Foldager Jonathan, Pesah Arthur, Hansen Lars Kai
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800, Kongens Lyngby, Denmark.
Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK.
Sci Rep. 2022 Mar 9;12(1):3862. doi: 10.1038/s41598-022-07296-z.
Preparing thermal states on a quantum computer can have a variety of applications, from simulating many-body quantum systems to training machine learning models. Variational circuits have been proposed for this task on near-term quantum computers, but several challenges remain, such as finding a scalable cost-function, avoiding the need of purification, and mitigating noise effects. We propose a new algorithm for thermal state preparation that tackles those three challenges by exploiting the noise of quantum circuits. We consider a variational architecture containing a depolarizing channel after each unitary layer, with the ability to directly control the level of noise. We derive a closed-form approximation for the free-energy of such circuit and use it as a cost function for our variational algorithm. By evaluating our method on a variety of Hamiltonians and system sizes, we find several systems for which the thermal state can be approximated with a high fidelity. However, we also show that the ability for our algorithm to learn the thermal state strongly depends on the temperature: while a high fidelity can be obtained for high and low temperatures, we identify a specific range for which the problem becomes more challenging. We hope that this first study on noise-assisted thermal state preparation will inspire future research on exploiting noise in variational algorithms.
在量子计算机上制备热态具有多种应用，从模拟多体量子系统到训练机器学习模型。对于近期量子计算机上的这项任务，已经提出了变分电路，但仍存在一些挑战，比如找到一个可扩展的代价函数、避免纯化的需求以及减轻噪声影响。我们提出了一种用于热态制备的新算法，该算法通过利用量子电路的噪声来应对这三个挑战。我们考虑一种变分架构，在每个酉层之后包含一个去极化信道，能够直接控制噪声水平。我们推导出这种电路自由能的闭式近似，并将其用作我们变分算法的代价函数。通过在各种哈密顿量和系统规模上评估我们的方法，我们找到了几个可以高保真近似热态的系统。然而，我们也表明我们的算法学习热态的能力强烈依赖于温度：虽然在高温和低温下可以获得高保真度，但我们确定了一个特定范围，在这个范围内问题变得更具挑战性。我们希望这项关于噪声辅助热态制备的首次研究将激发未来关于在变分算法中利用噪声的研究。
