Error mitigation and quantum-assisted simulation in the error corrected regime

TL;DR

This paper introduces the Quantum-assisted Robustness of Magic (QRoM), a measure of how non-ideal magic states can be used to enhance quantum simulation and error mitigation in fault-tolerant quantum computing.

Contribution

It develops a general framework for quantifying the value of non-ideal magic resources in quantum computation, extending error mitigation techniques to logical qubits.

Findings

QRoM quantifies the overhead of simulating ideal magic with noisy resources.

Extension of error mitigation techniques to logical qubits.

Protocols that interpolate between classical simulation and ideal quantum computation.

Abstract

A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general framework to discuss the value of the available, non-ideal magic resources, relative to those ideally required. We single out a quantity, the Quantum-assisted Robustness of Magic (QRoM), which measures the overhead of simulating the ideal resource with the non-ideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally developed for Noisy Intermediate Scale Quantum (NISQ) devices, to the case where qubits are logically encoded. The QRoM shows how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit and enables the construction of explicit protocols, interpolating between classical simulation and an ideal quantum computer.