A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz

TL;DR

This paper introduces a stabilizer-based noncontextual projection ansatz for the Contextual Subspace VQE method, enabling more practical quantum simulations of molecular energies on NISQ devices.

Contribution

It proposes a stabilizer formalism-based noncontextual projection ansatz for CS-VQE, improving its deployability on NISQ quantum computers.

Findings

Validated the noncontextual projection ansatz on quantum simulators

Demonstrated the approach with multiple trial molecules

Enhanced the feasibility of molecular energy estimation on NISQ devices

Abstract

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz - a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator, with results obtained herein for a suite of trial molecules.