Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver

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 noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with 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; the CS-VQE algorithm previously could cause an exponential increase in Hamiltonian terms, but with this modification now at worst will scale quadratically.

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Cited by in corpus (6)

• A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz
• Contextual Subspace Variational Quantum Eigensolver Calculation of the Dissociation Curve of Molecular Nitrogen on a Superconducting Quantum Computer
• Benchmarking Noisy Intermediate Scale Quantum Error Mitigation Strategies for Ground State Preparation of the HCl Molecule
• Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques
• Ladder Operator Block-Encoding
• Noncontextual Pauli Hamiltonians