近日，美国开源量子计算基金的Vincent Russo及其研究团队取得一项新进展。经过不懈努力，他们通过分层理查德森外推实现量子误差缓解。相关研究成果已于2024年12月17日在国际知名学术期刊《物理评论A》上发表。

该研究团队通过引入逐层理查德森外推法（LRE）来推广这一方法。LRE是一种误差缓解协议，通过放大不同单独层（或电路的更大块）的噪声，并将相关的期望值进行线性组合，以估计无噪声极限。线性组合的系数是通过多元拉格朗日插值理论解析获得的。

LRE利用了逐层酉折叠的灵活配置空间，通过将量子电路的每一层的噪声水平视为独立变量，实现了更细致的误差缓解。研究人员提供了数值模拟，展示了LRE相比传统（单变量）理查德森外推法表现出优越性能的场景。

据悉，在含噪量子计算机中，一种广泛使用的减少误差的方法是理查德森外推法。该技术通过一个参数来捕捉噪声对量子期望值估计的总体影响，该参数在按比例放大到更大值后，最终被外推到无噪声极限。

附：英文原文

Title: Quantum error mitigation by layerwise Richardson extrapolation

Author: Vincent Russo, Andrea Mari

Issue&Volume: 2024/12/17

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 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.

DOI: 10.1103/PhysRevA.110.062420

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062420