Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and R\'enyi entropies, as well as the measured relative entropy and measured R\'enyi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks.

翻译：熵度量量化了量子系统中存在的信息量和关联性。在实践中，当量子态未知且仅能获得其副本时，必须借助此类熵度量的估计方法。本文提出了一种变分量子算法，用于估计冯·诺依曼熵、Rényi熵，以及测量相对熵和测量Rényi相对熵。该方法首先通过量子电路和经典神经网络对目标度量的变分公式进行参数化，随后在参数空间中对所得目标函数进行优化。我们利用无噪声量子模拟器对该量子算法进行了数值模拟。结果表明，该算法在测试案例中能够准确估计各类熵度量，使其成为下游任务中颇具前景的实现方案。