通过交换子导出的量子滤波器对量子信道进行纯化与校正
Purification and correction of quantum channels by commutation-derived quantum filters
AI总结：
本文提出基于交换子导出的量子滤波器，结合QEM与QEC思想，通过辅助量子比特显式校正Clifford电路噪声，并实现指数级误差降低，为可扩展量子误差抑制提供新工具。
摘要：
减少误差对于可靠的量子计算至关重要。量子误差缓解（QEM）和量子误差校正（QEC）是完成此任务的两种主要方法，每种方法都面临挑战：QEM存在高采样成本且无法恢复态，而QEC则带来大量的量子比特和门开销。我们结合两者的思想，引入一种信息论设备，称为量子滤波器，它可以纯化或校正量子信道。我们提出了一种显式构造，能够使用2n个辅助量子比特，通过交换子导出的误差检测电路，校正n量子比特Clifford电路中的任意噪声。该方案还可以部分纯化非Clifford门（如T门和CCZ门）中的噪声。与QEC不同，它无需编码输入态即可实现确定性误差降低。在清洁辅助量子比特的假设下，它通过对信道的单次查询克服了QEM中的指数采样开销。我们还提出了一种辅助高效的泡利滤波器，仅使用两个辅助量子比特即可去除嘈杂Clifford电路中几乎所有低权重的错误泡利分量。对于局部去极化噪声，它实现了平均保真度误差的二次方降低。超越现有的QEM方法，我们的方法能够实现系统性的误差校正，因为随着每个额外辅助量子比特的加入，保真度误差可以指数级降低。通过在辅助噪声下的数值模拟，我们确定了量子滤波器优于其他技术的参数区间，展示了其作为量子信息处理中可扩展误差降低工具的有效性。
英文摘要：
Reducing errors is essential for reliable quantum computation. Quantum error mitigation (QEM) and quantum error correction (QEC) are two leading approaches for this task, each with challenges: QEM suffers from high sampling costs and cannot recover states, while QEC incurs large qubit and gate overheads. We combine ideas from both and introduce an information-theoretic device called a quantum filter that can purify or correct quantum channels. We present an explicit construction capable of correcting arbitrary noise in an n-qubit Clifford circuit using 2n ancillary qubits through a commutation-derived error-detection circuit. This scheme can also partially purify noise in non-Clifford gates such as T and CCZ. Unlike QEC, it achieves deterministic error reduction without encoding the input state. Under the assumption of clean ancillas, it overcomes the exponential sampling overhead in QEM using a single query to the channel. We also propose an ancilla-efficient Pauli filter that removes nearly all low-weight erroneous Pauli components in noisy Clifford circuits using only two ancillas. For local depolarizing noise, it achieves a quadratic reduction in average infidelity. Beyond existing QEM methods, our approach enables systematic error correction as the infidelity can be exponentially reduced with each added ancilla. Through numerical simulations under ancilla noise, we identify regimes where quantum filters outperform other techniques, demonstrating their effectiveness as a scalable error-reduction tool for quantum information processing.
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