论文标题
用纯热阴影预测吉布斯国家期望值
Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
论文作者
论文摘要
量子Gibbs状态的许多属性的制备和计算对于诸如量子半芬特编程和量子玻尔兹曼机等算法至关重要。我们提出了一种量子算法，该算法可以预测一个任意Gibbs状态的$ M $线性函数，仅具有$ \ MATHCAL {O}（\ log {M}）$实验测量值。我们的主要见解是，对于足够大的系统，我们不需要明确准备$ n $ qubit的混合吉布斯状态，但是，我们可以在想象的时间内发展一个随机的$ n $ qubit纯状态。然后，结果是通过构造这些随机纯状态的经典阴影。我们提出了一个量子电路，该电路通过使用量子信号处理来实现该算法，以进行假想时间的演变。我们通过模拟十个SPIN-1/2 XXZ-HEISENBERG模型的电路来验证算法的效率。此外，我们表明该算法可以成功用作训练八个Qubit完全连接的量子Boltzmann机器的子例程。
The preparation and computation of many properties of quantum Gibbs states is essential for algorithms such as quantum semidefinite programming and quantum Boltzmann machines. We propose a quantum algorithm that can predict $M$ linear functions of an arbitrary Gibbs state with only $\mathcal{O}(\log{M})$ experimental measurements. Our main insight is that for sufficiently large systems we do not need to prepare the $n$-qubit mixed Gibbs state explicitly but, instead, we can evolve a random $n$-qubit pure state in imaginary time. The result then follows by constructing classical shadows of these random pure states. We propose a quantum circuit that implements this algorithm by using quantum signal processing for the imaginary time evolution. We numerically verify the efficiency of the algorithm by simulating the circuit for a ten-spin-1/2 XXZ-Heisenberg model. In addition, we show that the algorithm can be successfully employed as a subroutine for training an eight-qubit fully connected quantum Boltzmann machine.
