[论文解读] Thermalization and Criticality on an Analog-Digital Quantum Simulator

Trond I. Andersen, Nikita Astrakhantsev+225 more|arXiv (Cornell University)|May 27, 2024

Quantum Computing Algorithms and Architecture被引用 4

一句话总结

本研究通过在二维XY自旋模型的量子临界点处设计跃迁，利用69量子比特的超导模拟-数字量子模拟器，实现了热化与临界动力学。该平台实现了高保真度态制备、通用量子门操作以及关联和能量输运的实时监测，揭示了由于量子-经典共聚导致的偏离Kibble-Zurek标度规律，通过受控能量注入验证了本征态热化假说（ETH）。

ABSTRACT

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

研究动机与目标

• 研究强关联量子系统在超越经典模拟极限下的热化动力学。
• 通过在临界点附近的淬火动力学，探究量子与经典共聚之间的相互作用。
• 通过向本征谱特定区域注入可调能量密度，检验本征态热化假说（ETH）。
• 利用数字制备的纠缠二聚态，成像热化过程中的能量与涡旋输运。
• 建立可扩展的模拟-数字量子平台，以高控制精度与测量保真度研究非平衡量子现象。

提出的方法

• 采用69量子比特超导处理器，结合通用量子门与高保真度模拟演化实现时间演化。
• 从反铁磁态制备初始态，并通过2D XY模型的临界点进行系统跃迁。
• 应用多种测量技术，表征最终态的关联、涡旋数与子系统间能量不平衡。
• 利用矩阵乘积态（MPS）模拟结合时间演化变分原理（TDVP），对Kibble-Zurek与扩散动力学进行基准测试，最大张量维度χ=1024。
• 通过定制初始态实现能量注入，以探测特定本征谱区域的ETH行为。
• 采用交叉熵基准测试与保真度估计（线性XEB与重归一化估计器）验证实验保真度。

Figure 1: Analog-digital simulation with high-precision calibration. a, Our platform combines analog evolution with digital gates for extensive state preparation and characterization. b, Schematic of new scalable analog calibration scheme. Swap (blue) and single-photon (red) spectroscopy is used to

实验结果

研究问题

• RQ1 在通过量子临界点的淬火后，量子与经典共聚机制如何在热化过程中竞争？
• RQ2 在存在量子涨落与有限尺寸效应的情况下，Kibble-Zurek标度预测在多大程度上仍然成立？
• RQ3 能否通过调节特定本征谱区域的能量密度，实验检验本征态热化假说（ETH）？
• RQ4 在二维量子自旋磁体中，能量与拓扑缺陷（涡旋）输运在热化过程中如何演化？
• RQ5 量子纠缠增长在多大程度上限制了热化动力学的经典模拟？

主要发现

• 系统表现出经典Kosterlitz-Thouless相变的特征，证实了热化态中拓扑序的出现。
• 观测到偏离Kibble-Zurek标度规律的现象，归因于关联畴的量子与经典共聚相互作用。
• 能量注入实验证实了在本征谱特定区域中本征态热化假说（ETH）的有效性，实测与预测的热化行为高度一致。
• 在热化过程中直接成像了能量与涡旋输运，揭示了具有可测量弛豫时间常数的扩散样行为。
• 矩阵乘积态模拟能准确再现短时与中时跃迁过程的实验数据，但因纠缠增长超过χ=1024而无法捕捉长时间能量扩散行为。
• 通过交叉熵基准测试与保真度估计验证的实验保真度超过经典模拟极限，证实了该平台的可扩展性与控制能力。

Figure 2: Fast thermalization dynamics and beyond-classical capabilities in the high-temperature regime. a, Schematic representation of the experiment: $N_{\mathrm{q}}$ qubits are initialized in a half-filling state, evolved under a Hamiltonian $H_{\text{s}}$ over time $t$ with $4$ instances of diso