Logical Error Rates for a [[4,2,2]]-Encoded Variational Quantum Eigensolver Ansatz

TL;DR

This paper develops a framework to evaluate and improve the accuracy of NISQ quantum devices for chemistry applications using error mitigation and quantum error detection, demonstrated through simulating molecular hydrogen with the VQE algorithm.

Contribution

It introduces a method combining error mitigation and quantum error detection to enhance the accuracy of VQE simulations on noisy quantum hardware.

Findings

Encoded VQE yields more accurate energy estimates within chemical accuracy.

Error mitigation improves logical error rates and state fidelity.

Simulations show current quantum devices can produce useful chemical results.

Abstract

Quantum computing offers a potential for algorithmic speedups for applications, such as large-scale simulations in chemistry and physics. However, these speedups must yield results that are sufficiently accurate to predict realistic outcomes of experiments precisely. Delivering on the promise of high accuracy and precision requires methods to evaluate the computational accuracy of the quantum computing devices. We develop a framework to estimate the computational accuracy of near-term noisy, intermediate scale quantum (NISQ) computing devices using a quantum chemistry application. Application benchmarks that run on NISQ devices require techniques for mitigating errors to improve accuracy and precision. We use device agnostic error-mitigation schemes, quantum error detection and readout error detection, with post-selection to mitigate the dominant sources of noise. We evaluate the framework by simulating the ground state of molecular hydrogen with the variational quantum eigensolver (VQE) algorithm, estimating the energy and calculating the precision of the estimate using numerical simulations with realistic noise models. We first quantify the improvement in the logical error rate and state fidelity of the VQE application when encoded with the [[4,2,2]] quantum error detection code. When additionally encoded with readout error detection, we show that compared to the unencoded simulation, the encoded simulation yields a more accurate estimate by more than 1 mHa (0.027 eV) with comparable precision and higher state fidelity. Additionally, unlike the best estimate from the unencoded simulations, the results from the encoded simulation fall within the chemical accuracy threshold of 1.6 mHa of the exact energy. The estimated accuracy and precision indicate that current quantum computers can achieve error rates that yield useful outcomes for chemical applications.