[论文解读] The Error Reconstruction and Compiled Calibration of Quantum Computing Cycles

Arnaud Carignan-Dugas, Dar Dahlen+7 more|arXiv (Cornell University)|Mar 30, 2023

Quantum Computing Algorithms and Architecture被引用 6

一句话总结

本文提出循环误差重构（CER）和随机校准（SC）两种可扩展协议，用于表征和抑制量子计算循环中的误差。CER 通过随机编译和循环基准测试，实现对有效循环中边缘误差概率的乘法精度估计；SC 则利用基于编译的相位校正来降低误差——在 IBM-Q 5 量子比特设备上，使电路性能提升最高达 5 倍。

ABSTRACT

Quantum computers are inhibited by physical errors that occur during computation. For this reason, the development of increasingly sophisticated error characterization and error suppression techniques is central to the progress of quantum computing. Error distributions are considerably influenced by the precise gate scheduling across the entire quantum processing unit. To account for this holistic feature, we may ascribe each error profile to a (clock) cycle, which is a scheduled list of instructions over an arbitrarily large fraction of the chip. A celebrated technique known as randomized compiling introduces some randomness within cycles' instructions, which yields effective cycles with simpler, stochastic error profiles. In the present work, we leverage the structure of cycle benchmarking (CB) circuits as well as known Pauli channel estimation techniques to derive a method, which we refer to as cycle error reconstruction (CER), to estimate with multiplicative precision the marginal error distribution associated with any effective cycle of interest. The CER protocol is designed to scale for an arbitrarily large number of qubits. Furthermore, we develop a fast compilation-based calibration method, referred to as stochastic calibration (SC), to identify and suppress local coherent error sources occurring in any effective cycle of interest. We performed both protocols on IBM-Q 5-qubit devices. Via our calibration scheme, we obtained up to a 5-fold improvement of the circuit performance.

研究动机与目标

• 开发一种可扩展的方法，用于估计考虑门调度与硬件特定噪声的量子计算循环中的误差分布。
• 解决多量子比特量子操作中相干的、与门相关的误差挑战，特别是串扰引起的 Z-旋转。
• 实现高效、基于编译的校准，以在无需完整误差模型重建的情况下提升电路保真度。
• 提供一种实用且与硬件无关的误差缓解框架，可扩展至大规模量子系统。
• 将误差诊断与抑制整合为适用于近期量子设备的统一工作流程。

提出的方法

• CER 利用随机编译将循环转化为具有近似随机误差分布的有效编译循环，从而简化误差估计。
• 使用循环基准测试（CB）电路通过泡利通道估计提取误差率，实现对边缘误差概率的乘法精度估计。
• 该协议通过聚焦于循环级别的误差分布而非单个门，可扩展至任意数量的量子比特。
• 随机校准（SC）采用参数化编译方案，通过应用虚拟 Z-旋转作为校正，最小化由循环基准测试数据导出的二次目标函数。
• SC 通过对旁观量子比特上的可调相位参数进行优化，以抑制相干误差，特别是由串扰引起的误差。
• 该方法结合加权最小二乘拟合误差数据至二次曲线，以高精度识别最优校准角度。

Figure 1: CB-structured circuits consist of repeated dressed cycles wrapped between state preparation and measurement circuits. The randomization of the easy cycles tailors the dressed cycle into an effective dressed cycle with a stochastic error profile. In this work, we introduce two CB-structured

实验结果

研究问题

• RQ1 能否仅通过循环基准测试与随机编译，以乘法精度估计量子计算循环的误差分布？
• RQ2 如何高效抑制多量子比特循环中的相干误差，特别是串扰引起的 Z-旋转？
• RQ3 编译后的相位校正能在多大程度上提升真实量子硬件中电路的保真度？
• RQ4 误差重构与校准协议是否可在不产生禁止性开销的前提下扩展至大规模多量子比特系统？
• RQ5 在门依赖性噪声存在的情况下，有效循环的误差特性与单个门的误差特性有何不同？

主要发现

• CER 在 IBM-Q 5 量子比特设备上成功实现了对多种循环的边缘误差概率的乘法精度估计，实现了详细的误差表征。
• 随机校准在 ibmq_burlington 芯片上将误差概率降低了最高达 5 倍，显著提升了电路性能。
• 校准参数被确定为 θ* = (-4.8(2)°, -15.1(4)°, -20.8(1)°)，对应于量子比特 {0, 2, 4}，表明对串扰引起的 Z-旋转实现了有效抑制。
• 该协议展现出良好的可扩展性与鲁棒性，在多个循环与量子比特配置中均观察到误差降低。
• 循环误差重构表明，即使在门依赖性噪声下，经随机编译后的有效循环也表现出主要的随机误差行为。
• CER 与 SC 集成至 True-Q 软件堆栈后，可实现面向量子硬件验证与优化的实际部署。

Figure 3: Circuit representations expressed in terms of cycles. Notice that the time flows from the right to the left to accommodate the matrix notation below each cycle. a) An application circuit can always be expressed as an alternating sequence of easy and hard cycles or, equivalently, as a seque