近日，巴西圣保罗大学的Guilherme Fiusa与巴西巴拉那联邦大学的Diego Paiva Pires等合作，研究了基于保真度的N量子比特近似量子误差修正的距离界限。相关成果已于2023年3月24日在国际权威学术期刊《物理评论A》上发表。

该研究小组采用基于子保真度和超保真度的两种距离度量作为约束误差逼近的方法，这可以降低计算成本。研究人员将缺乏精确纠错建模为等效于单个退相位通道的作用，分别在理论和数值上评估所提出的基于保真度的距离，同时得出了一般N量子比特量子态的闭合形式表达式。他们还通过两个典型的例子，N量子比特混合GHZ态和N量子比特混合W态，说明了他们的界限。

据悉，Eastin-Knill定理是量子纠错理论的核心结果之一，它指出量子代码不能精确纠正错误、具有连续对称性并横向实现一组通用门。为了规避这一结果，人们提出了几种方法，可以放弃精确的纠错或连续的对称性。在这种情况下，通常使用互补的保真度测量量来量化量子态可区分性，并评估纠错近似。尽管具有有用的特性，但评估保真度测量量对于具有大量纠缠量子比特的量子态来说是一项具有挑战性的任务。

附：英文原文

Title: Fidelity-based distance bounds for N-qubit approximate quantum error correction

Author: Guilherme Fiusa, Diogo O. Soares-Pinto, Diego Paiva Pires

Issue&Volume: 2023/03/24

Abstract: The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to circumvent this result, there are several approaches in which one gives up on either exact error correction or continuous symmetries. In this context, it is common to employ a complementary measure of fidelity as a way to quantify quantum state distinguishability and benchmark approximations in error correction. Despite having useful properties, evaluating fidelity measures stands as a challenging task for quantum states with a large number of entangled qubits. With that in mind, we address two distance measures based on the sub- and superfidelities as a way to bound error approximations, which in turn require a lower computational cost. We model the lack of exact error correction to be equivalent to the action of a single dephasing channel, evaluate the proposed fidelity-based distances both analytically and numerically, and obtain a closed-form expression for a general N-qubit quantum state. We illustrate our bounds with two paradigmatic examples, an N-qubit mixed GHZ state and an N-qubit mixed W state.

DOI: 10.1103/PhysRevA.107.032422

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.032422