Optimization of non-Gaussian state generation using tensor networks and automatic differentiation

Tensor networks have been eagerly developed in recent years as a simulation method for quantum computation on classical computers. The efficiency of tensor networks for simulating quantum computation has been shown by solving a task designed for demonstrating quantum computing supremacy. However, such a task is not useful for real application. Therefore, there is the room for research of finding specific applications suitable for exploiting tensor network simulation. As such an application, we propose optimization of circuits to generate non- Gaussian states. Non-Gaussian state is one of the crucial elements for achieving universal continuous variable quantum computation. We consider this problem as a variational optimization of optical circuits to generate desired non-Gaussian states. Tensor networks efficiently simulate the optical circuits, and their compatibility with automatic differentiation provides a heuristic way to optimize the circuits. We propose and report the result of our approach that combines tensor networks and automatic differentiation to perform variational optimization of circuits such that the desired non-Gaussian state is approximately generated. The complexity of contracting tensor networks is scaled by degree of entanglement, so we consider relatively shallow optical circuit. Such a restriction is beneficial for considering devices without error correction method, which are accessible in near-term.