[论文解读] Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer

R. Shen, Tianqi Chen+2 more|arXiv (Cornell University)|Nov 16, 2023

Quantum, superfluid, helium dynamics被引用 4

一句话总结

本研究首次在数字量子处理器上利用含噪声的含噪中等规模量子（NISQ）设备，实验观测到非厄米皮肤效应（NHSE）及其多体表现形式——费米皮肤效应。通过在辅助量子比特上采用后选择实现非幺正时间演化，并结合变分量子算法优化线路，作者展示了费米子系统中的非对称空间局域化与费米皮肤分布，标志着在当前量子硬件上模拟非厄米多体物理的重要里程碑。

ABSTRACT

Non-Hermitian physics has attracted considerable attention in recent years, particularly the non-Hermitian skin effect (NHSE) for its extreme sensitivity and non-locality. While the NHSE has been physically observed in various classical metamaterials and even ultracold atomic arrays, its highly-nontrivial implications in many-body dynamics have never been experimentally investigated. In this work, we report the first observation of the NHSE on a universal quantum processor, as well as its characteristic but elusive Fermi skin from many-fermion statistics. To implement NHSE dynamics on a quantum computer, the effective time-evolution circuit not only needs to be non-reciprocal and non-unitary but must also be scaled up to a sufficient number of lattice qubits to achieve spatial non-locality. We show how such a non-unitary operation can be systematically realized by post-selecting multiple ancilla qubits, as demonstrated through two paradigmatic non-reciprocal models on a noisy IBM quantum processor, with clear signatures of asymmetric spatial propagation and many-body Fermi skin accumulation. To minimize errors from inevitable device noise, time evolution is performed using a trainable, optimized quantum circuit produced with variational quantum algorithms. Our study represents a critical milestone in the quantum simulation of non-Hermitian lattice phenomena on present-day quantum computers and can be readily generalized to more sophisticated many-body models with the remarkable programmability of quantum computers.

研究动机与目标

• 在通用量子处理器上展示多体费米子系统中的非厄米皮肤效应（NHSE）。
• 观测由泡利不相容统计在NHSE动力学下产生的费米皮肤——一种实空间费米表面类似分布。
• 通过可扩展、误差缓解的量子线路，克服在幺正量子硬件上模拟非幺正动力学的挑战。
• 验证在当前含噪声量子处理器上模拟复杂非厄米多体现象的可行性。

提出的方法

• 通过在辅助量子比特上进行后选择，实现非幺正时间演化，以模拟非互易、非幺正的哈密顿量。
• 使用可训练的变分量子线路优化时间演化门，最小化器件噪声带来的误差。
• 通过具有可调非厄米跃迁的数字量子线路设计有效哈密顿量，其模型基于哈纳诺-内森与SSH模型。
• 通过加权本征态重叠，从短时间演化中提取费米皮肤分布，实现在早期观测费米-狄拉克类密度分布。
• 使用费米皮肤猜想 $ n_{\text{FS}}(x) = \left(1 + e^{\beta_{\text{eff}}(x - N)}\right)^{-1} $ 分析空间密度分布，其中在强NHSE极限下 $ \beta_{\text{eff}} \approx 4\kappa $。
• 数值模拟证实，初始态与本征态的重叠决定了早期动力学行为，使得在仅5–10个Trotter步长内即可观测到费米皮肤。

Figure 1: The non-Hermitian skin effect (NHSE) and its many-fermion counterpart. (a) At the single-particle level, the NHSE from asymmetric lattice hoppings amplifies all states towards one direction, resulting in boundary “skin” states with exponential localization lengths inversely proportional to

实验结果

研究问题

• RQ1 非厄米皮肤效应是否可在当前量子处理器上的多体费米子系统中实现？
• RQ2 NHSE与泡利不相容原理的相互作用是否会在实空中产生可观测的费米皮肤分布？
• RQ3 能否通过后选择与变分优化，在幺正量子计算机上有效模拟非幺正动力学？
• RQ4 费米皮肤分布最早可在时间演化中何时出现？何种初始态最有利于其观测？
• RQ5 非厄米参数 $ \kappa $ 与费米皮肤的有效反温度 $ \beta_{\text{eff}} $ 之间是否存在定量关系？

主要发现

• 通过在IBM量子处理器上采用后选择的非幺正演化，成功观测到非厄米皮肤效应，表现出明显的非对称空间局域化。
• 费米皮肤分布最早在5–10个Trotter步长内即已出现，表明多体非厄米效应可在极短时间内被探测。
• 费米皮肤的有效反温度 $ \beta_{\text{eff}} $ 通过实验经验发现其近似满足 $ \beta_{\text{eff}} \approx 4\kappa $，与理论预测一致。
• 与边缘局域本征态重叠较高的初始态（如半局域态）比均匀态或反铁磁序态更符合费米-狄拉克分布。
• 变分量子算法的使用显著降低了噪声引起的误差，实现了对非幺正动力学的可靠提取。
• 本研究建立了一个可扩展的框架，用于在NISQ设备上模拟非厄米多体物理，为未来研究非幺正量子临界性与拓扑相铺平道路。

Figure 2: Overview of the ancilla-based framework. (a) and (b) show the process of implementing non-unitary dynamics by our local and global ancilla-based circuits respectively. For each Trotter step, the non-unitary process $U_{\rm non-unitary}$ can be realized by coupling N physical qubits (red qu