Quantum error mitigation by layerwise Richardson extrapolation

TL;DR

Layerwise Richardson extrapolation (LRE) is a novel error mitigation method for quantum computing that individually amplifies and combines noise effects across circuit layers to better estimate zero-noise results.

Contribution

The paper introduces LRE, a generalized Richardson extrapolation technique that independently amplifies noise in each circuit layer and analytically determines optimal combination coefficients.

Findings

LRE outperforms traditional Richardson extrapolation in numerical simulations.

LRE effectively treats each circuit layer's noise as an independent variable.

Analytical coefficients derived from multivariate Lagrange interpolation enhance error mitigation.

Abstract

A widely used method for mitigating errors in noisy quantum computers is Richardson extrapolation, a technique in which the overall effect of noise on the estimation of quantum expectation values is captured by a single parameter that, after being scaled to larger values, is eventually extrapolated to the zero-noise limit. We generalize this approach by introducing \emph{layerwise Richardson extrapolation (LRE)}, an error mitigation protocol in which the noise of different individual layers (or larger chunks of the circuit) is amplified and the associated expectation values are linearly combined to estimate the zero-noise limit. The coefficients of the linear combination are analytically obtained from the theory of multivariate Lagrange interpolation. LRE leverages the flexible configurational space of layerwise unitary folding, allowing for a more nuanced mitigation of errors by treating the noise level of each layer of the quantum circuit as an independent variable. We provide numerical simulations demonstrating scenarios where LRE achieves superior performance compared to traditional (single-variable) Richardson extrapolation.