标题： 匹配门电路深度热化 显示英文标题

标题： Matchgate circuits deeply thermalize

摘要： 我们研究通过对随机匹配门（或自由费米子）量子电路的输出进行投影测量所生成的状态集合。 我们严格证明这个“投影集合”表现出深刻的热化：对于大系统尺寸，它收敛到一个在高斯费米子态流形上均匀的普遍集合。 除了证明这些集合的逐矩收敛外，我们还展示了投影集合中任何物理可观测量的完整分布与它的普遍形式在Wasserstein-1距离上接近，我们认为当研究深层热化时，这是一个适当且可高效计算的收敛度量。 使用这个度量，我们还数值发现局部匹配门电路在由量子信息扩散传播设定的时间尺度$t \sim L^2$后深度热化。 我们的工作为实验可访问的协议开辟了新途径，以探测量子统计力学的出现并基准量子模拟器。 显示英文摘要

摘要： We study the ensemble of states generated by performing projective measurements on the output of a random matchgate (or free-fermionic) quantum circuit. We rigorously show that this `projected ensemble' exhibits deep thermalization: For large system sizes, it converges towards a universal ensemble that is uniform over the manifold of Gaussian fermionic states. As well as proving moment-wise convergence of these ensembles, we demonstrate that the full distribution of any physical observable in the projected ensemble is close to its universal form in Wasserstein-1 distance, which we argue is an appropriate and efficiently computable measure of convergence when studying deep thermalization. Using this metric, we also numerically find that local matchgate circuits deeply thermalize after a timescale $t \sim L^2$ set by the diffusive spreading of quantum information. Our work opens up new avenues to experimentally accessible protocols to probe the emergence of quantum statistical mechanics and benchmark quantum simulators.