Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver

• URL: http://arxiv.org/abs/2207.03451v2
• Date: Sat, 13 Aug 2022 10:08:48 GMT
• Title: Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver
• Authors: Alexis Ralli and Tim Weaving and Andrew Tranter and William M. Kirby and Peter J. Love and Peter V. Coveney
• Abstract summary: The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground state energy of a given qubit Hamiltonian. We show that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontexual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared to solving the full Hamiltonian via traditional VQE. We simulate CS-VQE on different tapered molecular Hamiltonians and apply the unitary partitioning measurement reduction strategy to further reduce the number of measurements required to obtain the contextual correction. Our results indicate that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices. We also provide a modification to the CS-VQE algorithm, that previously could cause an exponential increase in Hamiltonian terms, that now at worst will scale quadratically.

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