Probing finite-temperature observables in quantum simulators with short-time dynamics
Probing finite-temperature observables in quantum simulators with short-time dynamics
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利用短时动力学探测量子模拟器中的有限温度可观测量
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
M. Knap
中科院分区：
文献类型：
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作者：
A. Schuckert;A. Bohrdt;E. Crane;M. Knap
在量子模拟器中制备低温态具有挑战性，因为它们与环境几乎完全隔离。在这里，我们展示了如何用一种算法获得有限温度的可观测值，该算法由初始状态的经典重要性采样和用量子模拟器测量Loscherton回声组成。我们将该方法用作量子启发的经典算法，并用矩阵积状态模拟该协议，以分析对量子模拟器的要求。通过这种方式，我们证明了长程横场伊辛模型中的有限温度相变可以在捕获离子量子模拟器中表征。我们提出了一个具体的测量协议的Loschirton回波，并讨论了测量噪声，移相，以及状态准备和测量误差的影响。我们认为，该算法是强大的，对现实条件下的这些缺陷。该算法可以很容易地应用于各种量子模拟平台上的低温特性研究。用Ramsey实验求出G_∞（t）的相位。Loschlord回波只需要测量到短时间Jt = O（1）[14]。c）一维长程横场伊辛模型表现出从铁磁体到顺磁网络的有限温度相变，α ≤ 2（且横场g <gc;这里g = J）。在α = 2时，跃迁属于Berenzinskiii-Kosterlitz-无核普适类。在本文中，我们关注α = 1。5（灰色虚线）。
Preparing low temperature states in quantum simulators is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm that consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions. The algorithm can be readily applied to study low-temperature properties in various quantum simulation platforms. for ob-taining the phase of G ψ ( t ) with Ramsey experiments. The Loschmidt echo only needs to be measured to short-times Jt = O (1) [14]. c) The one-dimensional long-range transverse field Ising model exhibits a finite temperature phase transition from a ferromagnet to a paramag-net for α ≤ 2 (and transverse field g < g c ; here g = J ). At α = 2, the transition is in the Berenzinskii-Kosterlitz-Thouless universality class. In this work, we focus on α = 1 . 5 (grey dashed line).
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