论文标题
带有截短的泰勒系列的变分量子吉布斯状态制备
Variational quantum Gibbs state preparation with a truncated Taylor series
论文作者
论文摘要
量子吉布斯状态的制备是量子计算的重要组成部分，并且在各个领域具有广泛的应用，包括量子模拟，量子优化和量子机学习。在本文中，我们提出了用于量子吉布斯状态制备的变分杂种量子古典算法。我们首先使用截短的泰勒系列来评估自由能，然后选择截短的自由能作为损失函数。然后，我们的协议训练参数化的量子电路以学习所需的量子吉布斯状态。值得注意的是，该算法可以在配备有参数化量子电路的近期量子计算机上实现。通过执行数值实验，我们表明只有一个额外的量子量的浅参数化电路可以训练以准备Ising链和自旋链吉布斯状态，其保真度高于95％。特别是，对于Ising链模型，我们发现只有一个参数和一个额外量子的简化电路ANSATZ可以接受训练，以实现Gibbs状态制备99％的忠诚度，在大于2的反向温度下。
The preparation of quantum Gibbs state is an essential part of quantum computation and has wide-ranging applications in various areas, including quantum simulation, quantum optimization, and quantum machine learning. In this paper, we propose variational hybrid quantum-classical algorithms for quantum Gibbs state preparation. We first utilize a truncated Taylor series to evaluate the free energy and choose the truncated free energy as the loss function. Our protocol then trains the parameterized quantum circuits to learn the desired quantum Gibbs state. Notably, this algorithm can be implemented on near-term quantum computers equipped with parameterized quantum circuits. By performing numerical experiments, we show that shallow parameterized circuits with only one additional qubit can be trained to prepare the Ising chain and spin chain Gibbs states with a fidelity higher than 95%. In particular, for the Ising chain model, we find that a simplified circuit ansatz with only one parameter and one additional qubit can be trained to realize a 99% fidelity in Gibbs state preparation at inverse temperatures larger than 2.
