Symmer

A Python package for reducing the quantum resource requirement of your problems, making them more NISQ-friendly!

Installation

To install this package either run:

pip install symmer

for the latest stable version OR from the root of the project run:

pip install .

Basic usage

For basic usage see readthedocs and the following notebooks

Included in symmer:

Qubit reduction techniques such as tapering and Contextual-Subspace VQE are effected by the underlying stabilizer subspace projection mechanism; such methods may be differentiated by the approach taken to selecting the stabilizers one wishes to project over.

.operators contains the following classes (in resolution order):

• PauliwordOp for representing general Pauli operators.
• QuantumState for representing quantum statevectors.
• IndependentOp represents algebraically independent sets of Pauli operators for stabilizer manipulation/projections.
• AnticommutingOp represents sets of anticommuting Pauli operators for the purposes of Unitary Partitioning and Linear Combination of Unitaries as in this paper.
• NoncontextualOp represents noncontextual Hamiltonians (defined here) that may be mapped onto a hidden-variable model and solved classically; various solvers are supplied in NoncontextualSolver.

.projection contains stabilizer subspace projection classes (in resolution order):

• S3_projection for rotating a StabilizerOp onto some basis of single-qubit Pauli operators via Clifford operations and projecting into the corresponding stabilizer subspace.
• QubitTapering
  • Performs the Qubit Tapering technique, exploiting $\mathbb{Z}_2$ symmetries to reduce the number of qubits in the input Hamiltonian while preserving the ground state energy exactly.
  • The stablizers are chosen to be an independent generating set of a Hamiltonian symmetry.
• ContextualSubspace
  • Implements the Contextual Subspace methodology, allowing one to specify precisely how many qubits they would like in the output Hamiltonian. Despite this process incurring some systematic error, it is possible to retain sufficient information to permit high precision simulations at a significant reduction in quantum resource. This is the updated approach to ContextualSubspaceVQE.
  • Here, the stabilizers are taken to be an independent generating set of a sub-Hamiltonian symmetry (defined by a noncontextual subset of terms) with an additional contribution encapsulating the remaining anticommuting terms therein.
• QubitSubspaceManager
  • Automates these qubit subspace methods for ease-of-use.

Performance

Why should you use Symmer? It has been designed for high efficiency when manipulating large Pauli operators -- addition, multiplication, Clifford/general rotations, commutativity/contextuality checks, symmetry generation, basis reconstruction and subspace projections have all been reformulated in the symplectic representation and implemented carefully to avoid unnecessary operations and redundancy. It also has a QASM simulator for evaluating expectation values, which is efficient when restricted to Clifford operations.

What can Symmer do on a standard laptop in just one second?

• Evaluate the expectation value of a 1,000-qubit Clifford circuit with a depth of 2,000.
• Perform a non-Clifford unitary rotation of a 1,000-qubit operator with 100,000 Pauli terms.
• Square a 1,000-qubit operator with 500 Pauli terms, involving a cleanup procedure over 250,000 cross terms.
• Multiply two 100,000,000-qubit Pauli terms together.

All this allows us to approach significantly larger systems than was previously possible, including those exceeding the realm of classical tractibility.

How to cite

When you use in a publication or other work, please cite as:

Tim Weaving, Alexis Ralli, Peter J. Love, Sauro Succi, and Peter V. Coveney. Contextual Subspace Variational Quantum Eigensolver Calculation of the Dissociation Curve of Molecular Nitrogen on a Superconducting Quantum Computer. arXiv preprint arXiv:2312.04392 (2023).

Alexis Ralli, Tim Weaving, Andrew Tranter, William M. Kirby, Peter J. Love, and Peter V. Coveney. Unitary partitioning and the contextual subspace variational quantum eigensolver. Phys. Rev. Research 5, 013095 (2023).

Tim Weaving, Alexis Ralli, William M. Kirby, Andrew Tranter, Peter J. Love, and Peter V. Coveney. A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz. J. Chem. Theory Comput. 2023, 19, 3, 808–821 (2023).

William M. Kirby, Andrew Tranter, and Peter J. Love, Contextual Subspace Variational Quantum Eigensolver, Quantum 5, 456 (2021).