Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. In this paper, we propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator components of the Hamiltonian. Its main subroutine is the practical log-partition function estimation algorithm, which is based on the minimization of the free energy of the system. Concretely, we devise a stochastic variational quantum eigensolver (SVQE) to diagonalize the Hamiltonians and then exploit the obtained eigenvalues to compute the free energy's global minimum using convex optimization. Our approach not only avoids the challenge of estimating von Neumann entropy in free energy minimization, but also reduces the quantum resources via importance sampling in Hamiltonian diagonalization, facilitating the implementation of our method on near-term quantum devices. Finally, we demonstrate our approach's validity by conducting numerical experiments with Hamiltonians of interest in quantum many-body physics.
翻译:汉密尔顿 学习对于量子装置和量子模拟器的认证至关重要。 在本文中, 我们提出一个混合量子古典汉密尔顿学习算法, 以寻找汉密尔顿号的保利操作器组件的系数。 它的主要子例程是实用的日志分配函数估算算法, 其基础是将系统的自由能源降到最低。 具体地说, 我们设计了一种随机变异量量量乙质素( SVQE), 以对汉密尔顿人进行分解, 然后利用获得的乙质值, 利用convex优化来计算自由能源的全球最低值。 我们的方法不仅避免了在自由能源最小化中估算冯纽曼的环球, 而且还通过汉密尔顿分解的重要性取样来减少量子资源, 便利我们近期量子装置方法的实施。 最后, 我们通过对量子体物理中有兴趣的汉密尔顿人进行数字实验, 来证明我们的方法的有效性。