Extraction of Hamiltonian parameters from quantum ground states using variational quantum convolutional neural network

Quantum convolutional neural network has been shown to be capable of efficiently and accurately classifying quantum states into topologically trivial and non-trivial phases. At the same time, recent work on hybrid quantum-classical neural networks has shown that such architectures can be used to perform classification tasks. Motivated by these developments, we construct and train a hybrid variational quantum convolutional neural network under the supervised regression mode. In particular, we demonstrate that given an input quantum circuit representing the ground state of a 1-dimensional Ising Hamiltonian, the hybrid network is capable of extracting the interaction parameters of the Hamiltonian. These input quantum circuits can be generated either by amplitude encoding or variational optimization. We further show that a network trained on a particular ansatz architecture can successfully process input circuits of a different architecture. This work thus illustrates the potential of hybrid quantum-classical neural networks in regression tasks, as well as in extracting information from quantum states prepared by near-term variational algorithms.