Variational quantum Gibbs state preparation with a truncated Taylor series
Variational quantum Gibbs state preparation with a truncated Taylor series
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DOI：
10.1103/physrevapplied.16.054035
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Youle Wang;Guangxi Li;Xin Wang
中科院分区：
文献类型：
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作者：
Youle Wang;Guangxi Li;Xin Wang
量子吉布斯态的制备是量子计算的重要组成部分，在量子模拟、量子优化、量子机器学习等领域有着广泛的应用。在本文中，我们提出了量子吉布斯态制备的变分混合量子经典算法。我们首先利用截断泰勒级数来计算自由能，并选择截断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来学习所需的量子吉布斯态。值得注意的是，该算法可以在配备参数化量子电路的近期量子计算机上实现。通过数值实验，我们表明，浅参数化电路，只有一个额外的量子比特可以被训练，以准备伊辛链和自旋链吉布斯态的保真度高于95%。特别是，对于伊辛链模型，我们发现，只有一个参数和一个额外的量子位的简化电路animator可以被训练，以实现99%的保真度在吉布斯态制备在逆温度大于2。
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.