[论文解读] Scalable tensor-network error mitigation for near-term quantum computing

Sergey K. Filippov, Matea Leahy+2 more|arXiv (Cornell University)|Jul 21, 2023

Quantum Computing Algorithms and Architecture被引用 12

一句话总结

TEM 通过在经典后处理阶段仅通过对全局噪声的紧凑张量网络表示取反来进行噪声抑制，相较于 PEC 在减少测量开销的前提下实现准确的观测值估计。它利用信息完备的测量和从中间向外的张量网络收缩。

ABSTRACT

Until fault-tolerance becomes implementable at scale, quantum computing will heavily rely on noise mitigation techniques. While methods such as zero noise extrapolation with probabilistic error amplification (ZNE-PEA) and probabilistic error cancellation (PEC) have been successfully tested on hardware recently, their scalability to larger circuits may be limited. Here, we introduce the tensor-network error mitigation (TEM) algorithm, which acts in post-processing to correct the noise-induced errors in estimations of physical observables. The method consists of the construction of a tensor network representing the inverse of the global noise channel affecting the state of the quantum processor, and the consequent application of the map to informationally complete measurement outcomes obtained from the noisy state. TEM does therefore not require additional quantum operations other than the implementation of informationally complete POVMs, which can be achieved through randomised local measurements. The key advantage of TEM is that the measurement overhead is quadratically smaller than in PEC. We test TEM extensively in numerical simulations in different regimes. We find that TEM can be applied to circuits of twice the depth compared to what is achievable with PEC under realistic conditions with sparse Pauli-Lindblad noise, such as those in [E. van den Berg et al., Nat. Phys. (2023)]. By using Clifford circuits, we explore the capabilities of the method in wider and deeper circuits with lower noise levels. We find that in the case of 100 qubits and depth 100, both PEC and ZNE fail to produce accurate results by using $\sim 10^5$ shots, while TEM succeeds.

研究动机与目标

• 激发并解决在近端量子设备中对可扩展误差抑制的需求。
• 介绍 TEM 作为一种使用逆噪声映射张量网络表示的后处理方法。
• 展示 TEM 相对于 PEC 降低测量开销并在现实噪声下实现更深的电路。
• 描述 TEM 如何利用信息完备测量在无需额外量子操作的情况下估计观测量。

提出的方法

• 构建一个具有紧凑键维度的全局噪声通道 { cal N}^{-1} 的张量网络表示。
• 将 TEM 映射 M 应用于 IC 测量结果，通过张量网络收缩获得去噪估计。
• 使用 MPO/张量的中间向外收缩来有效地计算 bar{O}_{n.m.} 及其不确定性。
• 假设初始化和测量是完美的，并将噪声归因于门。
• 在每次迭代后对演化的 MPO 进行压缩以控制键维度并确保可处理性。

实验结果

研究问题

• RQ1 TEM 能否在后处理步骤中使用紧凑的张量网络表示可靠地逆转带噪声的电路映射？
• RQ2 相对于 PEC 和 ZNE，TEM 在电路深度和噪声水平下如何影响测量开销？
• RQ3 TEM 要优于经典张量网络仿真和其他抑制方法的实际要求（键维度、IC 测量）是什么？
• RQ4 TEM 在深度较高、非局部观测量以及在近端设备典型的串扰/噪声模型下的表现如何？

主要发现

• TEM 通过收缩表示逆噪声映射的中间向外张量网络在后处理阶段实现噪声抑制。
• 在典型 Pauli-Lindblad 噪声下，TEM 的测量开销比 PEC 的二次缩放，且对深度电路具有二次优势。
• 在现实的稀疏 Pauli-Lindblad 噪声下，TEM 可以抑制比 PEC 更深的电路中的误差（如在某些情形下深度翻倍）。
• 在 100 量子比特和深度为 100 的情况下，TEM 能在所引用情景中以 ~10^5 次测量成功，而 PEC 和 ZNE 失败，展示了实际鲁棒性。
• 在典型噪声假设下，TEM 的开销大致为 PEC 开销的平方根，能够实现更深或更高精度的估计。