Error mitigation via error detection using Generalized Superfast Encodings

TL;DR

This paper introduces a quantum error detection scheme using Generalized Superfast Encodings to improve error mitigation in quantum chemistry simulations, especially for the Hubbard model, balancing additional circuitry with error detection benefits.

Contribution

The authors develop a novel error detection method based on Bravyi-Kitaev Superfast encoding that detects one-qubit errors and high-probability complex errors in quantum simulations.

Findings

Detects one-qubit errors in the Hubbard model

High-probability detection of complex errors

Implementation feasible with realistic qubit connectivity

Abstract

We provide a new approach to error mitigation for quantum chemistry simulation that uses a Bravyi-Kitaev Superfast encoding to implement a quantum error detecting code within the fermionic encoding. Our construction has low-weight parity checks as well. We show that for the spinless Hubbard model with nearest-neighbor repulsion terms, one-qubit errors are detectable, and more complicated errors are detectable with high probability. While our error-detection requires additional quantum circuitry, we argue that there is a regime in which the beneficial effect of error-mitigation outweighs the deleterious effects of additional errors due to additional circuitry. We show that our scheme can be implemented under realistic qubit connectivity requirements.