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.
翻译:量子 Gibs 状态的准备是量子计算的一个基本部分, 并具有各个领域的广泛应用, 包括量子模拟、 量子优化和量子机器学习。 在本文中, 我们提出用于量子 Gibs 状态准备的变式混合量子古典算法 。 我们首先使用短速泰勒序列来评估自由能源, 并选择短速自由能源作为损失函数 。 我们的协议然后训练参数化量子电路来学习想要的量子Gibs 状态 。 值得注意的是, 这种算法可以在配备参数化量子电路的近期量计算机上实施。 通过进行数字实验, 我们显示, 光线化参数化的电路, 只能用另外一种Qubs进行训练, 使Ising 链和旋转链状态的准备达到95%以上。 特别是对于Ising 链模型, 我们发现, 简化的电路由一个参数和另外一种qbit 能够使Gibbbs 状态准备达到99%的准确性, 大于 2 。