The preparation of thermal equilibrium states is important for the simulation of condensed matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators and demonstrate this technique experimentally using a gate-based quantum processor. Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation. The fidelity of generated states to the thermal-equilibrium state smoothly varies from 99 to 75% between infinite and near-zero simulated temperature, in quantitative agreement with numerical simulations of the noisy quantum processor with error parameters drawn from experiment.

热平衡状态的准备对于使用量子计算机模拟凝聚态和宇宙学系统很重要。我们提出了一种用幺正算子准备这种混合状态的方法，并使用基于门的量子处理器通过实验证明了这种技术。我们的方法的目标是使用由量子近似优化算法驱动的混合量子经典变分方法生成热场双态，而无需通过数值模拟预先计算最佳变分参数。生成状态对热平衡状态的保真度在无限大和接近零的模拟温度之间从 99% 到 75% 平滑变化，与噪声量子处理器的数值模拟定量一致，误差参数从实验中得出。