Learning Circuits with Infinite Tensor Networks

TL;DR

This paper introduces a tensor network-based method for quantum circuit design that efficiently simulates Hamiltonian dynamics with reduced gate depths, leveraging translation invariance to handle large systems.

Contribution

It presents a novel approach using datasets of tensor networks for unitary synthesis, significantly reducing circuit complexity for Hamiltonian simulation.

Findings

Achieves lower gate depths than Trotterized methods

Reduces T-count by 5.2 times for $e^{-iHt}$

Utilizes translation invariance to scale with system size

Abstract

Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support circuit design, with datasets of tensor networks enabling a unitary synthesis inspired by quantum machine learning. For a target simulation in the thermodynamic limit, translation invariance is exploited to significantly reduce the optimization complexity, avoiding a scaling with system size. Our approach finds circuits to efficiently prepare ground states, and perform time evolution on both infinite and finite systems with substantially lower gate depths than conventional Trotterized methods. In addition to reducing CNOT depths, we motivate similar utility for fault-tolerant quantum algorithms, with a demonstrated $5.2\times$ reduction in $T$-count to realize $e^{-iHt}$. The key output of our approach is the optimized unit-cell of a translation invariant circuit. This provides an advantage for Hamiltonian simulation of finite, yet arbitrarily large, systems on real quantum computers.