低深度量子Metropolis算法
Low-Depth Quantum Metropolis Algorithm
摘要：
我们构造了一个简单的量子版本的经典Metropolis算法来制备和观察量子热态。它诱导了一个混合量子热态的量子马尔可夫链和一个混合其可观察测量的经典马尔可夫链，并使低深度量子线路实现。量子相位估计的高斯滤波变体使得热化时间与温度的倒数和偏置误差的对数成比例。这与时间演化的热化时间相匹配，我们的算法表现良好。
英文摘要：
We construct a simple quantum version of the classical Metropolis algorithm to prepare and observe quantum thermal states. It induces both a quantum Markov chain that mixes the quantum thermal state and a classical Markov chain that mixes its observable measurements and enables a low-depth quantum circuit implementation. A Gaussian-filtered variant of quantum phase estimation enables thermalization times proportional to the reciprocal of temperature and the logarithm of biasing error. This matches the thermalization time of imaginary-time evolution, against which our algorithm performs favorably.
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