将泡利校验推广到基于量子位元的量子错误检测与缓解
Generalizing Pauli Checks for Qudit-based Quantum Error Detection and Mitigation
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- Grambling State University（格兰布林州立大学）
- Northwestern University（西北大学）
- Princeton University（普林斯顿大学）
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中文总结 AI 辅助
本文将仅适用于量子比特空间的泡利校验夹心法推广到任意维度量子位元空间，提出基于海森堡-外尔算子集的量子位元校验方法，经验证可检测任意维度错误，实现高于97.5%的错误缓解保真度。
中文摘要 AI 辅助
泡利校验夹心法（Pauli Check Sandwiching, PCS）是一种量子错误检测（QED）技术，它通过利用一对受控泡利算子（即校验）来保护量子电路，检测与校验反对易的错误。此外，PCS还可基于泡利校验症候群值的后选择用于量子错误缓解（QEM）。目前，PCS仅应用于量子比特空间。在本文中，我们提出一种通用方法，将基于PCS的QED和QEM应用于希尔伯特空间中任意维度的量子信息。每对扩展后的校验由海森堡-外尔算子集中的一系列门构成，该算子集将泡利算子扩展到量子位元（qudit）空间。这些量子位元校验至少使用一个辅助量子位元，以检测与该校验所选幺正算子不对易的量子位元错误。我们证明，所提出的量子位元QED方法可检测任意维度的错误。更具体地说，我们证明任意海森堡-外尔错误都会确定性地映射到唯一的辅助量子位元读数，且在无噪声校验极限下，对|0⟩读数进行后选择可保证单位保真度。我们在维度d=2到d=9的范围内对这些发现进行了数值验证，在现实的去极化错误率下，实现了高于97.5%的错误缓解保真度。
英文摘要
Pauli Check Sandwiching (PCS) is a quantum error detection (QED) technique that protects a quantum circuit by utilizing a pair of controlled Pauli operators, or checks, and detecting errors that anti-commute with the checks. Further, PCS can be used for quantum error mitigation (QEM) via post-selection based on the Pauli check syndrome values. Currently, PCS is leveraged in the qubit space. In this paper, we introduce a generalized approach for applying PCS-based QED and QEM to quantum information of arbitrary dimension in the Hilbert space. Each pair of these extended checks consists of a sequence of gates in the Heisenberg-Weyl operator set that extend Pauli operators into the qudit space. These qudit checks use at least one ancilla qudit to detect qudit errors that do not commute with the unitary selected for the check. We show that our proposed methods for qudit QED can detect errors of arbitrary dimensions. More specifically, we prove that an arbitrary Heisenberg-Weyl error maps deterministically to a unique ancilla readout, and further, post-selecting on the $|0 \rangle$ readout guarantees unit fidelity in the noiseless check limit. We validate these findings numerically across dimensions $d=2$ through $d=9$, achieving error-mitigated fidelities above $97.5\% $ under realistic depolarizing error rates.
