Optimization schemes for unitary tensor-network circuit

An efficient representation of a quantum circuit is of great importance in achieving a quantum advantage on current noisy intermediate scale quantum (NISQ) devices and the classical simulation of quantum many-body systems. The quantum circuits are playing the key ingredient in the performance of variational quantum algorithms and quantum dynamics in problems of physics and chemistry. In this paper, we study the role of the network structure of a quantum circuit in its performance. We discuss the variational optimization of quantum circuit (a unitary tensor-network circuit) with different network structures. The ansatz is performed based on a generalization of well-developed multiscale entanglement renormalization algorithm and also the conjugate-gradient method with an effective line search. We present the benchmarking calculations for different network structures by studying the Heisenberg model in a strongly disordered magnetic field and a tensor-network QR decomposition. Our work can contribute to achieve the most out of NISQ hardware and to classically develop isometric tensor network states.