Quantum Circuit Optimization using Differentiable Programming of Tensor Network States

TL;DR

This paper introduces a classical algorithm combining machine learning and tensor network methods to optimize quantum circuits, enabling efficient simulation of complex quantum many-body systems with high accuracy.

Contribution

It presents a novel differentiable programming approach for quantum circuit optimization using tensor network states, improving efficiency and scalability over previous methods.

Findings

Successfully finds shallow, accurate quantum circuits for various models.

Achieves high state fidelities within reasonable computational resources.

Demonstrates applicability to large system sizes up to L=100.

Abstract

Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network methods. The said algorithm runs on classical hardware and finds shallow, accurate quantum circuits by minimizing scalar cost functions. The gradients relevant for the optimization process are computed using the reverse mode automatic differentiation technique implemented on top of the time-evolved block decimation algorithm for matrix product states. A variation of the ADAM optimizer is utilized to perform a gradient descent on the manifolds of charge conserving unitary operators to find the optimal quantum circuit. The efficacy of this approach is demonstrated by finding the ground states of spin chain Hamiltonians for the Ising, three-state Potts and the massive Schwinger models for system sizes up to L=100. The first ten excited states of these models are also obtained for system sizes L=24. All circuits achieve high state fidelities within reasonable CPU time and modest memory requirements.