We present a variational quantum thermalizer (VQT), called quantum-VQT (qVQT), which extends the variational quantum eigensolver to finite temperatures. The qVQT makes use of an intermediate measurement between two variational circuits to encode a density matrix on a quantum device. A classical optimization provides the thermal state and, simultaneously, all associated excited states of a quantum mechanical system. We demonstrate the capabilities of the qVQT for two different spin systems. First, we analyze the performance of qVQT as a function of the circuit depth and the temperature for a one-dimensional Heisenberg chain. Second, we use the excited states to map the complete, temperature dependent phase diagram of a two-dimensional J₁–J₂ Heisenberg model. Numerical experiments on both quantum simulators and real quantum hardware demonstrate the efficiency of our approach, which can be readily applied to study various quantum many-body systems at finite temperatures on currently available noisy intermediate-scale quantum devices.

中文翻译：

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将变分量子本征求解器扩展到有限温度

我们提出了一种变分量子热化器 (VQT)，称为量子 VQT (qVQT)，它将变分量子本征解算器扩展到有限温度。qVQT 利用两个变分电路之间的中间测量来对量子设备上的密度矩阵进行编码。经典优化提供了热态，同时提供了量子力学系统的所有相关激发态。我们演示了 qVQT 对于两种不同自旋系统的功能。首先，我们分析 qVQT 的性能作为一维海森堡链的电路深度和温度的函数。其次，我们使用激发态来绘制二维 J ₁ –J ₂海森堡模型的完整的温度相关相图。量子模拟器和真实量子硬件上的数值实验证明了我们方法的效率，该方法可以很容易地应用于研究当前可用的嘈杂中尺度量子设备上有限温度下的各种量子多体系统。