Contextual Subspace Variational Quantum Eigensolver

TL;DR

The paper introduces CS-VQE, a hybrid quantum-classical algorithm that efficiently approximates ground state energies by combining noncontextual classical approximations with quantum variational corrections, reducing qubit and measurement requirements.

Contribution

It presents a novel hybrid algorithm that reduces quantum resource needs for eigenvalue problems by combining classical and quantum computations in a contextual framework.

Findings

CS-VQE reduces qubit requirements by over 50% for chemical accuracy.

The number of terms for the correction can be reduced by over ten times.

Simulation results show promise for noisy intermediate-scale quantum devices.

Abstract

We describe the contextual subspace variational quantum eigensolver (CS-VQE), a hybrid quantum-classical algorithm for approximating the ground state energy of a Hamiltonian. The approximation to the ground state energy is obtained as the sum of two contributions. The first contribution comes from a noncontextual approximation to the Hamiltonian, and is computed classically. The second contribution is obtained by using the variational quantum eigensolver (VQE) technique to compute a contextual correction on a quantum processor. In general the VQE computation of the contextual correction uses fewer qubits and measurements than the VQE computation of the original problem. Varying the number of qubits used for the contextual correction adjusts the quality of the approximation. We simulate CS-VQE on tapered Hamiltonians for small molecules, and find that the number of qubits required to reach chemical accuracy can be reduced by more than a factor of two. The number of terms required to compute the contextual correction can be reduced by more than a factor of ten, without the use of other measurement reduction schemes. This indicates that CS-VQE is a promising approach for eigenvalue computations on noisy intermediate-scale quantum devices.