    qml.Hadamard(wires=\"aux\")\n",
    "    return qml.state()\n",
    "\n",
    "qml.draw_mpl(real_u_circuit)(0.5, np.array([0, 1, 2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34335cd9-71ca-42f1-be5b-06ef4fb6dc85",
   "metadata": {},
   "source": [
    "### Exercises: \n",
    "\n",
    "- ***Exercise 2.1:*** Using the code above as a reference, can you find the phase angles to approximate $f(x) = sin(x)$?\n",
    "- ***Exercise 2.2:*** Using the code above as a reference, can you find the phase angles to approximate $g(x) = cos(x)$?\n",
    "\n",
    "***Bonus:*** Construct a circuit using the phase angles you computed above to perform the transformation below: (hint: use the method of LCUs) $$h(x) \\approx e^{ix} = cos(x) + i*sin(x)$$\n",
    "\n",
    "*Note:* The circuit you just created can be used to perform hamiltonian time evolution $e^{-iHt}$. This is another powerful application of QSP/QSVT."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26bd42c9-2d8e-4a6b-bf37-008525ebe0c5",
   "metadata": {},
   "source": [
    "## 3. Qubitized, Factorized and Generalized:\n",
    "\n",
    "The first section covered the concept of QSP, where one can transform an entry in a single-qubit space through a polynomial function. In the previous section, we learned how to tune the free parameters of our circuit in order to generate a specific transformation. It turns out that these ideas can be lifted from the single-qubit case to the multi-qubit case, in which we are able to transform multiple entries of a matrix. This section will explore the ideas of Qubitization, and in doing so, allow us to lift all of our results from QSP to the case of transforming elements of a matrix $a \\rightarrow A$.\n",
    "\n",
    "Recall that quantum computers only support unitary transformations. If we have an input state $|\\psi_{in}\\rangle$, any gate we apply to it must be unitary $\\hat{U}|\\psi_{in}\\rangle$. \n",
    "\n",
    "**How would we apply a non-unitary operation to a state using a quantum computer?**\n",
    "\n",
    "The answer is *Block Encodings*! The idea is rather simple, we can embed the non-unitary transformation inside a larger operator which is unitary. There is rich theory behind this idea, we point readers to [this demo](https://pennylane.ai/qml/demos/tutorial_lcu_blockencoding/) for more information. Consider a non-unitary, square transformation $A: \\mathbb{C}^{2^n} \\rightarrow \\mathbb{C}^{2^n}$ which can act on an $n$-qubit space (this is for simplicity and can be generalized to non-square matrices). We define a specific block encoding of $A$ as follows: \n",
    "\n",
    "$$\\hat{U}(A) \\coloneqq \\begin{bmatrix} A & * \\\\ * & * \\end{bmatrix}$$ \n",
    "\n",
    "Such that $\\hat{U}(A): \\mathbb{C}^{2^{m+n}} \\rightarrow \\mathbb{C}^{2^{m+n}}$ is a hermitian, unitary matrix defined on a larger $(m + n)$-qubit space. We can better understand how this operator works by considering its action on some particular states:\n",
    "\n",
    "$$\\hat{U}(A) |0^{m}\\rangle|\\psi\\rangle = |0^{m}\\rangle A|\\psi\\rangle + \\alpha |\\perp_{\\psi}\\rangle$$\n",
    "\n",
    "Where $\\alpha$ is some normalization factor. If we apply the block encoded unitary to a state which is in the all 0 state in the first $m$-qubits (i.e confined to the top-left block), then we get back $A|\\psi\\rangle$ in the remaining $n$-qubits plus another state which is completely orthogonal. Thus, if we measure the first $m$-qubits in the $|0^m\\rangle$ state after we have applied the block-encoded operator, then we know that the state of the remaining $n$-qubits is proportional to $A|\\psi\\rangle$. Using this property of block-encodings, we will explore qubitization and how it relates to QSP. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1482f6dd-157e-4b6e-b689-51e33a6fb228",
   "metadata": {},
   "source": [
    "### 3A) Qubitization as an Elevator of QSP\n",
    "\n",
    "Recall that we can express $A$ in terms of its Singular Value Decomposition (SVD) $A = \\hat{W} \\circ \\Sigma \\circ \\hat{V}^{\\dagger}$, or alternatively $\\ A = \\Sigma_{k} \\sigma_{k} |w_{k}\\rangle \\langle v_{k}| \\ \\ $. \n",
    "Let's consider what happens when we apply the block-encoded matrix onto a singular vector of A, for simplicity and without loss of generality we can assume $m = 1$.\n",
    "\n",
    "$$\\begin{align*} \\hat{U}(A) |0\\rangle|v_{i}\\rangle &= |0\\rangle A|v_i\\rangle \\ \\ + \\ \\ \\alpha |\\tilde{\\perp}_{i}\\rangle  \\\\ \n",
    "&= \\sigma_i|0\\rangle|w_i\\rangle \\ + \\sqrt{1-\\sigma^2_i}|\\tilde{\\perp}_{i}\\rangle \n",
    "\\end{align*}$$ \n",
    "\n",
    "Where $\\alpha = \\sqrt{1 - \\sigma_{i}^2}$ to ensure the state is normalized. It turns out, that the action of $\\hat{U}^{\\dagger}(A)$ is similar, on the left singular vectors. This can be seen if we think about the conjugate-transpose of our block-encoding matrix, the top-left corner becomes $A^{\\dagger}$.\n",
    "\n",
    "$$\\begin{align*} \\hat{U}^{\\dagger}(A) |0\\rangle|w_{i}\\rangle &= |0\\rangle A^{\\dagger}|w_i\\rangle \\ \\ + \\ \\ \\beta |\\perp_{i}\\rangle  \\\\ \n",
    "&= \\sigma_i|0\\rangle|v_i\\rangle \\ + \\sqrt{1-\\sigma^2_i}|\\perp_{i}\\rangle \n",
    "\\end{align*}$$\n",
    "\n",
    "Once again, the normalization factor $\\beta = \\sqrt{1 - \\sigma_{i}^2}$ is the same as before. Let's notice what happens if we apply $U^{\\dagger}(A)$ to both sides of the first equation: \n",
    "\n",
    "$$\\begin{align*} \\hat{U}^{\\dagger}(A) \\circ \\hat{U}(A) |0\\rangle|v_{i}\\rangle &= \\hat{U}^{\\dagger}(A) (\\sigma_i|0\\rangle|w_i\\rangle \\ + \\sqrt{1-\\sigma^2_i}|\\tilde{\\perp}_{i}\\rangle) \\\\\n",
    "\\mathbb{I} |0\\rangle|v_{i}\\rangle &= (\\sigma^2_i|0\\rangle|v_i\\rangle \\ + \\sigma_i\\sqrt{1-\\sigma^2_i}|\\perp_{i}\\rangle) + \\sqrt{1-\\sigma^2_i}\\hat{U}^{\\dagger}(A)|\\tilde{\\perp}_{i}\\rangle \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  \\text{Isolating for $|\\tilde{\\perp}_{i}\\rangle$,} \\\\ \n",
    "\\hat{U}^{\\dagger}(A)|\\tilde{\\perp}_{i}\\rangle &= \\sqrt{1-\\sigma^2_i}|0\\rangle|v_i\\rangle - \\sigma_i|\\perp_{i}\\rangle\n",
    "\\end{align*}$$\n",
    "\n",
    "Similarly, by applying $\\hat{U}(A)$ to both sides of the second equation, we can show that $\\hat{U}(A)|\\perp_{i}\\rangle = \\sqrt{1-\\sigma^2_i}|0\\rangle|w_i\\rangle -\\sigma_i|\\tilde{\\perp}_{i}\\rangle$. This may seem like pointless algebraic manipulation, but we have actually uncovered something powerful. We have identified two different spaces, $span\\{|0\\rangle|v_i\\rangle, |\\perp_{i}\\rangle\\}$ and $span\\{|0\\rangle|w_i\\rangle, |\\tilde{\\perp}_{i}\\rangle\\}$. Furthermore, we can map freely between the two spaces using $\\hat{U}(A)$ and $\\hat{U}^{\\dagger}(A)$. \n",
    "\n",
    "We can see this clearly by working through the following example: \n",
    "\n",
    "1. start in the state $|0\\rangle|v_i\\rangle$ and apply $\\hat{U}(A)$ to move to the $span\\{|0\\rangle|w_i\\rangle, |\\tilde{\\perp}_{i}\\rangle\\}$ space\n",
    "2. perform a reflection across the state $|0\\rangle|w_i\\rangle$\n",
    "3. apply $\\hat{U}^{\\dagger}(A)$ to move back to the $span\\{|0\\rangle|v_i\\rangle, |\\perp_{i}\\rangle\\}$ space\n",
    "\n",
    "Mathematically, this works out as follows: (where $\\tilde{\\Pi} \\coloneqq |0\\rangle|w_i\\rangle \\langle 0|\\langle w_i|$) \n",
    "\n",
    "$$\\begin{align*}\n",
    " \\hat{U}(A) |0\\rangle|v_{i}\\rangle &= \\sigma_i|0\\rangle|w_i\\rangle \\ + \\sqrt{1-\\sigma^2_i}|\\tilde{\\perp}_{i}\\rangle  \\ \\ \\ \\ \\ &\\text{(1)} \\\\\n",
    " (2\\tilde{\\Pi} - \\mathbb{I}) \\circ \\hat{U}(A) |0\\rangle|v_{i}\\rangle &= \\sigma_i|0\\rangle|w_i\\rangle \\ - \\sqrt{1-\\sigma^2_i}|\\tilde{\\perp}_{i}\\rangle \\ \\ \\ \\ \\ &\\text{(2)} \\\\\n",
    "  \\hat{U}^{\\dagger}(A) \\circ (2\\tilde{\\Pi} - \\mathbb{I}) \\circ \\hat{U}(A) |0\\rangle|v_{i}\\rangle &= \\hat{U}^{\\dagger}(A)(\\sigma_i|0\\rangle|w_i\\rangle \\ - \\sqrt{1-\\sigma^2_i}|\\tilde{\\perp}_{i}\\rangle) \\\\ \n",
    "  &= \\sigma_i^2|0\\rangle|v_i\\rangle \\ + \\sigma_i\\sqrt{1-\\sigma^2_i}|\\perp_{i}\\rangle - (1-\\sigma^2_i)|0\\rangle|v_i\\rangle + \\sigma_i\\sqrt{1-\\sigma^2_i}|\\perp_{i}\\rangle \\\\ \n",
    "  \\hat{U}^{\\dagger}(A) \\circ (2\\tilde{\\Pi} - \\mathbb{I}) \\circ \\hat{U}(A) |0\\rangle|v_{i}\\rangle &= (2\\sigma_i^2 - 1)|0\\rangle|v_i\\rangle + 2\\sigma_i\\sqrt{1-\\sigma^2_i}|\\perp_{i}\\rangle \\ \\ \\ \\ \\ &\\text{(3)}\n",
    "\\end{align*}$$\n",
    "\n",
    "Note the coefficients after applying step 3. If you recall back from the section on QSP after applying these transformations, we see the Chebyshev polynomials are appearing again and we are performing rotations! The following figure highlights the transformations we just applied:\n",
    "\n",
    "<br>\n",
    "\n",
    "<div>\n",
    "<img src=\"https://raw.githubusercontent.com/Jaybsoni/QSVT_Lab/17c65fa13b1bfffc22bc311dcf028e56ff521eb4/imgs/qubitized1.png\" width=\"750\"/>\n",
    "<!-- <img src=\"imgs/qubitized1.png\" width=\"750\"/> -->\n",
    "</div>\n",
    "\n",
    "<br>\n",
    "\n",
    "If we repeat the sequence $(2\\Pi - \\mathbb{I}) \\circ \\hat{U}^{\\dagger}(A) \\circ (2\\tilde{\\Pi} - \\mathbb{I}) \\circ \\hat{U}(A)$, then we end up performing exactly the same types of rotations as we have seen with QSP. The truely surprising insight is that all of the analysis we did in this section so far, was general for any singular value $\\sigma_i$ of $A$. This implies that we can perform these rotations to all of the singular values independantly at once! What we have shown, is that because the block encoding allows us to partition the space into these individual 2D subspaces (qubitized subspaces), we are able to perform QSP like rotations on each one individually.\n",
    "\n",
    "In order to tune these rotations, we again introduce phase rotations. Here we generalize the idea of $Z$-rotations, to projector controlled rotations, where we rotate across the axis of the reflection operator.\n",
    "\n",
    "$$ \\tilde{\\Pi}_{\\phi} \\coloneqq exp(i\\phi\\tilde{\\Pi}), \\ \\ \\ \\Pi_{\\phi} \\coloneqq exp(i\\phi\\Pi)$$\n",
    "\n",
    "Now we have all of the tools we need to understand the Quantum Singular Value Transformation theorem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99fa3bb9-751e-4aac-9d44-cc3510b8be4c",
   "metadata": {},
   "source": [
    "### 3B) Quantum Singular Value Transformation Theorem$^{[2]}$\n",
    "\n",
    "Given a block encoding for the (generally non-square) matrix $A = \\Sigma_{k} \\sigma_{k} |w_{k}\\rangle \\langle v_{k}|$: \n",
    "\n",
    " $$ \\hat{U}(A) = \\begin{bmatrix} A & *\\\\ * & * \\end{bmatrix}$$ \n",
    " \n",
    "Additionally, given access to *projector controlled phase-shifts* $\\hat{\\Pi}_{\\phi}$, $\\hat{\\tilde{\\Pi}}_{\\phi}$; The QSVT unitary is defined below\n",
    " \n",
    "$$\\begin{align*} \\hat{U}_{qsvt}(\\vec{\\phi}, A) &\\coloneqq \\hat{\\tilde{\\Pi}}_{\\phi_1}\\hat{U}(A)\\left[\\prod_{k=1}^{(d-1)/2}\\hat{\\Pi}_{\\phi_{2k}}\\hat{U}^\\dagger(A) \\hat{\\tilde{\\Pi}}_{\\phi_{2k+1}} \\hat{U}(A)\\right]\\hat{\\Pi}_{\\phi_{d+1}} \\ \\ \\ \\ &\\text{for $d$ odd,} \\\\\n",
    "\\hat{U}_{qsvt}(\\vec{\\phi}, A) &\\coloneqq \\left[\\prod_{k=1}^{d/2}\\hat{\\Pi}_{\\phi_{2k-1}}\\hat{U}^\\dagger(A) \\hat{\\tilde{\\Pi}}_{\\phi_{2k}} \\hat{U}(A)\\right]\\hat{\\Pi}_{\\phi_{d+1}} &\\text{for $d$ even.} \\end{align*}$$\n",
    "\n",
    "Such that, it can be expressed in matrix form as $\\hat{U}_{qsvt}(\\vec{\\phi}, A) = \\begin{bmatrix} P(A) & * \\\\ * & *\\end{bmatrix}$. The polynomial transformation of A is defined in terms of its singular value decomposition, and is subject to all of the same constraints (degree, parity and normalization) as in the QSP case. \n",
    "\n",
    "$$ P(A) = \\sum_k P(\\sigma_k)|w_k\\rangle \\langle v_k| $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2b7a8d5-7c7f-4f27-a882-a9625ef601a5",
   "metadata": {},
   "source": [
    "### 3C) Code Example \n",
    "\n",
    "In this section, we will use everything we have learned to transform the singular values of a matrix $A$. In order to more easily visualize the transformation, we choose $A$ to be diagonal, with its entries increasing from $a \\in [-1, 1]$, this way we can read of the singular values before and after the transformation $a \\rightarrow P(a)$ directly!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c98bac9a-1fac-47d4-92ed-6835cef77cfc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.   -0.87  0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.   -0.73  0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.   -0.6   0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.   -0.47  0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.   -0.33  0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.   -0.2   0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.   -0.07  0.    0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.07  0.    0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.2   0.    0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.33  0.\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.47\n",
      "   0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.6   0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.73  0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.87  0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.    1.  ]]\n"
     ]
    }
   ],
   "source": [
    "eigvals = np.linspace(-1, 1, 16)\n",
    "A = np.diag(eigvals)  # 16x16 diagonal matrix ==> 4 qubits to represent A \n",
    "\n",
    "print(np.round(A, 2)) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24c4cecc-9aee-41fd-9107-a1db48f1da6b",
   "metadata": {},
   "source": [
    "In order to apply the QSVT unitary, we again use the PennyLane function `qml.qsvt(A, wires)`. Here we use a 5 qubit system in order to block encode $A$. Since QSVT is a direct generalization of QSP, as long as we use the same convention for the block encoding as we have for the signal rotation operator, we can use the phase angles from QSP!\n",
    "\n",
    "In this case, we use the phase angles we trained for the heaviside step function! We can verify that we have applied the correct transformation by simplying plotting the diagonal elements of the top-left corner of $\\hat{U}_{qsvt}(A)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d7b614ab-d457-41f5-9e78-cce509ff33a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "wire_order = list(range(5))  # 5-qubit system (4-qubits to specify A, 1 qubit to block encode) \n",
    "\n",
    "U_A = qml.matrix(qml.qsvt, wire_order=wire_order)(A, trained_phase_angles, wires=wire_order)  \n",
    "qsvt_A = np.real(np.diagonal(U_A))[:16]  # retrieve transformed eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ba7dffb0-f52e-4b52-94d4-3509ca697c2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(eigvals, qsvt_A, \"--*\", label=\"trained\")\n",
    "plt.plot(eigvals, np.diagonal(A), \"--*\", label=\"initial\")\n",
    "plt.plot(a_vals, targeted_poly, label=\"target\")\n",
    "\n",
    "\n",
    "plt.vlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "plt.hlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9167a51-97af-48dc-a5a0-06c93cda8980",
   "metadata": {},
   "source": [
    "We were successfully able to transform the singular values of $A$ according to the phase angles for the step function! Now, let's do this for a non-diagonal $A$. In order for us to extract the transformation and verify it, we need to find the singular value decomposition (SVD) for $A$. Instead of starting from a non-diagonal matrix and finding the SVD, we instead start with the diagonal matrix (from above), and *\"scramble\"* it, so that we know the SVD to begin with. \n",
    "\n",
    "In the code below, we build a random 16 by 16 unitary matrix which will scrable our diagonal matrix such that $A_{new} = \\hat{V} \\circ A \\circ \\hat{V}^{\\dagger}$. In this framework, $\\hat{V} \\circ A \\circ \\hat{V}^{\\dagger}$ is the SVD of $A_{new}$. Notice that $A_{new}$ is clearly not diagonal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "742d2307-7b92-41c5-bac4-d1b7969f19bb",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-5.90098998e-01-1.20484572e-17j -6.66666667e-02-5.29877759e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01-6.89361942e-18j  8.00259926e-18+1.68944899e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   9.02105379e-18-4.64650494e-01j  6.59145749e-18-8.22897432e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   1.15305328e-17-3.98494134e-17j -4.59163890e-18-8.72284396e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [-6.66666667e-02-5.29877759e-18j -5.90098998e-01-1.20484572e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   8.00259926e-18+1.68944899e-18j -1.81943166e-01-6.89361942e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   6.59145749e-18-8.22897432e-18j  9.02105379e-18-4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -4.59163890e-18-8.72284396e-18j  1.15305328e-17-3.98494134e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -3.23432332e-01+7.27575360e-18j -6.66666667e-02+6.60203421e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01+7.32626660e-18j -1.75356115e-17+3.08207426e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -3.18986414e-18-4.64650494e-01j  1.45514066e-18-1.21233159e-19j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.31957499e-17+3.14350542e-17j  2.78740900e-18-3.67947855e-18j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02+6.60203421e-18j -3.23432332e-01+7.27575360e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.75356115e-17+3.08207426e-18j -1.81943166e-01+7.32626660e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   1.45514066e-18-1.21233159e-19j -3.18986414e-18-4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   2.78740900e-18-3.67947855e-18j -1.31957499e-17+3.14350542e-17j]\n",
      " [-1.81943166e-01+1.19574484e-17j  4.27642838e-18+3.65506285e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -2.00187237e-01+5.13158385e-18j -6.66666667e-02-5.13158385e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.25593653e-18-2.27217279e-17j  6.25593653e-18-1.19727416e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.62742946e-18-4.64650494e-01j -5.31146445e-18+2.60956714e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 4.27642838e-18+3.65506285e-18j -1.81943166e-01+1.19574484e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02-5.13158385e-18j -2.00187237e-01+5.13158385e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   6.25593653e-18-1.19727416e-17j -6.25593653e-18-2.27217279e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -5.31146445e-18+2.60956714e-17j -1.62742946e-18-4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01-1.63894335e-17j -1.75356115e-17-9.57801244e-19j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   6.64794292e-02-1.81408973e-18j -6.66666667e-02-5.12480418e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   8.07863106e-18+3.27853364e-17j  5.79915675e-18-5.02976079e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -2.33947210e-18-4.64650494e-01j -1.15383157e-17+9.87913885e-18j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.75356115e-17-9.57801244e-19j -1.81943166e-01-1.63894335e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02-5.12480418e-18j  6.64794292e-02-1.81408973e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   5.79915675e-18-5.02976079e-18j  8.07863106e-18+3.27853364e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.15383157e-17+9.87913885e-18j -2.33947210e-18-4.64650494e-01j]\n",
      " [ 8.28689240e-18+4.64650494e-01j  3.85617194e-18-1.41660127e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -9.61613990e-18+1.69488400e-18j  6.14669295e-18-1.55726718e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.64794292e-02-7.34829754e-18j -6.66666667e-02+2.14412711e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01+8.46260577e-18j -7.99927422e-19-8.46260577e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 3.85617194e-18-1.41660127e-18j  8.28689240e-18+4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   6.14669295e-18-1.55726718e-17j -9.61613990e-18+1.69488400e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02+2.14412711e-18j -6.64794292e-02-7.34829754e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -7.99927422e-19-8.46260577e-18j -1.81943166e-01+8.46260577e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   7.21847672e-18+4.64650494e-01j  1.35982050e-17+3.04036901e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   4.60918411e-18-2.00002420e-17j  9.26860370e-18+6.12245416e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   2.00187237e-01+1.79854693e-18j -6.66666667e-02+8.60979393e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01-1.51767913e-17j  6.83899482e-18+1.29900347e-18j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   1.35982050e-17+3.04036901e-17j  7.21847672e-18+4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   9.26860370e-18+6.12245416e-18j  4.60918411e-18-2.00002420e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02+8.60979393e-18j  2.00187237e-01+1.79854693e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   6.83899482e-18+1.29900347e-18j -1.81943166e-01-1.51767913e-17j]\n",
      " [ 6.93889390e-18+6.93889390e-18j  1.15032046e-18+5.75602096e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.04083409e-17+4.64650494e-01j -3.46944695e-18+3.46944695e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01-6.93889390e-18j  3.33510481e-18+3.68225757e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   3.23432332e-01+0.00000000e+00j -6.66666667e-02+1.73472348e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 1.15032046e-18+5.75602096e-18j  6.93889390e-18+6.93889390e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -3.46944695e-18+3.46944695e-18j -1.04083409e-17+4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   3.33510481e-18+3.68225757e-18j -1.81943166e-01-6.93889390e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02+1.73472348e-18j  3.23432332e-01+0.00000000e+00j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.38777878e-17-2.08166817e-17j -3.68897412e-18+9.98784946e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   1.38777878e-17+4.64650494e-01j -3.46944695e-18+1.04083409e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -1.81943166e-01+2.08166817e-17j -3.34778147e-18+1.76794086e-18j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "   5.90098998e-01+0.00000000e+00j -6.66666667e-02+0.00000000e+00j]\n",
      " [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -3.68897412e-18+9.98784946e-18j -1.38777878e-17-2.08166817e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -3.46944695e-18+1.04083409e-17j  1.38777878e-17+4.64650494e-01j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -3.34778147e-18+1.76794086e-18j -1.81943166e-01+2.08166817e-17j\n",
      "   0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j\n",
      "  -6.66666667e-02+0.00000000e+00j  5.90098998e-01+0.00000000e+00j]]\n"
     ]
    }
   ],
   "source": [
    "random_rotation_angles = (2*np.random.rand(3) - 1) * np.pi/2\n",
    "\n",
    "random_unitary = qml.prod(\n",
    "        qml.RX(random_rotation_angles[0], 0),\n",
    "        qml.RY(random_rotation_angles[1], 1),\n",
    "        qml.RZ(random_rotation_angles[2], 2),\n",
    "        qml.Hadamard(4),\n",
    ")\n",
    "\n",
    "new_A = qml.matrix(random_unitary) @ A @ qml.matrix(qml.adjoint(random_unitary))\n",
    "print(new_A)  # Clearly not diagonal 16 x 16 matrix "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "143ae3e2-2e9e-465a-882e-9446651cb9e9",
   "metadata": {},
   "source": [
    "We can pass the $A_{new}$ matrix directly into the QSVT algorithm just as was done above. The QSVT algorithm will perform the polynomial transformation to the singular values of $A_{new}$, thus to extract the results we need to *undo* this singular value decomposition $ \\hat{U}_{qsvt}(A_{new}): A_{new} \\rightarrow P(A_{new})$: \n",
    "\n",
    "$$\\begin{align*} \n",
    "\\hat{U}_{qsvt}(A_{new}) &\\sim \\hat{V} \\circ P(A) \\circ \\hat{V}^{\\dagger} \\\\ P(A) &\\sim \\hat{V}^{\\dagger} \\circ \\hat{U}_{qsvt}(A_{new}) \\circ \\hat{V}\n",
    "\\end{align*}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3fdb11ba-765d-4ef0-ac3a-49a33b33635c",
   "metadata": {},
   "outputs": [],
   "source": [
    "U_new_A = qml.matrix(qml.qsvt, wire_order=wire_order)(new_A, trained_phase_angles, wires=wire_order)[:16, :16]  \n",
    "\n",
    "unscrambled_U_new_A = qml.matrix(qml.adjoint(random_unitary)) @ U_new_A @ qml.matrix(random_unitary) \n",
    "\n",
    "qsvt_new_A = np.real(np.diagonal(unscrambled_U_new_A))  # retrieve transformed eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "97a7ab51-4f5a-4c6b-851a-8573be57160b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGdCAYAAAAfTAk2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAACIfklEQVR4nO3dd3xT9frA8U+S7k3pLoWyN5RZQRCUXjaIoAJyZchwcb1cRBQHivwUUFQcXFFk6HWgTDeKLFmy9xRoKRTaAqUtnWmT8/vj0NDQQVuSJk2f9+uVV3rO+ebkOU2bPPlOjaIoCkIIIYQQDkRr6wCEEEIIISxNEhwhhBBCOBxJcIQQQgjhcCTBEUIIIYTDkQRHCCGEEA5HEhwhhBBCOBxJcIQQQgjhcCTBEUIIIYTDcbJ1ALZgNBq5ePEi3t7eaDQaW4cjhBBCiDJQFIXr168TFhaGVlt6HU21THAuXrxIRESErcMQQgghRAWcP3+eWrVqlVqmWiY43t7egPoL8vHxsXE0QgghhCiL9PR0IiIiTJ/jpamWCU5Bs5SPj48kOEIIIUQVU5buJdLJWAghhBAORxIcIYQQQjgcSXCEEEII4XCqZR+cslAUhfz8fAwGg61DqbZ0Oh1OTk4ylF8IIUS5SYJTDL1ez6VLl8jKyrJ1KNWeh4cHoaGhuLi42DoUIYQQVYgkOLcwGo3Exsai0+kICwvDxcVFahBsQFEU9Ho9ly9fJjY2loYNG952UichhBCigCQ4t9Dr9RiNRiIiIvDw8LB1ONWau7s7zs7OnDt3Dr1ej5ubm61DEkIIUUXIV+ISSG2BfZDXQQghREXIp4cQQgghHI5VE5w///yTAQMGEBYWhkajYc2aNbd9zKZNm2jbti2urq40aNCApUuXFikzf/58IiMjcXNzIzo6ml27dlk+eCGEEEJUTMI+WNpfvbcRqyY4mZmZtG7dmvnz55epfGxsLP369ePee+/lwIEDTJo0iXHjxvHbb7+Zynz77bdMnjyZV199lX379tG6dWt69epFcnKytS6jWoqMjGTevHlWf57u3bszadIkqz+PEMJ+HLqQyvBP/+LQhVRbhyKs5eAyiNsCh761WQhW7WTcp08f+vTpU+byCxYsoG7durzzzjsANG3alK1bt/Lee+/Rq1cvAN59913Gjx/PmDFjTI/5+eefWbx4MS+88ILlL+IOHLqQyqxfTjCtbxNa1fKz+vN1796dqKgoiyQmu3fvxtPT886DEkKIW6zal8COs1dZtS+hUt4bRSVJjYesq4AGjq5S9x1ZCa2HAwp41AS/2pUWjl2NotqxYwcxMTFm+3r16mX6hq/X69m7dy/Tpk0zHddqtcTExLBjx44Sz5ubm0tubq5pOz093bKBl8De/okVRcFgMODkdPuXPTAwsBIiEsL69AY9/zv2P65kX7F1KNXa9dw8cvOMAPx+LhHXYCOrz2nJ3BACgKuzFm9XZ1uGKO7UX/+9+bOrhtZ40DvzCnza7eb+19IqLRy7SnASExMJDg422xccHEx6ejrZ2dlcu3YNg8FQbJkTJ06UeN5Zs2YxY8aMO44vS59f4jGtRoObs44L17K4lplHbr6BHw5eBOCHgxfp3yoUBQU/Dxcianjg5qwr9bweLuV7aUaPHs3mzZvZvHkz77//PgBLlixhzJgx/PLLL7z88sscPnyY33//nYiICCZPnsxff/1FZmYmTZs2ZdasWWbJZWRkJJMmTTIllxqNhoULF/Lzzz/z22+/ER4ezjvvvMPAgQNNjzly5AjPPfccW7ZswdPTk549e/Lee+8REBAAqE2WTz75JKtWrcLb25spU6aU6xqFuJ3MzEy8vLwAyMjIwNPTk20J25i3b55tAxPmfMAFMAJrz9s6GGExvj5mm7np0DvzxoS5WicY9HGlhmNXCY61TJs2jcmTJ5u209PTiYiIKPd5mk3/rcRj9zYOZMmYjnSZs7HIsZRMPQ8uuFnDFF3Xn28f72Ta7jJnIymZerPHxM3uV67Y3n//fU6dOkWLFi14/fXXATh69CgAL7zwAnPnzqVevXrUqFGD8+fP07dvX9544w1cXV354osvGDBgACdPnqR27ZKrD2fMmMFbb73F22+/zYcffsiIESM4d+4c/v7+pKamct999zFu3Djee+89srOzef7553n44YfZsGEDAM899xybN2/m+++/JygoiBdffJF9+/YRFRVVrmsVojzS9Oo3xgjvCHpH9rZxNNXXyaTrrD+ehFEpvdy9jQNpHuYLQEpWLqeTMvH3dMHP0xk/d2ecZOoI+2Q0QNxW8AqCkz8D0CK30OfauPUQFlWpIdlVghMSEkJSUpLZvqSkJHx8fHB3d0en06HT6YotExISUuJ5XV1dcXV1tUrMt5o3NIopyw+Sf7v/Ygvz9fXFxcUFDw8P0++ioFbr9ddf5x//+IeprL+/P61btzZtz5w5k9WrV/PDDz8wceLEEp9j9OjRDB8+HIA333yTDz74gF27dtG7d28++ugj2rRpw5tvvmkqv3jxYiIiIjh16hRhYWEsWrSIL7/8kh49egDw+eefU6tWLcv9EoQoht6gvsk29GvIM22fsXE01Y8+38jRi2k807YGR1ql0f/DrUXKPNy+FmnZeZy5nMmElq1oV6cGAN/simfp7sOmcloNRPh7UD/Qi/qBngztEEGDIO8yx1LZ/SKrjWvnYMUYSNgLvhGQloY6hslY6L7y2VWC06lTJ3755RezfevWraNTJ7W2w8XFhXbt2rF+/XoGDRoEqEsrrF+/vtQPZks59nqvEo9pbyznMKhNOA2CvIr9J17xRCeahfmYyhbY+vy9lg30Fu3btzfbzsjI4LXXXuPnn3/m0qVL5Ofnk52dTXx8fKnnadWqlelnT09PfHx8TKPXDh48yMaNG03NA4WdOXOG7Oxs9Ho90dHRpv3+/v40btz4Ti5NiNvKM+YB4KKT9cwqk6IobDiRzP/9fJyk9Bw2PNvddEyjAUW5eT+yUyQtwn2LnKOOvwcPtqvFmcsZnE7O4HpOPueuZnHuahYbTsB9TYJpEKSW/fnQJT7fHkf9IE81AQryokGgF2F+7ui06nuuvfWLdAjHf4Tvn4acNHDzhW5TYcNM8AmHtiNh3xeQngCeld+v06oJTkZGBqdPnzZtx8bGcuDAAfz9/alduzbTpk0jISGBL774AoAnnniCjz76iKlTp/LYY4+xYcMGvvvuO37++WfTOSZPnsyoUaNo3749HTt2ZN68eWRmZppGVVlTefvF3PpP7OasK/Yc5T1ved06GmrKlCmsW7eOuXPn0qBBA9zd3XnwwQfR6/UlnEHl7GzeAVCj0WA0qpl5RkYGAwYMYM6cOUUeFxoaavZ3IIS1aLVaunXrZvoZbtbgSIJTeU4nX+f1n47z56nLAAR6u3Luaia1a3oQ6OVKqJ8bQztE8O3u81xKzaGmV/GvTecGAXRuoPbhUxSFyxm5nEnONCU8jYJvfqE6lJDKrrgUdsWlmJ3DRachzM+dZ3s25scb/SJ/PHiRB9vVQlGghqcztWrIsjzllp8Lv78Cuz5Rt2t1gAcXq6OkWg0FnYv64dduDBj04FQ5rSiFWfWTdc+ePdx7783aiYJ+MKNGjWLp0qVcunTJrNagbt26/Pzzz/znP//h/fffp1atWnz22WemIeIAQ4cO5fLly0yfPp3ExESioqJYu3ZtkY7HtlTTy6Vc/8SW4uLigsFguG25bdu2MXr0aB544AFATU7i4uLu6Lnbtm3LypUriYyMLHaUVv369XF2dmbnzp2mfj7Xrl3j1KlTpg8kIe6Uu7s7mzZtMttXkOA4a2WEjrWlZefx/h9/88WOOPKNCi46LY91qcvE+xrg5aq+L2x94V5cdFo0Gg2PdKyN3mDE1Ul3mzOrX6iCvN0I8najU/2aRY4P71CbZqE+nEnO4MxlNQk6eyUTfb6RuKtZ/Oub/RTUnV/N1JvVspe3z2O1l3kVvhwMlw6o252fgR7TQXfjf6xwMqPR2CS5ASsnON27d0dRSu6LUtwsxd27d2f//v2lnnfixImV0iRVUaG+7hX+J74TkZGR7Ny5k7i4OLy8vEy1K7dq2LAhq1atYsCAAWg0Gl555ZUSy5bV008/zcKFCxk+fDhTp07F39+f06dPs2zZMj777DO8vLwYO3Yszz33HDVr1iQoKIiXXnpJ1poSVqc3Sg1OZcjJM9DrvT9JTM8B4B/Ngnmpb1MiA8xrkAu/D2o0Gou9L0YGeBZ5LoNRYcm2WN785ThGBYr7NOpUryZnLmdQP7Bo87oogbuf2hzl7g8PLIBGJXffsCX5dLESVycdmht9bSz5T1yaKVOmoNPpaNasGYGBgSX2qXn33XepUaMGnTt3ZsCAAfTq1Yu2bdve0XOHhYWxbds2DAYDPXv2pGXLlkyaNAk/Pz9TEvP222/TtWtXBgwYQExMDF26dKFdu3Z39LxC3E6e4UYfHK0kONbk5qzj/qgwGgZ58b+xHVk4sn2RhKOy6bQaxnWtxw8Tu5RYZsfZq/R4ZzNjl+7mr7NXS/1SXq3l5ag3AK0OhnwGT2y12+QGQKNUw1czPT0dX19f0tLS8PExH7efk5NDbGwsdevWxc3NzUYRigLyeojyyMzMJDIyEoC4uDg8PT2ZvWs2Xx3/ivEtx8soKgu6cC2LWb+e4PF76pk67ObkGdBpNTjr7Ou785EEdfTWrf0iZw1uyfrjyaw/kUTBJ+Gjd9Vh5qAWtg3Y3lz5G5aPVvvZDJhn01BK+/y+lV2NohJCiDt15Yr5jMWmPjg66YNjCVn6fBZsOsMnf54lN9/I5fRcvntCHelaeAJTe1JSv8jujQMZ3rE2Zy5nsGhrLCv3XuC+JkGmx6XnqLV/Pm7V+G/n0Hfw4yTIy4TriXDvS+BVNWa6lwRHCOHQTKOopInqjiiKwg8HLzL71xNcSlObKu6q58+rA5rbOLLbu12/yPqBXrz5QEum9GyMn/vNZOazP8+yeFscwzpEMKZLXcL93G11CZVPnwW/ToX9/1O3I7uqzVJVJLkBSXCEEA5OOhnfuSMJabz2w1H2nLsGQK0a7rzUtym9W4SY+hrau7J0bvb3vPk3oigKf8WmkJGbz2dbY1myPY5+LUMZ37UeLWsVnbPHoSSfUJukLh8HNNDteXV+G6191tCVRBIcIYRDk07Gd+7ghVT2nLuGu7OOp++tz7iu9ey2OcpSNBoNy8bfxeZTl1m45Szbz1zlh4MX+eHgRaLr+vNE9/rc2zjo9ieqavL18OUQSL8AXsEweCHUq5pTeUiCI4RwaFKDU376fCPnr2WZhk4P61CbhGvZjOwUSYhv9ensr9VquLdJEPc2CeJIQhqLtsby48GL7IxNoV6gl2MmOE4u0G8u7PwEBn+qri1VRdlXV3chhLAw6WRcskMXUhn+6V8cupAKFCyvkESveX8yctEucvLUiUN1Wg1TezepVsnNrVqE+/Le0Ci2PH8vj3erx9gudU3HjiSk8d66U1zJyLVhhHcg6Sic3XRzu3EfeHR1lU5uQGpwhBAORKvVmtZeK7JUgzRRFVF4bSYPFydm/nSMzTeWVwjwcuXM5QzTyt5CFerrzrQ+Tc32ffrnWX44eJGPN59hSNtwxnapR4OgQstI2Osin4qirhX161RwdlfntfG9sQByFelbVRpJcIQQDsPd3Z3du3eb7ZPFNs1duJbFtcw8NBpMazMt2x3P/3bEYVDASQtju9Zj4r0N8K7Ow6PLoU+LEM6lZHHwfCrf7DrPN7vOc1+TIMZ3rcdd9fztc5HP3Ovq8O8jK9TtyK7gZLlRYvaQ1EmC40C6d+9OVFQU8+bNu23ZuLg46taty/79+4mKirLIOQE2bdrEvffey7Vr1/Dz8yvTY4SwplyD2mwgNTiqLnM2FtmXk3dzqZZ8I0VqKETp+rQMpXeLEPacu8bCP8+y7ngSG04ks+FEMh0j/TlzOQOwo0U+Lx1SR0mlnAGNTl1HqvMzYMGlc+whqZMEx4GsWrWqyIrfJYmIiODSpUsEBKgr9ZaUmJTnnELYI+mDY27e0CimLD9IvrHoJPZOWg1zH2ptg6iqPo1GQ4dIfzpE+hN7JZN7524CYFdcin0t8rn7M1j7IhhywaeWugJ47WiLnLq42kFbJnWS4FhTwj5YNx3+8TqE39laT2Xh7+9f5rI6nY6QkBCLnlMIW8vKyqJZs2YAHDt2DA8PD2miusWgNuE0CPIy+6AtsObpu2kRLn1u7lTdAE/mDY3i2eUHMRiVYhf5DPRyZdqqQ9xVryZ31atJsI8VOnAX9xmUeFhNbhr1gUH/BQ/LvMcrilJs7WCKDZM6GUVlTQeXQdwWOPRtpTxd9+7dmTRpEqCuLP7mm2/y2GOP4e3tTe3atfn0009NZePi4tBoNBw4cIC4uDjuvfdeAGrUqIFGo2H06NFFzgnwv//9j/bt2+Pt7U1ISAiPPPIIycnJlXJ9QtyOoiicO3eOc+fOmRZNlE7GRZ1OVptMCvqROkB/UrszqE043z99d7HHNMDljFy+2XWefy87QPSb67l37iYOX0izbBAFn0EHl93c13s23D8fhn9jseRm1i/H6fjm+mKPFSR3TloN84ZGWeT5ykpqcMpDn1nyMY0OnN0gNR6yrkJ+DhxZqR47vAKaD1JfaQ9/8Kut9lgv7bwud74K7zvvvMPMmTN58cUXWbFiBU8++STdunWjcePGZuUiIiJYuXIlQ4YM4eTJk/j4+ODuXnxns7y8PGbOnEnjxo1JTk5m8uTJjB49ml9++eWO4xXCGmQeHHNxVzJ5fuVBnLQaGod480h0bdPaTDW95HdkDbcu8vnNhLvIzM3nr7NX+etsCkcvphF7JZNQv5u1ON/siufQhVTuqleT6Lo1yz5Ev+AzCA0cvfEZtHcJtB6mBuBRE9r8s1zx5xmMnEy8zv7zqRw8n8qRhDTWPH23abLHTH0+l6/notNqqOPvwdkrRT/TbFE7KAlOebwZVvKxhj1hxHKY17LosawrsLj3ze06XWDMzze357W88QdZyGt3nsn37duXp556CoDnn3+e9957j40bNxZJcHQ6nakpKigoqNTOwY899pjp53r16vHBBx/QoUMHMjIy8PLyKvFxQtiK1ODcZDQqPLfiILn5CnfV8+ersdHodNoiazMJyyhpkc86NT0I9XWnR9NgANKy8ziSkEaAl6vpsT8fusTW01f4Ztd5QG32uque/+0TnuI+gwx6WHjvze0yfL7sPZfCL4cTOXAjocnNN5odP3oxnXZ1agAwslMkg6LCaR7my5nLGcWu3G4LkuBY2uCFsOZJMObbOhJatWpl+lmj0RASEnLHzUl79+7ltdde4+DBg1y7dg2jUf2jj4+PN/V9EMKeFCzVIJ2MYcn2OHbHXcPTRcfbD7ZGp1N7KZS0NpO4M7db5LOAr7szdzcIMNs3/p56NA31Nqvhib2SyTe7zuPpouPgqz1xuvH6ZeTm4+V64+N88EJY/QQohqIBaZ1g0Mdmu9Ky8jh4IZUD51N5sF0twm4sKLrvXCqLtsaaynm7OREV4UdUhB+ta/nRKPjmF9pGwd6mn0tK6mxROygJTnm8eLHkY5obf7CtHoaARvBpMWt3PLYWQlqB5pauT5MOWy7GQm4d/aTRaEwJSUVkZmbSq1cvevXqxVdffUVgYCDx8fH06tULvV5/p+EKYXFGxUi+on7ZqO5NVGcvZ/D2bycAmNa3KRH+NhqiXM2UZZHP4nRrFEi3RurK3WnZeeyJSzE1aQV6u5qSG4ABH25FURQ61a3BCOUUzYHiulXljfmDY9TlwPY4Dp5Xk5rCzUkR/u480Ead6K9zg5qM7FSH1rX8iKrtR92anmi1t++sVdakrjJIglMe5e4XowWMN++d3Is/hwX629wpFxf1zd9gKCbrv+HEiRNcvXqV2bNnExERAcCePXsqJT4hKqKgeQqqdxOVwajw3IpD5OQZ6dIggBHRtW0dkigHX3dnejQNNjVpGQoN8b+akcu5q5kYFRiV9jEtnH4zHTMqGrQaBSMatCj8cCiBZ7cU/aJep6YHURF+hPjc7HvZPMyX1++vWJ+ZiiZ1liYJjjV4BqprePiEQ9uR6lTY6QnqfjtVp04dNBoNP/30E3379sXd3b1In5ratWvj4uLChx9+yBNPPMGRI0eYOXOmjSIWoiiNRmNqKtVoNKYOxlC9a3CWbItl77lreLk6MXtISzQybKpK0xWqSanp5cr+6T3ZE5fC2SP5pB3Zwn/zBzLW6VcuKTX5Nv9ehuo2Eqq5yttbUoCadGsUqDY31Vabm/w9HfN/QxIca/ANh0lHQOei9rBqN0bt5OXkevvH2kh4eDgzZszghRdeYMyYMYwcOZKlS5ealQkMDGTp0qW8+OKLfPDBB7Rt25a5c+cycOBA2wQtxC08PDw4evSoaftK9hXTz87a6tsH5+4GATQP82FEdB3bzZ4rLM9ohEv78Q1vd6OG535+qtOEz9acYUluH/Q4ARq+NtyHC/kYtS6892ArHmhby9aRVwqNotiqf7PtpKen4+vrS1paGj4+PmbHcnJyiI2NpW7duri5Vd+Vc+2FvB7iTlzKuETPlT1x1jqz79F9tg7HpvIMRpy0Gqm9cRQZl2H14xD7Jzz2G9RqZzp0JCGt2Ikcf/pXlyo/kWNpn9+3kon+hBAOq7rPgZOadbOJzvlGp0/hAOK2woIucGa9OjIq9Vyxxar7RI6S4AghHEZWVhbNmzenefPmZGVlVes5cE4nZ3D37A288/tJ8g0VHz0p7IjRAJvfgs8HQEYiBDSGCRuhxWCzYgVDtVuG+/LGAy1oGe5LoJdrtZvIUfrgCCEchqIoHDt2zPRzQQ1OdZsDx2BUmLL8IJl6A4cupJl1ShVV1PUkWDUeYjer21H/hL5vFTsK156GatuSJDhCCIdVMMlfdavBWbjlLAfOp+Ito6Ycx7Hv1eTG2QP6v6cuvVAKexmqbUuS4AghHJapiaoa9cH5O+k67647BcAr/ZsR6lv8unKiiuk4Xu1r03YUBDaydTRVgvTBEUI4rOrWyTjfYGTK8oPo8410bxzIQ+2rx3Bgh5R+Cb5/GnLVld/RaKDXG5LclIPU4AghHFZ162T86ZazHLyQhrebE7MHt5Kmqarq7z9g9QR1EWaNDgZ+YOuIqiRJcIQQDqu6dTL2dXfG3VnH9P7NSl5tWtgvQz5s/D/Y+p66HdIS7v63bWOqwiTBEUI4DI1GQ506dUw/V7dOxiOi69CjSTDBPvY7a7ooQdoFWDEWzv+lbncYBz3fAGdJVCuqUvrgzJ8/n8jISNzc3IiOjmbXrl0llu3evTsajabIrV+/fqYyo0ePLnK8d+/elXEpQgg75uHhQVxcHHFxcXh4eFSbTsbGQosvhvi6SdNUVRP/lzpx3/m/wNUHHvoc+r0jyc0dsnqC8+233zJ58mReffVV9u3bR+vWrenVqxfJycnFll+1ahWXLl0y3Y4cOYJOp+Ohhx4yK9e7d2+zct988421L8Xude/enUmTJtk6DBN7i0dUP9Whk/HJxOv8473N/HX2qq1DERVVo646I3FYG3j8T2g+yNYROQSrJzjvvvsu48ePZ8yYMTRr1owFCxbg4eHB4sWLiy3v7+9PSEiI6bZu3To8PDyKJDiurq5m5WrUqGHtS6kW9Hr97QsJUUUU1OA46kKbeTdGTZ25nMlnW2JtHY4oj6yUmz97B8Oon9Q1pfzr2i4mB2PVBEev17N3715iYmJuPqFWS0xMDDt27CjTORYtWsSwYcPw9DSfrXHTpk0EBQXRuHFjnnzySa5eLfnbS25uLunp6WY3RzN69Gg2b97M+++/b2q2O3PmDGPHjqVu3bq4u7vTuHFj3n///SKPGzRoEG+88QZhYWE0btwYgO3btxMVFYWbmxvt27dnzZo1aDQaDhw4YHrskSNH6NOnD15eXgQHB/Poo49y5cqVEuOJi4urrF+HqKays7Pp0KEDHTp0IDs7mzzjjT44DlqDs2DTGQ4npOHr7sybD7SwdTiiJAn7YGl/9R7g+E/wQRQcWXWzTFATcJK+U5Zk1U7GV65cwWAwEBwcbLY/ODiYEydO3Pbxu3bt4siRIyxatMhsf+/evRk8eDB169blzJkzvPjii/Tp04cdO3ag0xWdrXHWrFnMmDGjwtehKArZ+dkVfnxFuTu5l7kt/f333+fUqVO0aNGC119/HYAaNWpQq1Ytli9fTs2aNdm+fTsTJkwgNDSUhx9+2PTY9evX4+Pjw7p16wB1tdYBAwbQt29fvv76a86dO1ekqSk1NZX77ruPcePG8d5775Gdnc3zzz/Pww8/zIYNG4qNJzAw0AK/FSFKZjQa2bNnj+lnRx4mfvxSOh9s+BuA1wY2I8hH+mvYrYPLIG4LHPgaDn0LOxeo+/d/Cc0fqL6rYVqZXY+iWrRoES1btqRjx45m+4cNuzlFdcuWLWnVqhX169dn06ZN9OjRo8h5pk2bxuTJk03b6enpRERElDmO7Pxsor+OrsAV3Jmdj+zEw9mjTGV9fX1xcXHBw8ODkJAQ0/7CiV3dunXZsWMH3333nVmC4+npyWeffYaLi/ohsGDBAjQaDQsXLsTNzY1mzZqRkJDA+PHjTY/56KOPaNOmDW+++aZp3+LFi4mIiODUqVM0atSo2HiEqEyO2sm4oGkqz6AQ0zSYQVHhtg5J3Co1Xp3HBg0cvVFTs3cJGPPVn9uOUjsSS3JjNVZNcAICAtDpdCQlJZntT0pKuu2HXmZmJsuWLTN9+y9NvXr1CAgI4PTp08UmOK6urri6Vs+qv/nz57N48WLi4+PJzs5Gr9cTFRVlVqZly5am5Abg5MmTtGrVCje3m98Ib00yDx48yMaNG/Hy8irynGfOnKFRI5ltU9ieo86D89+NZzh6MR0/D2feHNxCRk3Zo3kti+4rSG4A9n0uE/hZmVUTHBcXF9q1a8f69esZNGgQoFYbr1+/nokTJ5b62OXLl5Obm8s///nP2z7PhQsXuHr1KqGhoZYIuwh3J3d2PrLTKue+3fPeiWXLljFlyhTeeecdOnXqhLe3N2+//TY7d5pfy639m8oiIyODAQMGMGfOnCLHrPU6CFFejthEpSgKJ5PUfoQzBjYnyFuapuzS4IWw5knzpKaA1gkGfVz5MVUzVm+imjx5MqNGjaJ9+/Z07NiRefPmkZmZyZgxYwAYOXIk4eHhzJo1y+xxixYtYtCgQdSsWdNsf0ZGBjNmzGDIkCGEhIRw5swZpk6dSoMGDejVq5dVrkGj0ZS5qciWXFxcMBgMpu1t27bRuXNnnnrqKdO+M2fO3PY8jRs35ssvvyQ3N9dU87V7926zMm3btmXlypVERkbi5FT8n9Gt8QhR2Ryxk7FGo2H+I23ZceYqnerXvP0DhG20ehgCGsGn3YoeG7cewqIqPaTqxurDxIcOHcrcuXOZPn06UVFRHDhwgLVr15o6HsfHx3Pp0iWzx5w8eZKtW7cyduzYIufT6XQcOnSIgQMH0qhRI8aOHUu7du3YsmVLtW2GKhAZGcnOnTuJi4vjypUrNGzYkD179vDbb79x6tQpXnnllSKJSnEeeeQRjEYjEyZM4Pjx4/z222/MnTsXwFQV/vTTT5OSksLw4cPZvXs3Z86c4bfffmPMmDGmpObWeIxGo/UuXohiOGINDqj/h50bBEjTlL06slKdmdik4HWS9a0rU6X8tidOnMi5c+fIzc1l586dREff7LC7adMmli5dala+cePGKIrCP/7xjyLncnd357fffiM5ORm9Xk9cXByffvppkZFa1dGUKVPQ6XQ0a9aMwMBAevXqxeDBgxk6dCjR0dFcvXrVrDanJD4+Pvz4448cOHCAqKgoXnrpJaZPnw5g6pcTFhbGtm3bMBgM9OzZk5YtWzJp0iT8/PzQarXFxhMfH2+9ixfihoCAAAICAoBC8+A4QB+coxfTePa7g6RmyVxVdkufBT/8C1Y8pi674F4DvILU2pr+70FYa3XbU0aUVgaNoijK7Ys5lvT0dHx9fUlLS8PHx8fsWE5ODrGxsdStW9esk21199VXXzFmzBjS0tJwd7+zvkHlIa+HuBP/2vAvNp3fxPRO03mo0UO3LW+v9PlG7p+/jeOX0hneMYJZg1vZOiRxq8snYfloSD4GaKDbVOj2vNoHR+eijpZSFDDoZb6bO1Da5/et7HqYuLCdL774gnr16hEeHs7BgwdNc9xUZnIjxJ1ylMU2P9p4muOX0vH3dOHZno1tHY641YGv4ednIS8LPINgyGdQ70bfG22hudk0GkluKpEkOKJYiYmJTJ8+ncTEREJDQ3nooYd44403bB2WEOXiCGtRHUlI478bTwPw+v3NCfCSD0i7oc9SE5uDX6vb9bqro6e8gmwallBJgiOKNXXqVKZOnWrrMIQol+zsbPr06QPAr7/+WuU7Gevz1Qn98o0KfVuG0L9VmK1DEre6dAA0Wuj+InSdbF5jI2xKEhwhhMMwGo1s3rzZ9HNV72T84Ya/OZF4nZqeLsy8X9aasgsF3VY1GnDxgIc+h8xkiOxi27hEETJmTQjhsKryPDjZegMr96pDjWcOakFNaZqyvdzrsGo8bJl7c19gI0lu7JTU4JSgGg4us0vyOog7UZWbqNxddPz673v44WACfVvK7OA2d+kQrBgDV0+DzhWi/gk+8rrYM6nBuYWzs1qVnZWVZeNIBNx8HQpeFyHKo6p3Mvb1cObRTpG2DqN6UxTY/Rl8FqMmNz7hMOoHSW6qAKnBuYVOp8PPz4/k5GQAPDw8ZLZQG1AUhaysLJKTk/Hz80Onk457ovxMfXC0VSdBPnQhlb+TMhjcNlzee2wtJw1+/DccXa1uN+qtriHl4W/buESZSIJTjIKVzguSHGE7fn5+t115XoiSmObBqSI1OLn5Bp797iB/J2eQkqln/D31bB1S9WXIh0W94PJxdXHMmBnQ6Wm1c7GoEiTBKYZGoyE0NJSgoCDy8vJsHU615ezsLDU3otw8PG4ujFtVmqgOXUhl1i8nCPNz4+/kDAK8XHmwXS1bh1W96Zyg4zjY+j48tARqtbd1RKKcJMEphU6nkw9YIaoQT09PMjMzAbWZs6p0Ml61L4EdZ6+att94oAU1PO07ZoeUnQoZSRB4Y7bo9mOh1VBw9bZpWKJiJMERQjikfCUfBXUUnj3W4Fy4lsW1zDw0Gvjh4EXT/m6NAgjzdefCtSxq1fAo5QzCoi7sUUdJoYHH/wR3P7U5SpKbKksSHCGEQyrofwP22cm4y5yNxe7ffOoKm09tBSBudr/KDKl6UhTYMR/+eFVdGLNGJGQkqwmOqNJkmLgQwmHk5OTQr18/+vXrR3pmumm/PdbgzBsahZO2+A6rTloN84ZGVW5A1VFWCnwzDH5/SU1umj+g1t4ENrJ1ZMICpAZHCOEwDAYDv/zyCwDZedkAaDVanLT291Y3qE04DYK86P/h1iLH1jx9Ny3CfW0QlYNL2AfrpsM/XgeDHlaMhfQL6sR9vWdB+8dklJQDsb//eiGEsADTEHE772AM6meqoty8F1ZycBnEbYFD30LqeTW58a8PDy2F0Fa2jk5YmCQ4QgiHVDBE3J4X2vT3dCbQy5VQPzeGdojg293nuZSaQ00v+0/KqozUeMi6Cmjg6Cp135GVMGQROLvBPc9BUFObhiisQxIcIYRDsvcaHEVReOabA9zfJoynu9enhqcrj3Ssjd5gxNVJpqewmHkti+7LvAJfDFR/PrISXkur3JhEpZBOxkIIh2SaA8cOOxgDbD51mT3nrrFs13l0OvWtWKPRSHJjaQ98AppbP+putANqnWDwwkoPSVQOqcERQjikPKN9L9OwaGssAEM7RODjZr/NaFXa9SQ48DUoxuKPj1sPYVGVGpKoPJLgCCEckj0v03D8Ujpb/r6CVgOjO0faOhzHdHYTrBwPmcng5Ab5OaiNFsZC98KRSROVEMJheHp6oigKiqLg5KZ+f7PHPjgFtTd9WoYS4S+zFVvc9o/gi0FqchPUDEYsB68gCGsN/d9T772CwDPQ1pEKK5IaHCGEQ7LXPjjJ6Tl8fyABgHFd6to4GgcV3Ey9bzsK+swBZ3eYdAR0LupY/HZj1HlwnFxtG6ewKklwhBAOyV4X2vxixznyDArt6tSgTe0atg7HcWReBc+a6s/174Mnt0Fw85vHCyczGo0kN9WAJDhCCIeRk5PDo48+CsBDrz0E2N88OA+3jyAjN58uDQJsHYpjMOTDxv+DPYthwibwr6fuL5zciGpJEhwhhMMwGAysWLECgAEvDgDsrwandk0PXhsoH74WkXZBXW7h/F/q9olfoPNE28Yk7IYkOEIIh2Tvw8TFHTr1G6x+HLKvgasPDPxAXSxTiBtkFJUQwiGZZjK2kwRn/fEkHv/fHvbFX7N1KFWbIQ9+ewm+flhNbkKj4PHNktyIIqQGRwjhkExrUWntow/Op3+eZWdsCpEBnrSVzsUVt+tT2PGR+nP0E+rK4NJhWBRDEhwhhEOyp4n+Dl9IY2dsCk5ajUzsd6c6jIfTf0D7sdC0v62jEXasUpqo5s+fT2RkJG5ubkRHR7Nr164Syy5duhSNRmN2c3NzMyujKArTp08nNDQUd3d3YmJi+Pvvv619GUKIKsSeFtv8bOtZAPq3CiXU193G0VQx+bnw18fqaCkAJxf45ypJbsRtWT3B+fbbb5k8eTKvvvoq+/bto3Xr1vTq1Yvk5OQSH+Pj48OlS5dMt3Pnzpkdf+utt/jggw9YsGABO3fuxNPTk169epGTk2PtyxFCVBH20sn4Ymo2Px+6BMC4rvVsGkuVk3IWFvWEtS/Apjdv7tdobBeTqDKsnuC8++67jB8/njFjxtCsWTMWLFiAh4cHixcvLvExGo2GkJAQ0y04ONh0TFEU5s2bx8svv8z9999Pq1at+OKLL7h48SJr1qyx9uUIIeyYh4cHGRkZZGRkoDirK0bbeh6cz3fEkW9UuKuePy3CfW0aS5VydDV80g0uHQD3GlCro60jElWMVRMcvV7P3r17iYmJufmEWi0xMTHs2LGjxMdlZGRQp04dIiIiuP/++zl69KjpWGxsLImJiWbn9PX1JTo6usRz5ubmkp6ebnYTQjgejUaDp6cnnp6eN2twbNhElZGbz9c74wEY10Vqb8okLwd+mgzLR0NuOkTcBU9shca9bR2ZqGKsmuBcuXIFg8FgVgMDEBwcTGJiYrGPady4MYsXL+b777/nyy+/xGg00rlzZy5cuABgelx5zjlr1ix8fX1Nt4iIiDu9NCGEnbOHTsZOWg3P/qMR9zQK5L4mQTaLo8q4egYWxcCeRep2l8kw+mfwrWXbuESVZHejqDp16kSnTp1M2507d6Zp06Z88sknzJw5s0LnnDZtGpMnTzZtp6enS5IjhAPKzc3l8ccfB8B7uDdg2xocN2cdo++uy+i7ZVHNMjHkqUmORwAM/gQaxNz+MUKUwKo1OAEBAeh0OpKSksz2JyUlERISUqZzODs706ZNG06fPg1gelx5zunq6oqPj4/ZTQjhePLz8/n888/5/PPPyc3LBWzfyVgUI2EfLO2v3huNN/cHNYGH/6c2SUlyI+6QVRMcFxcX2rVrx/r16037jEYj69evN6ulKY3BYODw4cOEhoYCULduXUJCQszOmZ6ezs6dO8t8TiGE4zNN9GejTsbPrzjEir0XyM032OT57drBZRC3BXYugE/vgXPbbx5rGAM+obaLTTgMqzdRTZ48mVGjRtG+fXs6duzIvHnzyMzMZMyYMQCMHDmS8PBwZs2aBcDrr7/OXXfdRYMGDUhNTeXtt9/m3LlzjBs3DlA7EU6aNIn/+7//o2HDhtStW5dXXnmFsLAwBg0aZO3LEUJUEXrDjT44Nmii2hd/jW/3nGf1/gTuaRRAkLeu0mOwO6nxkHUV0MDRVeq+Q9+q9z/+G0asgBp1bBaecDxWT3CGDh3K5cuXmT59OomJiURFRbF27VpTJ+H4+Hi02psVSdeuXWP8+PEkJiZSo0YN2rVrx/bt22nWrJmpzNSpU8nMzGTChAmkpqbSpUsX1q5dW2RCQCFE9ZVvVCeGs0UT1aItsQAMjAojyFvelwCY17LkY1dOwfut4LW0yotHODyNoiiKrYOobOnp6fj6+pKWlib9cYRwIJmZmXh5eQFw/7f3cyb7DJ/EfELn8M6VFsP5lCy6vb0RowJrJ3WlSYi8xwBw6DtY/QQoxTTZaZ1g0MfQ6uHKj0tUKeX5/La7UVRCCGEJtuqDs2RbHEYFujYMkOSmsNAoNZExFJPgjFsPYVGVHZFwcJWyFpUQQlQ2Ux+cSmyiSs/J49vdNyb2k2UZzAU0hNp33dgoWGpBPoKE9chflxDCYXh4eJCcnExycjJGJ3X4cWV2Mv5213ky9QYaBnlxT8OASnteu5V4BHJu9KvRaKDfu+AZpNbW9H8PwlqDVxB4Bto0TOGYpIlKCOEwNBoNgYHqh2WeUvmLbbYI96VLgwAGtg5DU50XhFQU2LMY1k5Tl1h46HM1wQloAP85AjoXdbvdGDDowcnV1hELByQJjhDCIdlimHin+jXpVL8m1XDsxk05aeqw76Or1e38XMjPAWd3dbtwMqPRSHIjrEYSHCGEw8jNzTUty5LTLgd0tpnor9rW3lzcry6SeS1O7VAc8xp0mqgmMkJUMklwhBAOIz8/n//+978ANPukGVqdtlKaqPaeu8amk8k82qlO9Zz3RlFg16fw+8tqk5NvbXhwMUR0sHVkohqTBEcI4dAqo4nqk81n+P1YElcz9bz5QCkT2jmqnDTYOk9Nbpr0h/s/Avcato5KVHOS4AghHJq1a3Bir2Sy7ri6+O9j1XXVcHc/eHARXDoE0Y9Lk5SwC5LgCCEcmrPWun1wlmyLRVHgviZBNAjysupz2Q1FgR3zwTMAWg9T99XprN6EsBOS4AghHJaz1tmqHX5Ts/Qs33MBgHFdqkntTVYKrHkSTq0FZw+oczf4Rdg6KiGKkARHCOGwrN089dXOeLLzDDQL9aFT/ZpWfS67EL8TVjwG6RdA5wo9Z4JvLVtHJUSxJMERQjgsa3Yw1ucb+Xx7HADjutZ17KHhRiNsfx/Wz1QXy/SvDw8thdBWto5MiBLJUg1CCIfh7u5ObGwsv+/7HY2zxqpz4GTrDcQ0Cyaypgf9W4VZ7XlszmiAb4bCH6+pyU3Lh+DxzZLcCLsnNThCCIeh1WqJjIwk1SMVzSGNVWtwfD2cefOBluQbjDjpHPi7olYHIS0h9k/o+za0eVRGSYkqQRIcIYTDyTNW3jpUDpncGA2QnQqeN/oVdX8RWg9XVwQXooqQBEcI4TD0ej0vvfQSCdcTMHYwWi3BWbD5DJ3r16RVLT+rnN+mrifBqvGQex0e+w2cXEDnJMmNqHIc8KuHEKK6ysvLY+7cuXzzyTdgsE4n47+TrjP71xPcP38bl9KyLX7+SpWwD5b2V+8Bzm6CBV0gdjNcPgGJh2wanhB3QmpwhBAOyxqdjBdviwWgZ7NgQn3dLX7+SnVwGcRtgYPfqPPabH4LUCCwqTpKKqiJrSMUosIkwRFCOCxL1+Bcychl5b4EAMZ1rWfRc1ea1HjIugpo4Ogqdd+eJXCj3xLNB8P988HFw2YhCmEJkuAIIRyWpfvgfPnXOfT5RlpH+NG+ThVdTHJe4cVAb4yGKkhuQE16HlpSqSEJYQ3SB0cI4bAsmeDk5Bn4345zgLosQ5Wd2G/wQtAWfLdVzI9pndTjQjgASXCEEA7LkgttrtmfwNVMPeF+7vRpEWKx81a6OndDl2eLPzZuPbR6uHLjEcJKpIlKCOGwLFmD4+KkJdTXjTF3R1bduW9O/Qarn4DslBs7tICx0L0QjkMSHCGEw3B3d+fIkSMsO7GM1emrLdrJeHDbWgxoHYbBqNy+sL0x5MH6GbD9Q3U7qClkJINfbWg7EvZ9AekJ4Blo2ziFsCBJcIQQDkOr1dK8eXMCcgPQHNZYvJOxs06Ls86ip7S+1Hh1BfALu9Xtjo+rq4AD6FzUZRfajQGDHpxcbRenEBYmCY4QwuHoDXrAMvPgnE6+ztGL6fRtGYpzVWuaOvELrHkCctLAzVcd/t10QNFyGo0kN8LhSIIjhHAYer2eN998kz8v/Imxk9EiTVQfbzrLyn0X2BWbwhsPtLz9A+xJ9jU1uQlvBw8ugRp1bB2REJVGEhwhhMPIy8tjxowZADTr2OyOm6iS03P44aA6sd9D7SPuOL5KYTSC9kZNU5sRas1M04HqmlJCVCNVrL5VCCHK7k5rcD7fEUeeQaF9nRpERfhZJihrOroGFtwNWSk397V8UJIbUS1JgiOEcFh30gcnS5/PVzvjARjXta6lQrKOvBz4+VlYPgqSj8H2D2wdkRA2VykJzvz584mMjMTNzY3o6Gh27dpVYtmFCxfStWtXatSoQY0aNYiJiSlSfvTo0Wg0GrNb7969rX0ZQogq5k6aqFbuSyA1K4/a/h78o5kdT+x39QwsioHdn6nbd0+Ce1+yaUhC2AOrJzjffvstkydP5tVXX2Xfvn20bt2aXr16kZycXGz5TZs2MXz4cDZu3MiOHTuIiIigZ8+eJCQkmJXr3bs3ly5dMt2++eYba1+KEKKKqWgTldGosHirumr4Y3dHotPa6bIMh1fAJ/dA4mHwqAkjVsI/ZoAVVlEXoqqxeoLz7rvvMn78eMaMGUOzZs1YsGABHh4eLF68uNjyX331FU899RRRUVE0adKEzz77DKPRyPr1683Kubq6EhISYrrVqFFFF74TQlhNRWtwrmbqCfRyxcfNyX47F+9dCivHgj5DXX7hia3QMMbWUQlhN6ya4Oj1evbu3UtMzM1/Oq1WS0xMDDt27CjTObKyssjLy8Pf399s/6ZNmwgKCqJx48Y8+eSTXL16tcRz5Obmkp6ebnYTQji+itbgBHq78t0Tnfhjcjc8Xe10sGmzQVCjLtzzHIz8AXzCbB2REHbFqgnOlStXMBgMBAcHm+0PDg4mMTGxTOd4/vnnCQsLM0uSevfuzRdffMH69euZM2cOmzdvpk+fPhgMhmLPMWvWLHx9fU23iAg7/UYmhLgjbm5u7Nq1ix7v9EDjrLnjif6CfNwsFJmFxG4B5cZSEe5+8OR2uO9l0NlpEiaEDdn1KKrZs2ezbNkyVq9ejZvbzTeaYcOGMXDgQFq2bMmgQYP46aef2L17N5s2bSr2PNOmTSMtLc10O3/+fCVdgRCiMul0Ojp06IB3fW802vIv1XDoQio939vM1r8vWynCCtJnwpqn4PP+sKdQ876Lh+1iEsLOWTXBCQgIQKfTkZSUZLY/KSmJkJDSRyXMnTuX2bNn8/vvv9OqVatSy9arV4+AgABOnz5d7HFXV1d8fHzMbkIIx1WwVEN5m6i+2HGOU0kZjFqyi8S0HGuEVn7Jx2HhfXDgK9Bo1ZmJhRC3ZdUEx8XFhXbt2pl1EC7oMNypU6cSH/fWW28xc+ZM1q5dS/v27W/7PBcuXODq1auEhoZaJG4hRNWk1+t5++23ObX6FMZ8Y5lqcC5cy+LwhTSOJKTx06GLAGjQcCUjl8MX0rhwLcvaYRdPUdRVvj+9Fy6fAK8Qta9N18m2iUeIKsbqDbeTJ09m1KhRtG/fno4dOzJv3jwyMzMZM2YMACNHjiQ8PJxZs2YBMGfOHKZPn87XX39NZGSkqa+Ol5cXXl5eZGRkMGPGDIYMGUJISAhnzpxh6tSpNGjQgF69eln7coQQdiwvL4+pU6cC0KxrM5y1t++D02XOxiL78o0K/T/catqOm93PckGWRe51+GkyHP5O3a5/HzzwKXgFVm4cQlRhVu+DM3ToUObOncv06dOJioriwIEDrF271tTxOD4+nkuXLpnKf/zxx+j1eh588EFCQ0NNt7lz5wJqG/uhQ4cYOHAgjRo1YuzYsbRr144tW7bg6iqr4QohbipLDc68oVE4lTDPjZNWw7yhURaOqhgJ+2Bpf/UeIOkoHFkBGh30mK7ObyPJjRDlolGUgi751Ud6ejq+vr6kpaVJfxwhHEhmZiZeXl4ANPukGb8/8jvhXuG3fdyRhDSzGpsCP/2rCy3CfS0eZxG/TIVdn0D0E9Bnjrpv10IIbgF1Sm7OF6K6Kc/nt4wtFEI4rLJ2Mj6fkmm2rdHcHI1tNanxkHUV0Ki1NQCHvoXWwwEFGvUCv9pWDkIIxyUJjhDCYZV1mPjFVHXElI+bE8/3acK3u89zKTWHml5WXIV7Xsui+7Kvwafdbm6/JiOmhKgoSXCEEA6rLJ2MAcZ2rUfflqHk5huIDPDikY610RuMuDrprBfcA5/CmidAMRY9pnWCQR9b77mFqAYkwRFCOKzyTPQX6udu+lmj0Vg3uclOhRM/Fp/cAIxbD2FR1nt+IaoBu57JWAghysPNzY1Vv64i8vlIdC46nLS3/w6XkJpdCZEVcu0cfNIVjv8ImoL4CkZxyVuyEJYi/01CCIeh0+nocHcHvJp64ep0+2kjzl7O4O7ZGxj6yQ7yDCXUpliaTzh4h0GNSBj2NXgFqbU1/d+DsNbqtqcMCRfiTkkTlRDCoeiN6jINZVlo89vd6rp0Hi46nHVW/L6XlQIuXuDkoi6M+fDn4OwObr5Q/wjoXNShW+3GgEEPZUjOhBClkxocIYTDyMvLY+knS7n6x1WcjKV/f9PnG1mx9wIAwztacTh2/E5Y0BXWz7i5zztETW5ATWY0N5qoNBpJboSwEElwhBAOQ6/XM/P5mVz68hLOSuk1OH8cT+Jqpp4gb1fuaxJk+WCMRtg6D5b0gfQLcPJXyM2w/PMIIYolTVRCCId0uyaqb3bFA/BQ+1o4Wbp5KvMKrH4CTq9Tt1s8CAPmgauXZZ9HCFEiSXCEEA6ptDlwzqdkseXvKwAM62Dh5qm4bbByLFy/BE5u6tILbUfdbIYSQlQKSXCEEA6ptDlwCvredG0YQIS/h+WeNPc6LHsEclKhZkN4aCmEtLDc+YUQZSYJjhDCIZW2DtWT3etTL9CTYB83yz6pq7c63PvUb9DvHWmSEsKGJMERQjik0vrguDnruD/q9quMl8nZzWrzU9171O0Wg9WbEMKmZBSVEMIhldQHR7HUMuFGA2ycBV/cDyvGwvUky5xXCGERkuAIIRyGq6srzy94njqT6uDu5l7keEJqNj3e2cyCzWfuLNG5nqgmNptnAwo06qk2Twkh7IYkOEIIh+Hk5ETLe1riHeWNm0vR/jXf7j7P2SuZbD55GU1FRzWdXg8f3w1xW8DZU10V/P754GLBzspCiDsmfXCEEA5Fb1CXari1k3G+wcjyPerSDMOjKzA03GiEjf8HW94FFAhuoY6SCmh4hxELIaxBEhwhhMPIy8tj06pNXIu/hq6uzuzY5lOXuZSWQw0PZ3o1Dy7/yTUaSEsAFGj/GPR6U11PSghhlyTBEUI4DL1ezxevfgGAdoR5C/w3u9TamyFta+HqpCvy2BIZDaDVqQlOv3eg2UBo0s9iMQshrEP64AghHFLhif4S03LYcEId5TSsY0TJD0rYB0v7q/eGPPj9Ffj2n1DQIdnVS5IbIaoIqcERQjikwvPgLN9zHqMCHSP9aRBUyming8vUzsO7P4Mrp+DCbnV/7J9Qr5uVIxZCWJIkOEIIh1S4k3GXhgGcvZJZ/KrhqfGQdRXQwNFV6r4DXwMKOHtBz5mS3AhRBUmCI4RwSIUn+mtTuwZtatcovuC8lsXsvNEklZcBP/8HOjxm+QCFEFYlfXCEEA6ptLWozAxeCNoSvutpndTjQogqRxIcIYRDctY5k3w9h9d+OMrJxOslF2z1MIxbX/yxcevV40KIKkcSHCGEw3B1daXnKz2JeCoCT3dPVuy9wNLtcbyw6lDRwnk5cG7HLTsLZjeWt0YhqjrpgyOEcBhOTk7U7lKbi5cu4ursxre7b8xc3PGWmYuvnoHlo+HySRi/ATwDwSsIfMKh7UjY9wWkJ6j7hRBVkiQ4QgiHUrBUQ9yVXM5d1eLt6kT/VqE3CxxeAT9OAv118KgJ2SkQ0gImHQGdizqhX7sxYNCDk6ttLkIIccckwRFCOIz8/HzO/HmGtPQ0tnIVqMX9bcLwcHGCvGxY+wLsXaoWrt0ZHlwEPmHqduFkRqOR5EaIKk4SHCGEw8jNzWXb7G0AuAZcA2oxrENtuHxKbZJKPgpo4J4p0O0F0MlboBCOqlJ60s2fP5/IyEjc3NyIjo5m165dpZZfvnw5TZo0wc3NjZYtW/LLL7+YHVcUhenTpxMaGoq7uzsxMTH8/fff1rwEIUQVk2/Q0aqWLy3CfeH492py4xkIj66C+16W5EYIB2f1BOfbb79l8uTJvPrqq+zbt4/WrVvTq1cvkpOTiy2/fft2hg8fztixY9m/fz+DBg1i0KBBHDlyxFTmrbfe4oMPPmDBggXs3LkTT09PevXqRU5OjrUvRwhRRfi4uau1NwBdJkOX/8ATW6H+fbYNTAhRKTSKUrCKnHVER0fToUMHPvroIwCMRiMRERH861//4oUXXihSfujQoWRmZvLTTz+Z9t11111ERUWxYMECFEUhLCyMZ599lilTpgCQlpZGcHAwS5cuZdiwYbeNKT09HV9fX9LS0vDx8bHQld6UmZlZ4jGdToebm1uZymq1Wtzd3StUNisri5JeWo1Gg4eHR4XKZmdnYzQaS4zD09OzQmVzcnIwGAwWKevh4YFGow73zc3NJT8/3yJl3d3d0WrV7wR6vZ68vDyLlHVzc0On05W7bF5eHnq9vsSyrq6uODk5lbtsfn4+ubm5JZZ1cXHB2dm53GUNBkOpX0KcnZ1xcXEpd1mj0Uh2djag/o8EBwcDsGnBAFoOWYiXT41iyxbHyckJV1e1742iKGRlZVmkbHn+7+U9oviy8h5RNd8jLK1cn9+KFeXm5io6nU5ZvXq12f6RI0cqAwcOLPYxERERynvvvWe2b/r06UqrVq0URVGUM2fOKICyf/9+szL33HOP8swzzxR7zpycHCUtLc10O3/+vAIoaWlpFbqu20Gd573YW9++fc3Kenh4lFi2W7duZmUDAgJKLNu+fXuzsnXq1CmxbLNmzczKNmvWrMSyderUMSvbvn37EssGBASYle3WrVuJZT08PMzK9u3bt9TfW2EPPvhgqWUzMjJMZUeNGlVq2eTkZFPZp556qtSysbGxprJTpkwpteyRI0dMZV999dVSy+7atctU9q233iq17MaNG01lP/roo1LL/vTTT6ayS5YsKbXsd999Zyr73XfflVp2yZIlprI//fRTqWU/+ugjU9mNGzeWWvatt94yld21a1epZV999VVT2SNHjpRadsqUKaaysbGxpZZ96qmnTGWTk5NLLTtq1ChT2YyMjFLLPvjgg2Z/w6WVlfcI9SbvETdvVfk9wtLS0tIUKNvnt1WbqK5cuYLBYDB9oyoQHBxMYmJisY9JTEwstXzBfXnOOWvWLHx9fU23iIiICl2PEEIIIaoGqzZRXbx4kfDwcLZv306nTp1M+6dOncrmzZvZuXNnkce4uLjw+eefM3z4cNO+//73v8yYMYOkpCS2b9/O3XffzcWLFwkNvTm3xcMPP4xGo+Hbb78tcs7c3Fyz6rT09HQiIiKkiaoCZaX6Waqf7bKJKm4PrHqczMTTBL+TAcDhMwepG1y/xOas4kgTlUreIypWVt4jVPbSRGXVYQQBAQHodDqSkpLM9iclJRESElLsY0JCQkotX3CflJRkluAkJSURFRVV7DldXV1Nb0SVofA/mq3KFn7DsWTZwm+Qlixb+A3dkmXL89qXp6yLi4vpQ9NWZZ2dncv8JlKesk5OTqY3MkuW1el0Zf4bLk9Z7alf8VzxGOTncM0jgPCxvgAEBAQVOYdWqy3zeTUajVXKgrxHVKSsvEeUv6w9vEfYklWbqFxcXGjXrh3r199cyM5oNLJ+/XqzGp3COnXqZFYeYN26dabydevWJSQkxKxMeno6O3fuLPGcQggHFtIKnNxIC+9O/7zXqdG1BjW61sDTrewf9kIIx2P1FGzy5MmMGjWK9u3b07FjR+bNm0dmZiZjxowBYOTIkYSHhzNr1iwA/v3vf9OtWzfeeecd+vXrx7Jly9izZw+ffvopoH5TmjRpEv/3f/9Hw4YNqVu3Lq+88gphYWEMGjTI2pcjhLAH1xPB+0YtsF8EjN/A/61PJ1VzFu8bRVx0ZfuWK4RwTFZPcIYOHcrly5eZPn06iYmJREVFsXbtWlMn4fj4eFM7JEDnzp35+uuvefnll3nxxRdp2LAha9asoUWLFqYyU6dOJTMzkwkTJpCamkqXLl1Yu3ZtuaolhRBVkKLA7s/gt5fg4S+gcW8A0jxq8+PhP0DJ5fqB6wBoHtGAzpbBCiFsyerz4Ngja8+DI4SwguxU+OFfcPwHdTtqBAz6LwD/2xHHK98fJdL/OpufVwcoZGRklKtPihDC/tlNJ2MhhLCIhL2wfAykngOtM/zjdbjrSdPhv2JTAOjVIoDNtopRCGFXJMERQtifhH2wbrqayMT/pf5szAO/OvDQEghvZ1b8o+FteOzuuuTmx9ooYCGEvZEERwhhfw4ug7gtsPVdOP6juq/pQBj4Ibj7FSmu0WhoV6cGe+LPVG6cQgi7JQmOEMI+pMZD1lVAA0dXqfvi/4Lmg8GvNrR/rEhyk5NnwGBU8HS9MVmZoeQJ0IQQ1YskOEII+zCvZdF9mVduJjvb5sFraWaHV+9P4I2fj/Nk9/o8fW8D8hRJcIQQKqtO9CeEEGXW711Ac8vOG4M8tU4weGGRh3yzK56M3HxcdDemvDeUPNW8EKJ6kRocIYTtndsOf87FlNDcatx6CIsy23UkIY1DF9Jw1mkY3DYcAEWrEPrPUMK9wss8nb0QwjFJgiOEsB2jUe1IvPFNUAzgGwFp51Erl42F7otatjsegF7NQ6jppa4PZNQZqRlTk+bBza222J8QomqQJiohhG1kpcBXQ2DDTDW5aTUM/rkKvIIgrDX0f0+99woCz0Dzh+rz+X7/RQCGd6xt2l/QROWildobIao7qcERQtiGzlkdOeXkDv3mqjMTazQw6QjoXNSf240Bgx6czFdw/unQJa7n5lOnpged6tU07c/JyyHjeAaXr1zG0MOATidrNQhRXUmCI4SoPEYDaLRq8uLqra4npdFCUNObZQonMxpNkeQG4Nvd5wEY1qE2Wu3NjsmZWZnEzYkjjjhynsiRpRqEqMakiUoIUTmuJ8IX98NfH9/cF9zcPLkpo3lDo5h4bwMebFfLbL/MgyOEKCA1OEII6zuzAVZNgMzLkHgY2owAN98Kny7C34MpvRoX2a83yjBxIYRKEhwhhPUY8mHTLNjyDqBAUHN4aOkdJTelyTNKDY4QQiUJjhDCOtISYOU4iN+ubrcbA71ngbN7hU/5/YEEfjx4kcfurkvnBgFFjksNjhCigCQ4QgjL02fCwvsgIxFcvGHAPGj54B2f9qu/4tkVl0KrWn7FJjjSB0cIUUA6GQshLM/FEzpPhJBW8PhmiyQ3p5Mz2BWXglYDD7ePKLaMLNUghCggNThCCMtIPQ95WRB4o/PvXU9DxwnFDvOuiGW71JmL72sSRIivW7FljFojwQ8Hc3f43TKTsRDVnCQ4Qog7d+IXWPOkOuPwhE3g6gVaLWgtk9zk5htYue8CYD5z8a0MWgOBfQMZ0G6ArEUlRDUnTVRCiIrL18PaF2HZcMhJVROb3HSLP81vR5O4lpVHiI8b3RoFlliuoJOxs05qb4So7qQGRwhRMdfiYMVjkLBX3b7rKYiZAU6WrzkpaJ56uEMETrqSv5fl6HPIOptFvGc8hkayVIMQ1ZkkOEKI8jv2A3w/EXLTwM0PBn0MTfpa5akURaFfq1Cu5+TzcPtapZbNzsnm7OtneZEXeSbjGVmqQYhqTBIcIUT5KArs/kxNbmp1gAcXg1/J/WLulEajYUR0HUZE17ltWZnoTwhRQPrgCCFKlrAPlvZX7wtoNDB4IXR7Acb8atXkprxkHhwhRAFJcIQQJTu4DOK2wMY34PdXbu73DoZ7p4GVO/NuP32Fr3ae43pO2RIXmclYCFFAmqiEEOZS4yHrKqCBIyvVfaf/UG++EdC4d6XV2ny8+Qxb/r7CpdScYhfXvJVM9CeEKCAJjhDC3LyWJR/79Tn19lqa1cM4n5LFlr+vACXPXHwr6YMjhCggTVRCCHODF4KmhLcGrZN63MoOXUhl2Kd/AdC1YQC1a3qU6XHSB0cIUUBqcIQQ5i4dBMVY/LFx6yEsyuohrNh7gYTUbACGdSh7c1ieJo/A+wN5uPHDslSDENWc1OAIIczV6QxobmwU3Fv/reLCtSwOX0jjSEIaq/cnmJ49zM+NwxfSuHAt67bnyNfmE/xAMM+++Kws1SBENSc1OEIISL8IPmHqz036qcO/l48En3BoOxL2fQHpCepaU1bSZc7GIvsU4IH/bjdtx83uV+o5CpqoXHSS3AhR3Vn1a1lKSgojRozAx8cHPz8/xo4dS0ZGRqnl//Wvf9G4cWPc3d2pXbs2zzzzDGlp5h0aNRpNkduyZcuseSlCOKbcDFj9BHzcGdISbu6v0wkmHYHxG6H9Y+r9pCPgG261UOYNjcJJqyn2mJNWw7yhUbc9R25+LjkJOZw9cRajsYRmNiFEtWDVGpwRI0Zw6dIl1q1bR15eHmPGjGHChAl8/fXXxZa/ePEiFy9eZO7cuTRr1oxz587xxBNPcPHiRVasWGFWdsmSJfTu3du07efnZ81LEcLxJB6BFWPgyim1U3HcVmg99OZxp0IrgWs05ttWMKhNOA2CvOj/4dYix9Y8fTctwn1LfXy+MR+D3sDpl05zz0v3kJGRIUs1CFGNWS3BOX78OGvXrmX37t20b98egA8//JC+ffsyd+5cwsLCijymRYsWrFy50rRdv3593njjDf75z3+Sn5+Pk9PNcP38/AgJCbFW+EI4LkWBvUth7QuQnwPeoTBkEUTebevITDQaNcyC+7KQOXCEEIVZrYlqx44d+Pn5mZIbgJiYGLRaLTt37izzedLS0vDx8TFLbgCefvppAgIC6NixI4sXL0Yp5V0wNzeX9PR0s5sQ1VJOOqwcCz9NUpObBv+AJ7baTXJz9koG/p4utAz35Y0HWtAy3JdAL1dqet2+T43MgSOEKMxqNTiJiYkEBQWZP5mTE/7+/iQmJpbpHFeuXGHmzJlMmDDBbP/rr7/Offfdh4eHB7///jtPPfUUGRkZPPPMM8WeZ9asWcyYMaNiFyKEI9n2vjo7sUYHPaZD52dAax+DKfX5Rt74+TjXMvV8ODyKuxsE8kjH2ugNRlyddLd/vNTgCCEKKXeC88ILLzBnzpxSyxw/frzCARVIT0+nX79+NGvWjNdee83s2Cuv3FwTp02bNmRmZvL222+XmOBMmzaNyZMnm507IqJsM6MK4VDumQKJh6Hrs1A72tbRmPnp0EWS0nMJ8nalQ2RNQB1QUJbkBmQdKiGEuXInOM8++yyjR48utUy9evUICQkhOTnZbH9+fj4pKSm37Ttz/fp1evfujbe3N6tXr77thF3R0dHMnDmT3NxcXF2LdoR0dXUtdr8QDi8nDXYthC6T1ZoaZ3cY8Z2toypCURQ+2xILwKjOkbg4lb9WSWpwhBCFlTvBCQwMJDDw9nNhdOrUidTUVPbu3Uu7du0A2LBhA0ajkejokr85pqen06tXL1xdXfnhhx9wc3O77XMdOHCAGjVqSBIjRGEJe2H5GEg9p27fM8W28ZRix9mrHLuUjruzjhHRFVvIUxIcIURhVuuD07RpU3r37s348eNZsGABeXl5TJw4kWHDhplGUCUkJNCjRw+++OILOnbsSHp6Oj179iQrK4svv/zSrENwYGAgOp2OH3/8kaSkJO666y7c3NxYt24db775JlOm2O+btxCVSlFg5wL4/RUw5qkrf9e719ZRlaqg9ubBdrXw86jYJH15xjzQQZ0BdXio8UOyVIMQ1ZxV58H56quvmDhxIj169ECr1TJkyBA++OAD0/G8vDxOnjxJVpY6Bfu+fftMI6waNGhgdq7Y2FgiIyNxdnZm/vz5/Oc//0FRFBo0aMC7777L+PHjrXkpQlQNWSnw/UQ4+bO63XQADPwI3P1sGlZpTidnsOFEMhoNPNalboXPozfo0TppaTGmBW8/8LYFIxRCVEVWTXD8/f1LnNQPIDIy0mx4d/fu3Usd7g3Qu3dvswn+hBA3JOyF70ZB2nnQuUDPN6DjeHUyGTt2Ovk63q5O3FW/JnUDKj4xX0EnY2et1NwIIWQtKiEch9YZMpKhRl14aGmlrPptCb1bhNKlYSBp2Xc2j43eoEcxKuRdySMuLo7atWujtZMh8EKIyicJjhBVmSEfdDf+jUNbwfBvoFYHcPOxbVzl5OXqhJfrnb0d5RnyUPIUfn78Z37mZ1mqQYhqTr7eCFFVndsOH7WDhH039zXoUWWSm5w8A9vPXLlts3RZyTw4QojCJMERoipI2AdL+6v3RiP8OVfdvhYHG9+0dXQV8sOBizyycCfjv9hjkfPJMHEhRGHSRCVEVXBwGcRtURfJTDsPZzao+1sNhX7v2jS0ilAUhc+2ngWgY11/i5xTanCEEIVJgiOEvUqNh6yrgAaOrlL37f8fKEbQucK9L8Hdz9j9KKni/Pn3FU4lZeDpomNoh4pN7HcrqcERQhQmCY4Q9mpey6L7FKN6b8iFP6ZDl39XbkwW8tkWtfbm4Q4R+LpbZlh3nkFWExdC3CR9cISwV4MXgraE7yBaJ/V4FXQiMZ0tf19Bq4HH7q74xH63kiYqIURhUoMjhL3yCYNRP8GSYia2HLe+ysxzc6tFN5Zl6N0ihAh/D4udV2/QgxaiB0fTLqQdTk7y9iZEdSbvAELYG0M+bJ6tjpRq2PPGTi1gLHRfNeUbjBxOSANgXNd6Fj233qhH66xlyAtDeK7DcxY9txCi6pEERwh7kn4RVo6Dc9vUbTcf8AwC33BoOxL2fQHpCeAZaNs4K8hJp+WXZ7qyKy6FtrVrWPTcBX1wXHQVW6xTCOFYJMERwl78/QesnqCOnHLxggHvQ8sHIT9XXVtKo4F2Y8CgBydXW0dbYVqthrvq1bT4efUGPYqikJuay+XLlwkICEBTBUeYCSEsQzoZC2FrhjxY9yp8NURNbkJaweN/qskNqMlMwQe1RlNlk5vTydfJyTNY7fx6ox5Fr/B8j+cJCgoiKyvLas8lhLB/kuAIYWvZ12D/l+rPHcbD2HVQs75tY7Iwo1Fhwhd7uXv2BvbFX7PKc8g8OEKIwqSJSghb8wqCIQshJx2aD7J1NFax8WQyZ69k4u3mRKNgb6s8R55R5sERQtwkCY4QlS1fD+tnqKt+FyQ09e+zaUjW9tmNoeGPdKx9x6uGl0RqcIQQhUmCI0RluhYHKx6DhL3g6gt17wEPy6zFZK+OJKSx4+xVnLQaRnWOtNrzSIIjhChMEhwhKsuxH+D7iZCbBm6+MOhjh09uABZtVWtv+rUKJczP3WrPk2vItdq5hRBVjyQ4Qlhbfi78/jLs+lTdrtUBHlwMfpZZZNKeXUrL5seDFwEY18WyE/vdSvrgCCEKkwRHCGvKy4HFveDSAXW78zPQYzroLLPApL3bcuoK+UaF6Lr+tKzla9XnKliqoc9DfQjyCJKlGoSo5uQdQAhrcnaD2p0gNR4eWACNetk6okr1cIcI2tbxIyfP+stLFCzVMOODGXQI6WD15xNC2DdJcISwtLwcyL0OXjeWU/jHDLj7GXXxzGqoQZB1hoXfqqCTsbO2etSOCSFKJxP9CWFJV07DZzHw3aPqopmgzjxczZIbg1HhUlp2pT5nniEPRVHIz8knMzMTRVEq9fmFEPZFEhwhLOXQd/DJPZB0GK78DddibR2Rzaw7lkjXORt59fsjlfacBUs1dKjTAS8vL1mqQYhqTpqohLhT+iz4dSrs/5+6HdkVhnwG3iG2jcuGPtsSS75Rwcut8t5iZB4cIURhkuAIcSeST8Dy0XD5OKCBbs9Dt6mg1dk6MpvZH3+NPeeu4azTMKpTZKU9r94oCY4Q4iZpohKiPBL2wdL+6r2iwPdPqcmNVzCM/B7unVatkxuAz25M7DewdThBPm6V8pxGxUi+Mb9SnksIUTVIgiNEeRxcBnFb4NC3oNHA/f+Fxn3hia1Qr5uto7O58ylZ/Hr4EgDjutattOeVSf6EELeSJiohbic1HrKuAho4/J2678hKaD0cUKDPHHVFcMHS7XEYFejaMICmoT6V9rzS/0YIcStJcIS4nXkti+7LvAyfFqqxeS2t8uKxU3kGo2lZhrFdKq/2BiTBEUIUJQmOELcz4AP48d9AMfOqaJ3URTMFzjot6/7TjR8PXaRbo8BKfe6CJionnRMPPvggADpd9e4LJUR1Z9U+OCkpKYwYMQIfHx/8/PwYO3YsGRkZpT6me/fuaDQas9sTTzxhViY+Pp5+/frh4eFBUFAQzz33HPn50sFQWMGlg7BtHsUmNwDj1kOrhyszIrvm6+HMP++qg0ajqdTnLajBcXNzY/ny5Sxfvhw3t8rp4CyEsE9WrcEZMWIEly5dYt26deTl5TFmzBgmTJjA119/Xerjxo8fz+uvv27a9vDwMP1sMBjo168fISEhbN++nUuXLjFy5EicnZ158803rXYtohrauxR+mQqGXPAMgsxk1O8ExkL3AiAtOw8fN6dKT2wKFCQ4LjoXmzy/EML+WK0G5/jx46xdu5bPPvuM6OhounTpwocffsiyZcu4ePFiqY/18PAgJCTEdPPxudlZ8ffff+fYsWN8+eWXREVF0adPH2bOnMn8+fPR66UdXliQIU9Nbhr3hZFr1I7EYa2h/3vqvVcQeFZuU4w9UhSFRxft5IH/budk4nWbxFAwB46LVhIcIYTKagnOjh078PPzo3379qZ9MTExaLVadu7cWepjv/rqKwICAmjRogXTpk0zm3J9x44dtGzZkuDgYNO+Xr16kZ6eztGjR4s9X25uLunp6WY3IYplKDTcuMM4GPYNDPsagpvDpCMwfiO0f0y9n3QEfMNtF6ud2B13jUMX0jh2KZ0AL9skGAU1OJq8m03bmZmZNolFCGEfrNZElZiYSFCQ+dBZJycn/P39SUxMLPFxjzzyCHXq1CEsLIxDhw7x/PPPc/LkSVatWmU6b+HkBjBtl3TeWbNmMWPGjDu5HOHoFAV2fgJ7FsO4deDmq85z06TvzTJOrjd/1mjMt6uxz7acBWBI23Bqetnmd1LQyViaqIQQBcqd4LzwwgvMmTOn1DLHjx+vcEATJkww/dyyZUtCQ0Pp0aMHZ86coX79+hU657Rp05g8ebJpOz09nYiIiArHKBxM9jX4fiKc+End3v8ldHratjFVEbFXMll3PAmo/KHhhZn64EgTlRDihnInOM8++yyjR48utUy9evUICQkhOTnZbH9+fj4pKSmEhJR9EcLo6GgATp8+Tf369QkJCWHXrl1mZZKS1DfYks7r6uqKq6t82xbFuLAHlo+BtHjQuUDPN6DjeFtHVWUs2RaLosC9jQNpEORtszikk7EQ4lblTnACAwMJDLx9x8pOnTqRmprK3r17adeuHQAbNmzAaDSakpayOHDgAAChoaGm877xxhskJyebmsDWrVuHj48PzZo1K+fViGrLaIS/5sMfr4ExH2rUhYeWQliUjQOrOlKz9CzfcwGAcV3r2TSWgk7GTlqZ2ksIobJaJ+OmTZvSu3dvxo8fz65du9i2bRsTJ05k2LBhhIWFAZCQkECTJk1MNTJnzpxh5syZ7N27l7i4OH744QdGjhzJPffcQ6tWrQDo2bMnzZo149FHH+XgwYP89ttvvPzyyzz99NNSSyPKbss78PvLanLTfDA8/qckN+W0en8C2XkGmob60Ll+TZvGIjU4QohbWfXrzldffcXEiRPp0aMHWq2WIUOG8MEHH5iO5+XlcfLkSdMoKRcXF/744w/mzZtHZmYmERERDBkyhJdfftn0GJ1Ox08//cSTTz5Jp06d8PT0ZNSoUWbz5ghxW+3HwIGv4O5noN0YtdOwKJeRnSIJ9XXDzVlns/lvCpg6GUsfHCHEDRpFUUqYotVxpaen4+vrS1pamtkcO8KBGY3w9+/QuPfNffl6cJIPREew7MQy3tj5Bt1DunP2A3VU18qVK2U2YyEcTHk+v6XBWji+jMuw+nE4sx4GLYCo4ep+SW4qRFEU8gwKLk5WXemlXAqaqNzd3fn5559tHI0Qwh7YzzuUENYQtxUWdFGTGyd3W0fjEHacuUqXORtM89/YA5nJWAhxK6nBEY7JaFA7Em+aBYoRAhrDw59DUFNbR1blfbY1luTrucSnZN2+cCXJM8hEf0IIc5LgCMdzPQlWjYfYzep21D+h71vg4mnbuBzA6eTrbDiRjEYDj91tu4n9blVQg4MePD3V1zk5Odn0sxCi+pEERzie5KNqcuPsCf3fhdbDbB2Rw1i0NQ6AfzQNJjLAfpKHgj44zlpns7XrhBDVlyQ4wvHUvw/6zoW63SCwka2jcRhXM3JZtc8+Jva7lSnB0TnbOBIhhL2QTsaiakrYB0v7q/fpF+Gb4ZASe/N4x/GS3FjYl3/Fk5tvpFUtXzpE1rB1OGZkHhwhxK2kBkdUTQeXQdwW+PNtOL8Tsq6CPgNG/WjryBxSnsHI//6KA9TaG1tP7HcrWWxTCHErSXBE1ZEaryYyaODISnXfyV/U+5oN4J6pNgvN0TnrtHzxWDTf7TlPnxZlXyy3shR0MpYmKiFEAUlwRNUxr2XJx66ehs/7w2tplRdPNdMszIfXBja3dRjFKtzJWAghQPrgiKpk8ELQ6Io/pnVSjwuLqwqruRTU4Lg6u9KtWze6deuGVitvb0JUZ1KDI6qOVg9DjbqwKKbosXHrZTVwKzh0IZVRi3fRtnYNXh/UgnA/+5wNumCiP28PbzZt2mTbYIQQdkG+4gj7l5YAhnz1Z1Mfi4JOrvInbE2fbY3lWlYe608kYzTab02OqZOxzGQshLhBPh2EfTv+E3zcCTbPVrc9A8ErSK2t6f8ehLVWtz0DbRqmI7lwLYvDF9I4kpDGb0cSAXDRaUnLzuPwhTQuXLO/ifRMa1FJgiOEuEGaqIR9ys+FddNh5wJ1O/ZPMOSBbzhMOgI6F9BooN0YMOjBydW28TqQLnM2FtmnNxjp/+FW03bc7H6VGdJtFdTg5OfkExioJrtxcXGyVIMQ1ZjU4Aj7k3IWFvW8mdx0fgZG/3yzecrJVU1uQL2X5Mai5g2NQqctfp4bJ62GeUOjKjegMig80d+VK1e4cuWKjSMSQtia1OAI+3J0NfzwDOSmg7s/PLAAGvWydVTVyqA24eyJS+HLnfFFjq15+m5ahPvaIKrSyTBxIcStJMER9uN6Eqx5CvKyoHYnGLJIbZISlUqfb2TDyWRA7cqtoFaU2fNocelkLIS4lTRRCfvhHawuktllMoz6SZIbG3FxUmct9nJ1omW4L2880IKW4b4EerlS08s+EwiZyVgIcSupwRG2dWg5+EVA7bvU7TYjbBuPAKBBkBd7X4nBRadFo9HwSMfa6A1GXJ1KmGjRxgrmwZG1qIQQBaQGR9iGPgt++BesGgcrHoOsFFtHVO0du5jOVzvPmWYudnXSmRbV1Gg0dpvcgNTgCCGKkhocUfkun4TloyH5GKCBNv8EN/vruFqd5BmMTFl+kGOX0knJ0POvHg1tHVKZ5RvzMSpGANyc3Gjfvj2ALNUgRDUnCY6oXAe+hp+fVTsSewbBkIVQr7uto6r25m88zbFL6dTwcGZYx9q2DqdcCjoYA/h6+bJ7924bRiOEsBeS4IjKka+HH/8NB79Wt+t1VxfH9AqyaVgCjl5M46MNpwGYcX8LAr2r1rxCBXPggDRRCSFukgRHVA6dM+ivg0YL3V+ErpNBa799OqoLfb6RZ787SL5RoU+LEAa0CrV1SOVWUIOjQYOTRt7ShBAqeTcQ1qMo6vIKTjeWVRj4Edz1NNTpZOvIxA0fbTzNicTr+Hu6MHNQC1On4qqk8DpU2dnZNGvWDIBjx47h4eFhy9CEEDYkCY6wjtzr8NNkMObBg0vUBMfdT5IbO3L5ei4LNp8B4PX7mxPgVbWapgqYJvnTuqAoCufOnQMwjQYTQlRPkuAIy7t0CFaMgaunQaODxMMQ2srWUYlbBHq78u2Eu1h7NJH+rcJsHU6FmZZpkP43QohCJMERlqMosGcRrH0RDLngUwseXCzJjR1rU7sGbWrXsHUYd8S00KYs0yCEKEQSHHFnEvbBuunQbSrsWawulgnQqA8M+i94+Ns2PlHE8UvpOGk1NAz2tnUoFlFQg+Oqq5pNbEII65AER9yZg8sgbovaHHX9EmidIGYGdHpa7Xcj7EpuvoF/L9tP3NUs/vtIW2KaBds6pDtmmsVYVhIXQhRi1ak+U1JSGDFiBD4+Pvj5+TF27FgyMjJKLB8XF4dGoyn2tnz5clO54o4vW7bMmpciCkuNh4v74eIBOLpK3ZeXBd5hMPBDaDZQkhs79cH6vzmVlIGPmxNt61TtpqkCspK4EKI4Vq3BGTFiBJcuXWLdunXk5eUxZswYJkyYwNdff11s+YiICC5dumS279NPP+Xtt9+mT58+ZvuXLFlC7969Tdt+fn4Wj1+UYF7LQhs3EpmcdMhJgzVPqtuvpVV6WKJ0B8+n8vEmddTU/w1qgb+nYyQEhRfa1Gg0pmHiVXHIuxDCcqyW4Bw/fpy1a9eye/du09owH374IX379mXu3LmEhRUdtaHT6QgJCTHbt3r1ah5++GG8vLzM9vv5+RUpKypJ92mwadaNDcX8XusEgz62RVSiFDl5BqYsP4hRgQGtw+jdoupN6FeSwvPgeHh4cPToURtHJISwB1ZrotqxYwd+fn6m5AYgJiYGrVbLzp07y3SOvXv3cuDAAcaOHVvk2NNPP01AQAAdO3Zk8eLFpc55kZubS3p6utlNVICiwPaP4M+3Sy4zbj20erjyYhJl8v76v/k7OYMAL1deH9jc1uFYlAwTF0IUx2o1OImJiQQFma8z5OTkhL+/P4mJiWU6x6JFi2jatCmdO3c22//6669z33334eHhwe+//85TTz1FRkYGzzzzTLHnmTVrFjNmzKjYhQhVVora/HRqrbpd7144uxE1RzYWuhf25ujFND65MaHfGw+0oIaDNE0VMNXgaB3ruoQQd6bcNTgvvPBCiR2BC24nTpy448Cys7P5+uuvi629eeWVV7j77rtp06YNzz//PFOnTuXtt0uuVZg2bRppaWmm2/nz5+84vmolfics6KomNzpX6Pcu3P+RulBmWGvo/5567xUEnoG2jlbconGwN1N6NeahdrXo1dzxmnULdzLOysqiefPmNG/enKysLBtHJoSwpXLX4Dz77LOMHj261DL16tUjJCSE5ORks/35+fmkpKSUqe/MihUryMrKYuTIkbctGx0dzcyZM8nNzcXVtehcGK6ursXuF2V06ldIvwA1G8BDSyHkRifjSUdAd2OdqXZjwKAHJ/k92xsnnZanujdw2KULCncyVhSFY8eOAbJUgxDVXbkTnMDAQAIDb/8tvVOnTqSmprJ3717atWsHwIYNGzAajURHR9/28YsWLWLgwIFleq4DBw5Qo0YNSWKs5d6XwNkD7noSXAtNDlc4mdFoJLmxM/FXswjyccXNWV213VFHFRXuZCyEEAWs1sm4adOm9O7dm/Hjx7Nr1y62bdvGxIkTGTZsmGkEVUJCAk2aNGHXrl1mjz19+jR//vkn48aNK3LeH3/8kc8++4wjR45w+vRpPv74Y958803+9a9/WetSqp+4rbBsBOSrHxzonNWZil0dY+bb6iAnz8DopbsY8OFWzlwuee4pR2DqZCwT/QkhCrHqPDhfffUVEydOpEePHmi1WoYMGcIHH3xgOp6Xl8fJkyeLtJUvXryYWrVq0bNnzyLndHZ2Zv78+fznP/9BURQaNGjAu+++y/jx4615KdWD0QBb3lGHgCtG2PERdJ1s66hEBby77hRnL2cS5O1KgKdj16xJDY4QojhWTXD8/f1LnNQPIDIysth28jfffJM333yz2Mf07t3bbII/YSHXk2DVeIjdrG5HjYDox20bk6iQvedSWLjlLACzBrfE18OxazZMfXAkwRFCFCJrUQk4uwlWjofMZLWvTb93IWq4raMSFZCTZ+C55YdQFBjcNpweTav+WlO3YxpFJcPEhRCFSIJT3e39HH78N6BAUDN1lFRgY1tHJSpo7m8nOXslk2AfV17t71gT+pXEtNimzhmNRkOdOnUAx+1ULYQoG0lwqrvILuDiBS0GQ5854Oxu64hEBe2JS2HRtlgAZg9u5fBNUwUK1+B4eHgQFxdn24CEEHZBEpzqKCUW/OuqP9esD0//Bb61bBuTuGMhvm50qleTMD937m0SdPsHOIg8o/TBEUIUJQlOdWLIh43/B9s+gH+uhPr3qvsluXEItWp48OXYaPSG6rVkRuGZjIUQooDV5sERlevQhVSGf/oXhy6kFl8g7QIs7Qdb3wPFoM51IxxCZm6+6WetVmOa2K+6KDwPTnZ2Nh06dKBDhw5kZ2fbODIhhC1JDY6DWLUvgR1nr7JqXwKtavmZHzz1G6x+HLKvgasPDHhf7XMjqrwsfT79P9xK5/o1ebFvUzxdq9+/dOF5cIxGI3v27AHAaKxeNVlCCHPV793QgVy4lsW1zDw0Gvjx4EVAvX+wXS0UBWq4Qa19b8P2D9UHhEbBQ0vAv57tghYW9dbak8ReySQnz8DzfZrYOhybKLwWlRBCFJAEp4oyGhW6zNlo2i4YEJuSqaf/h2rzU0/tbj51uZHcRD8J/5gh60U5kJ1nr7J0exwAs4e0wseteoyaupXMZCyEKI4kOFXE1YxcDpxP5eD5VPbfuC+sheYs05y+Zlb+IxxW1Bqaq+ExnPJIxK95DIEdhsi8IA4kS5/PcysOATCsQwTdGt1+UVpHJZ2MhRDFkQTHDuXkGbhwLYsGQTcXtxz40TYSUs07Tbo4aakX4MGJxAwG67bQWXeM1zVLGKOfSire7D2fRk8GwEkI+WMDd9Xzp1+rMP7RzPFnt3V0b609SXxKFmG+brzUr6mtw7EpWWxTCFEcSXBszGhUOHslkwPnUzlw/hoHz6dx/FI6Xm5O7H/lH6Zal6jafrg5a4mKqEFUbT+iavnRxP0a586f59/fxnK/bhsAbbRnWOA8j2t3T+eC3oN1F13Zf/4aiek5rDlwkSAfN1OCk6XP54cDF7mrXk3q1PSQGp4q4q9CTVNzHmyFdzVtmiogTVRCiOJIgmNhhy6kMuuXE0zr26ToaKZbzPrlOF/viud6Tn6RY05aLVcy9AR6q31mPhjWBp32lgTktdo0AH52hYIlSxXgLt1x+EtdS2r8a2lk6w3sj7/GX2ev0q3xzaaMPXHXeGHVYQCCfVy5q15N0y1SEh67lZGTTw0PZ3q3CKVrw+rbNFXg1k7GAQEBtgxHCGEnJMGxsMLDtRsGeXM4IY2D51Nv1NCk8vMzXfDzUN+INRoN13PycXPW0jLcl6gIP1MNTZivm1mCUSS5Abh/Pnw/EVBMnYxNpbROMOhjANxddHRuEEDnBuZv/FqNho51/TkQn0pSei7fH7jI9wfU0VjBPq689WDr2/btKE9CJywjplkwv/+nG27OMo0VmNfgeHp6cvnyZRtHJISwB5LgWEDh4dqr9l8A4H9/neOLHXEYFfOyBy+kmZKGEdG1GdA6lMbB3jjpyvlhlRoPOxdws+7mFuPWQ1hUqafo0jCALg0DyMkzsC/+Gn+dTeGvs1dNCU+Ij5up7E+HLrLuWFKRGp5S598RFqMmkseZ1rcprWr5mWr2hHQyFkIUTxIcCyg8XLuA4ZbM5vneTWgdodbSFIjw96j4k7p6Q04auPmq92gBY6H7snNz1tG5fgCd66s1PAUJT8MgL1OZP44lmdXw+Hs60zLclz3nrgG3zL/j6UytGndwbaKIb3efZ8fZFN5bd4olYzraOhy7oSiKaS0q6WQshChMEhwLmDc0iinLD5J/a3UN4KTVMPeh1gxqE37nT5SfCzoX0GjAvQYM+wYMevhmKPiEQ9uRsO8LSE8Az4r3zShIeAp7tFMktWt68tfZq+yKTSElM4/Np66Yjl8tNP8OQNzsfhV+fqEqqBlUFIUVe9Wawc2nLrP3XAouOp0kktxcaBPUGpzs7Gz69OkDwK+//oq7u7utQhNC2JhGUZQS2jgcV3p6Or6+vqSlpeHj42ORcx5JSDP7gC/w07+60CLc986f4PJJWD4aOk6A9mPMjxVOfBRFTXqsOKHf8j3neWHlIQzF/OU4aTVM6dmIx7vVl07KdyjyhZ9vW6a6J5IZ+gw6fdMJgD3/3EN+Tj5eXmrNY0ZGBp6enrYMTwhhYeX5/JZeihZW8Jlu0c/2A9/Ap90h+RhsfVdNaApzcjV/YivPVvxQ+wi+n9il2GOLR7fn3XV/0+f9LazYewF9vqwHVBFJ6Tm0j6xR4nEnrYZ5Q6MqLyA7VdDBGKSJSghhTpqoLKSmlwuBXq6E+rkxtEME3+4+z6XUHGp63UHHR30m/PIcHPhK3a7bDQYvtKvlFgoqjQruz1zOwEmn4UTidaYsP8hba08wqnMkI6Jrm0aPidLp840M/GgrSem5JZZZ8/TdlqkZrOIKOhg7aZ3QauT7mhDiJklwLCTU152tL9yLi06LRqPhkY610RuMuDrpKnbCpGNqk9SVk6DRQvdp0PVZ0FbwfBZWUkLXu0Uog9tE8NWucyzdFkfy9Vze/u0kH204zcPtazHxvoYyAqgYiqKYmvRcnLSM7VKXX48k8uhddZj83cEiiaRQyUKbQoiSSIJjQYWTGY1GU/HkJvMKLPoH6DPAOxSGfAaRxTcJ2crtErqnujdgXJd6/HjwIgu3nOVE4nWW7T7PMz0a2jhy+3MiMZ3XfzzG493qm6YQeOzuuozvWo/E9BzL1ww6EJnFWAhREklw7JFnAHR+Bs7vhMGfqtt26HYJnYuTliHtajG4bThbT18h7komNb1u1t689sNRouv607N5SPETGTq4a5l63vvjFF/+dQ6jAmnZedzTMACNRmOaF8niNYMOxjQHjtTgCCFuIQmOvbh0CJw9IKCBun3PFEAD2qrfr0Cj0dC1YaDZsgIHz6eydHscS7fHUdvfg7Fd6vJQ+1p4uDj+n2S+wcjXu+J5d90pUrPUJpY+LUJ4sW/TYkeeWaxm0AEV1OA46252MPbwqN5D54UQKsf/NLF3igJ7FsHaFyGgIYz7A5zd7aavjbWE13Bn4r0N+HLnOeJTsnj1h6O8u+4UI6JrM7pzJEGFZlF2JLvjUnhp9WFOJWUA0CTEm+n9mxVZRkOUza2zGHt6epKZmWnLkIQQdkISHFvKSYMf/w1HV6vbPuHqEHBnx5+cLMDLlSm9GvPUvfVZufcCi7bGEnc1i/9uOsPCLWdZNqET7eqUPEy6qrqaoedUUgZ+Hs4827MxwztElH+ZDmEinYyFECWRBMdWLu6H5WPgWqy6MGbMa9BpooUn0LF/Hi5OPNopkkei6/DH8SQ+23KWhGvZtKp1cwj0xdRsQm9ZfLSqLPKZmZvPyaTrtK2tJmu9mgfz6oBmPNAmXIbNW4B0MhZClEQSnMqmKLBrIfz+kjrjsG9teHAxRHSwdWQ2pdNq6NU8hF7NQ0jJ1ON8o1Yjz2DkwY+34+PuzNgudRkYFYark87uF/k0GhXWHEhg9q8nyDMY2TilO34eLmg0GsbcXdfW4TmMgiaqgkn+cnJyGDJkCAArV67Ezc0xmzqFELcnCU5lMxrg8HI1uWnSH+7/SF1XSpj4e978Nn4y8Tqp2XlcTMvhuRWHePOX4wxoHcZPB9VFP+1xkc/98deY8eMxDpxPBaBOTQ8SUrOlxsYKbq3BMRgM/PLLL6afhRDVlyQ4lU3npNbYnFoLHcZVuyap8moR7suOaT34Zlc8s389wbWsPL7Ycc503J4W+UxKz2HO2hOs2pcAgKeLjn/1aMiYuyNl5JOVmPrgSBOVEOIWkuBYm6LAjvmQdUXtZwPgFwEdx9s0rKrE192ZJ7rVJ8DThakrD1HMou04aTX0bhFCxzf+oH6gF/WDPKkf6EWDIC/qB3oV6cNjaalZemLe2cz13HwAHmxXi6m9GjvsaDB7IfPgCCFKYrXhG2+88QadO3fGw8MDPz+/Mj1GURSmT59OaGgo7u7uxMTE8Pfff5uVSUlJYcSIEfj4+ODn58fYsWPJyMiwwhVUUMI+WNpfvc9KgW+Gqf1ttr4HCXttHV2V9mD7CH4oYZHPNU/fjauTjuTruew4e5Uv/4pnxo/HeHTRLjrP3kDzV3/jzOWbfyexVzI5mXid3PzyNWMcupDK8E//4tCFVLP9fh4u9G8dSpvafnz/9N3Mfai1JDeVoLh5cIQQAqxYg6PX63nooYfo1KkTixYtKtNj3nrrLT744AM+//xz6tatyyuvvEKvXr04duyYqbPgiBEjuHTpEuvWrSMvL48xY8YwYcIEvv76a2tdSvkcXAZxW2Db+3BhD6RfAJ0r9H4TwtraOjqHUdzaTK8NbMbITnU4czmD08kZnLmcwZnLmcRdySQ7z0C4383h95/+eYZvdp1Hq4Ha/h43an28qB/oSYMgL1rV8jN1dC6soHPz4q2xpGbn8Ur/ZtQP9AJgev/muDpp0VbDWZltRWpwhBAlsVqCM2PGDACWLl1apvKKojBv3jxefvll7r//fgC++OILgoODWbNmDcOGDeP48eOsXbuW3bt30759ewA+/PBD+vbty9y5cwkLC7PKtdxWajxkXQU0cGSluu/YGvXepxb0fw8a9bRNbA6mtFXbvd2caR3hR+sIP7PH5BmMJFzLxs3ZfEZgb1cnrufmE3c1i7irWaw/kWw6fnRGL1OCs2RbLBeuZVGrhgdr9qv9a9YcUDs55+gPM/fh1tSq4YG7i/SzqWwyTFwIURK76YMTGxtLYmIiMTExpn2+vr5ER0ezY8cOhg0bxo4dO/Dz8zMlNwAxMTFotVp27tzJAw88UOy5c3Nzyc3NNW2np6dbNvh5LQE44OrCb54e4OZX6GAGrB0PqU9Z9jmrsQdijGi1Gi6goXNHBaNR4YuTZWj+O3vzR99wGBGukK03kJqdR1p2HmlZeaRm55GXb+Sjg0dMZRfvir35QB9w9bm5uT8LeixVF8cUle9A8gFAEhwhRFF2k+AkJiYCEBwcbLY/ODjYdCwxMZGgoCCz405OTvj7+5vKFGfWrFmmGiWrGLwQ1jzJ3y7OfOnrU3yZ419a7/mF5WgBF/jy+M1dLv63f9iXx7dZLSRxe36ufoC6VIOiFNMLXQhR7ZQrwXnhhReYM2dOqWWOHz9OkyZN7igoS5s2bRqTJ082baenpxMREWG5J2j1MAQ0ounSfzA+Nc38WJtHwSu4+MeJKuPy9Ry+3XOhyP6h7WsR6C2diW3Jw9mDBxs+aOswhBB2plwJzrPPPsvo0aNLLVOvXr0KBRISEgJAUlISoaGhpv1JSUlERUWZyiQnJ5s9Lj8/n5SUFNPji+Pq6oqrq2uF4iqPFno9LfT5gBG1KsAIDR6CsCirP7ewriMJafzv161FOjcPbdCFFuG+tz+BEEKISlWuBCcwMJDAwECrBFK3bl1CQkJYv369KaFJT09n586dPPnkkwB06tSJ1NRU9u7dS7t27QDYsGEDRqOR6Ohoq8RVZp6B4BWkLpjZdiTs+wLSE9T9osorrXOzEEII+6NRrNRgHR8fT0pKCj/88ANvv/02W7ZsAaBBgwZ4eanDaps0acKsWbNMnYPnzJnD7NmzzYaJHzp0yGyYeJ8+fUhKSmLBggWmYeLt27cv1zDx9PR0fH19SUtLw8enhD4zFZGfCzqXm1/vDXpwsn7NkagcufkGXHRaNBoNiqKgNxhlhmIhhKhE5fn8tlon4+nTp/P555+bttu0aQPAxo0b6d69OwAnT54kLe1mn5WpU6eSmZnJhAkTSE1NpUuXLqxdu9ZswbyvvvqKiRMn0qNHD7RaLUOGDOGDDz6w1mWUT+FkRqOR5MbBFE5mNBqNJDdCCGHHrFaDY8+sVoMjhBBCCKspz+e31ZZqEEIIIYSwFUlwhBBCCOFwJMERQgghhMORBEcIIYQQDkcSHCGEEEI4HElwhBBCCOFwJMERQgghhMORBEcIIYQQDkcSHCGEEEI4HKst1WDPCiZvTk9Pt3EkQgghhCirgs/tsizCUC0TnOvXrwMQERFh40iEEEIIUV7Xr1/H19e31DLVci0qo9HIxYsX8fb2RqPRWPTc6enpREREcP78eYdc50qur+pz9GuU66v6HP0aHf36wHrXqCgK169fJywsDK229F421bIGR6vVUqtWLas+h4+Pj8P+4YJcnyNw9GuU66v6HP0aHf36wDrXeLuamwLSyVgIIYQQDkcSHCGEEEI4HElwLMzV1ZVXX30VV1dXW4diFXJ9VZ+jX6NcX9Xn6Nfo6NcH9nGN1bKTsRBCCCEcm9TgCCGEEMLhSIIjhBBCCIcjCY4QQgghHI4kOEIIIYRwOJLglNMbb7xB586d8fDwwM/Pr0yPURSF6dOnExoairu7OzExMfz9999mZVJSUhgxYgQ+Pj74+fkxduxYMjIyrHAFpStvHHFxcWg0mmJvy5cvN5Ur7viyZcsq45KKqMjvunv37kXif+KJJ8zKxMfH069fPzw8PAgKCuK5554jPz/fmpdSrPJeX0pKCv/6179o3Lgx7u7u1K5dm2eeeYa0tDSzcrZ8DefPn09kZCRubm5ER0eza9euUssvX76cJk2a4ObmRsuWLfnll1/Mjpflf7Iylef6Fi5cSNeuXalRowY1atQgJiamSPnRo0cXea169+5t7csoUXmub+nSpUVid3NzMytjb68flO8ai3s/0Wg09OvXz1TGnl7DP//8kwEDBhAWFoZGo2HNmjW3fcymTZto27Ytrq6uNGjQgKVLlxYpU97/63JTRLlMnz5deffdd5XJkycrvr6+ZXrM7NmzFV9fX2XNmjXKwYMHlYEDByp169ZVsrOzTWV69+6ttG7dWvnrr7+ULVu2KA0aNFCGDx9upasoWXnjyM/PVy5dumR2mzFjhuLl5aVcv37dVA5QlixZYlau8PVXpor8rrt166aMHz/eLP60tDTT8fz8fKVFixZKTEyMsn//fuWXX35RAgIClGnTpln7cooo7/UdPnxYGTx4sPLDDz8op0+fVtavX680bNhQGTJkiFk5W72Gy5YtU1xcXJTFixcrR48eVcaPH6/4+fkpSUlJxZbftm2botPplLfeeks5duyY8vLLLyvOzs7K4cOHTWXK8j9ZWcp7fY888ogyf/58Zf/+/crx48eV0aNHK76+vsqFCxdMZUaNGqX07t3b7LVKSUmprEsyU97rW7JkieLj42MWe2JiolkZe3r9FKX813j16lWz6zty5Iii0+mUJUuWmMrY02v4yy+/KC+99JKyatUqBVBWr15davmzZ88qHh4eyuTJk5Vjx44pH374oaLT6ZS1a9eaypT3d1YRkuBU0JIlS8qU4BiNRiUkJER5++23TftSU1MVV1dX5ZtvvlEURVGOHTumAMru3btNZX799VdFo9EoCQkJFo+9JJaKIyoqSnnsscfM9pXln6IyVPQau3Xrpvz73/8u8fgvv/yiaLVaszfijz/+WPHx8VFyc3MtEntZWOo1/O677xQXFxclLy/PtM9Wr2HHjh2Vp59+2rRtMBiUsLAwZdasWcWWf/jhh5V+/fqZ7YuOjlYef/xxRVHK9j9Zmcp7fbfKz89XvL29lc8//9y0b9SoUcr9999v6VArpLzXd7v3Vnt7/RTlzl/D9957T/H29lYyMjJM++zpNSysLO8DU6dOVZo3b262b+jQoUqvXr1M23f6OysLaaKystjYWBITE4mJiTHt8/X1JTo6mh07dgCwY8cO/Pz8aN++valMTEwMWq2WnTt3Vlqslohj7969HDhwgLFjxxY59vTTTxMQEEDHjh1ZvHhxmZa7t7Q7ucavvvqKgIAAWrRowbRp08jKyjI7b8uWLQkODjbt69WrF+np6Rw9etTyF1ICS/0tpaWl4ePjg5OT+XJ1lf0a6vV69u7da/b/o9VqiYmJMf3/3GrHjh1m5UF9LQrKl+V/srJU5PpulZWVRV5eHv7+/mb7N23aRFBQEI0bN+bJJ5/k6tWrFo29LCp6fRkZGdSpU4eIiAjuv/9+s/8he3r9wDKv4aJFixg2bBienp5m++3hNayI2/0PWuJ3VhbVcrHNypSYmAhg9sFXsF1wLDExkaCgILPjTk5O+Pv7m8pUBkvEsWjRIpo2bUrnzp3N9r/++uvcd999eHh48Pvvv/PUU0+RkZHBM888Y7H4y6Ki1/jII49Qp04dwsLCOHToEM8//zwnT55k1apVpvMW9xoXHKsslngNr1y5wsyZM5kwYYLZflu8hleuXMFgMBT7uz1x4kSxjynptSj8/1awr6QylaUi13er559/nrCwMLMPi969ezN48GDq1q3LmTNnePHFF+nTpw87duxAp9NZ9BpKU5Hra9y4MYsXL6ZVq1akpaUxd+5cOnfuzNGjR6lVq5ZdvX5w56/hrl27OHLkCIsWLTLbby+vYUWU9D+Ynp5OdnY2165du+O/+7KQBAd44YUXmDNnTqlljh8/TpMmTSopIssq6/XdqezsbL7++mteeeWVIscK72vTpg2ZmZm8/fbbFvtwtPY1Fv6wb9myJaGhofTo0YMzZ85Qv379Cp+3rCrrNUxPT6dfv340a9aM1157zeyYtV9DUX6zZ89m2bJlbNq0yawj7rBhw0w/t2zZklatWlG/fn02bdpEjx49bBFqmXXq1IlOnTqZtjt37kzTpk355JNPmDlzpg0js45FixbRsmVLOnbsaLa/Kr+G9kISHODZZ59l9OjRpZapV69ehc4dEhICQFJSEqGhoab9SUlJREVFmcokJyebPS4/P5+UlBTT4+9EWa/vTuNYsWIFWVlZjBw58rZlo6OjmTlzJrm5uRZZq6SyrrFAdHQ0AKdPn6Z+/fqEhIQUGQGQlJQEUGVew+vXr9O7d2+8vb1ZvXo1zs7OpZa39GtYnICAAHQ6nel3WSApKanE6wkJCSm1fFn+JytLRa6vwNy5c5k9ezZ//PEHrVq1KrVsvXr1CAgI4PTp05X64Xgn11fA2dmZNm3acPr0acC+Xj+4s2vMzMxk2bJlvP7667d9Hlu9hhVR0v+gj48P7u7u6HS6O/67KBOL9eapZsrbyXju3LmmfWlpacV2Mt6zZ4+pzG+//WazTsYVjaNbt25FRt6U5P/+7/+UGjVqVDjWirLU73rr1q0KoBw8eFBRlJudjAuPAPjkk08UHx8fJScnx3IXcBsVvb60tDTlrrvuUrp166ZkZmaW6bkq6zXs2LGjMnHiRNO2wWBQwsPDS+1k3L9/f7N9nTp1KtLJuLT/ycpU3utTFEWZM2eO4uPjo+zYsaNMz3H+/HlFo9Eo33///R3HW14Vub7C8vPzlcaNGyv/+c9/FEWxv9dPUSp+jUuWLFFcXV2VK1eu3PY5bPkaFkYZOxm3aNHCbN/w4cOLdDK+k7+LMsVqsTNVE+fOnVP2799vGgq9f/9+Zf/+/WZDohs3bqysWrXKtD179mzFz89P+f7775VDhw4p999/f7HDxNu0aaPs3LlT2bp1q9KwYUObDRMvLY4LFy4ojRs3Vnbu3Gn2uL///lvRaDTKr7/+WuScP/zwg7Jw4ULl8OHDyt9//63897//VTw8PJTp06db/XqKU95rPH36tPL6668re/bsUWJjY5Xvv/9eqVevnnLPPfeYHlMwTLxnz57KgQMHlLVr1yqBgYE2GyZenutLS0tToqOjlZYtWyqnT582G5aan5+vKIptX8Nly5Yprq6uytKlS5Vjx44pEyZMUPz8/Ewj1h599FHlhRdeMJXftm2b4uTkpMydO1c5fvy48uqrrxY7TPx2/5OVpbzXN3v2bMXFxUVZsWKF2WtV8B50/fp1ZcqUKcqOHTuU2NhY5Y8//lDatm2rNGzYsFKT7Ype34wZM5TffvtNOXPmjLJ3715l2LBhipubm3L06FFTGXt6/RSl/NdYoEuXLsrQoUOL7Le31/D69eumzzpAeffdd5X9+/cr586dUxRFUV544QXl0UcfNZUvGCb+3HPPKcePH1fmz59f7DDx0n5nliAJTjmNGjVKAYrcNm7caCrDjflCChiNRuWVV15RgoODFVdXV6VHjx7KyZMnzc579epVZfjw4YqXl5fi4+OjjBkzxixpqiy3iyM2NrbI9SqKokybNk2JiIhQDAZDkXP++uuvSlRUlOLl5aV4enoqrVu3VhYsWFBs2cpQ3muMj49X7rnnHsXf319xdXVVGjRooDz33HNm8+AoiqLExcUpffr0Udzd3ZWAgADl2WefNRtmXVnKe30bN24s9m8aUGJjYxVFsf1r+OGHHyq1a9dWXFxclI4dOyp//fWX6Vi3bt2UUaNGmZX/7rvvlEaNGikuLi5K8+bNlZ9//tnseFn+JytTea6vTp06xb5Wr776qqIoipKVlaX07NlTCQwMVJydnZU6deoo48ePt+gHR3mV5/omTZpkKhscHKz07dtX2bdvn9n57O31U5Ty/42eOHFCAZTff/+9yLns7TUs6T2i4JpGjRqldOvWrchjoqKiFBcXF6VevXpmn4kFSvudWYJGUWwwVlcIIYQQwopkHhwhhBBCOBxJcIQQQgjhcCTBEUIIIYTDkQRHCCGEEA5HEhwhhBBCOBxJcIQQQgjhcCTBEUIIIYTDkQRHCCGEEA5HEhwhhBBCOBxJcIQQQgjhcCTBEUIIIYTDkQRHCCGEEA7n/wGbkCcR/1lOkwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(eigvals, qsvt_new_A, \"--*\", label=\"trained\")\n",
    "plt.plot(eigvals, np.diagonal(A), \"--*\", label=\"initial\")\n",
    "plt.plot(a_vals, targeted_poly, label=\"target\")\n",
    "\n",
    "\n",
    "plt.vlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "plt.hlines(0.0, -1.0, 1.0, color=\"black\", linestyle=\"--\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "357d65c4-d6b0-4e53-b619-8e4d80b9c767",
   "metadata": {},
   "source": [
    "We were successfully able to transform the singular values of $A_{new}$! Notice how remarkable this is, the QSVT algorithm allowed us to perform this transformation without having to compute the singular value decomposition at all."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f04ed1a-b083-40e1-b74a-e289c944700b",
   "metadata": {},
   "source": [
    "## 4. Conclusions and Further Readings\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a361449d-930d-40c0-94d3-91167bdfb1cf",
   "metadata": {},
   "source": [
    "In this lab we explored one of the most fundamental algorithmic building blocks in modern quantum computation, the Quantum Singular Value Transformation. Beginning with Quantum Signal Processing, we learned that repeated applications of a fixed signal rotation operator with interweaving phased rotations gives us tuneable polynomials. By manipulating the phase angles, we were able to control the types of polynomial transformations we generated. We then learned about qubitization, which allowed us to *\"copy-paste\"* the result of QSP to each 2D singular vector subspace of our target (block encoded) matrix $A$. Along the way, we used PennyLane to create quantum circuits, run experiments and test our knowledge in practice. I hope this lab has helped you build an intuative understanding for this algorithm! This leaves just one final question: \n",
    "\n",
    "**What comes next?**\n",
    "\n",
    "Some immediate next steps would be to read \"Grand Unification of Quantum Algorithms\"$^{[2]}$ which explores how the framework of QSP and QSVT can be used to explain some of the most popular quantum algorithms (Hamiltonian Simulation, Unstructured Search, Matrix Inversion). For the problem of matrix inversion, I also recommend [this demo](https://pennylane.ai/qml/demos/tutorial_apply_qsvt/) which solves the problem using PennyLane! \n",
    "\n",
    "Since the initial publication of these ideas, there has been a growing interest in this algorithm. Here I list a few follow up works and directions for the keen readers. The two-axis rotations of QSP were further generalized to arbitrary axis rotations. This had some nice results for the complexity of the algorithm as well as the efficiency with which one could compute phase angles: \n",
    "\n",
    "- [Generalized Quantum Signal Processing](https://arxiv.org/abs/2308.01501)\n",
    "- [Robust Angle Finding for Generalized Quantum Signal Processing](https://arxiv.org/abs/2402.03016)\n",
    "- [Doubling the Efficiency of Hamiltonian Simulation via Generalized Quantum Signal Processing](https://arxiv.org/abs/2401.10321)\n",
    "\n",
    "This idea was also lifted to QSVT:\n",
    "\n",
    "- [Generalized Quantum Singular Value Transformation](https://arxiv.org/abs/2312.00723)\n",
    "\n",
    "There was also work looking at dequantizing QSP:\n",
    "\n",
    "- [Towards Dequantizing Quantum Signal Processing](https://arxiv.org/abs/2311.01533)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "576617cc-b3dd-4cf9-bf04-ccc221e9ffd8",
   "metadata": {},
   "source": [
    "## 5. References:\n",
    "\n",
    "- [1] András Gilyén, Yuan Su, Guang Hao Low, Nathan Wiebe, “[Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics](https://arxiv.org/abs/1806.01838)”, Proceedings of the 51st Annual ACM SIGACT Symposium on the Theory of Computing, 2019\n",
    "- [2] John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang, “[Grand Unification of Quantum Algorithms](https://arxiv.org/pdf/2105.02859)”, PRX Quantum 2, 040203, 2021\n",
    "- [3] Dong Y, Meng X, Whaley K, Lin L, “[Efficient phase-factor evaluation in quantum signal processing](https://arxiv.org/pdf/2002.11649)”, Phys. Rev. A 103, 042419 –, 2021\n",
    "- [4] Chao R, Ding D, Gilyen A, Huang C, Szegedy M, “[Finding Angles for Quantum Signal Processing with Machine Precision](https://arxiv.org/abs/2003.02831)”, arXiv, 2003.02831, 2020\n",
    "- [5] Haah J, “[Product decomposition of periodic functions in quantum signal processing](https://quantum-journal.org/papers/q-2019-10-07-190/)”, Quantum 3, 190, 2019"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "99fe6fb5-a464-4f3f-86b8-8e2db1b759ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time for notebook:  195.83499121665955  seconds\n"
     ]
    }
   ],
   "source": [
    "et = time.time()\n",
    "print(\"Execution time for notebook: \",et-st, \" seconds\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}