We extend the ability of an unitary quantum circuit by interfacing it with a classical autoregressive neural network. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit to solve quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a byproduct, the algorithm also gives access to low energy excitation states. We demonstrate applications of the approach to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.

我们通过与经典自回归神经网络接口来扩展extend量子电路的功能。组合模型将变异密度矩阵参数化为量子纯态的经典混合物，其中自回归网络生成位串样本作为量子电路的输入状态。我们设计了一种有效的变分算法来共同优化经典神经网络和量子电路，以解决量子统计力学问题。可以获得热观测值，例如变化的自由能，熵和比热。作为副产品，该算法还可以访问低能激发态。我们利用在近期量子计算机上可行的资源，论证了该方法在量子伊辛模型的热性质和激发光谱中的应用。