Proposal for Quantum Simulation via All-Optically Generated Tensor Network States

TL;DR

This paper proposes an all-optical method to generate complex entangled photonic states using tensor networks, enabling simulation of many-body quantum systems with current optical technology.

Contribution

It introduces a novel all-optical scheme for creating tensor network states and demonstrates its application in simulating ground states of quantum many-body models.

Findings

Successfully generates entangled tensor network states with optical devices.

Demonstrates the scheme's robustness against losses and mode mismatch.

Simulates ground-state properties of the spin-1/2 Heisenberg model.

Abstract

We devise an all-optical scheme for the generation of entangled multimode photonic states encoded in temporal modes of light. The scheme employs a nonlinear down-conversion process in an optical loop to generate one- and higher-dimensional tensor network states of light. We illustrate the principle with the generation of two different classes of entangled tensor network states and report on a variational algorithm to simulate the ground-state physics of many-body systems. We demonstrate that state-of-the-art optical devices are capable of determining the ground-state properties of the spin-1/2 Heisenberg model. Finally, implementations of the scheme are demonstrated to be robust against realistic losses and mode mismatch.