# Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports

## TL;DR

This paper demonstrates how arrays of directionally unbiased linear optical multiports can simulate discrete-time Hamiltonian systems, enabling scalable, resource-efficient quantum simulations using only linear optics.

## Contribution

It introduces a novel approach using directionally unbiased multiports for simulating discrete-time Hamiltonians, including systems with spatial and internal degrees of freedom.

## Key findings

- Allows simulation of a range of discrete-time Hamiltonian systems
- Resource savings due to ports serving as both input and output
- Scalable implementation using only linear optics

## Abstract

Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a realistic linear optical scattering vertex for quantum walks on arbitrary graph structures. Here, it is shown that arrays of these multiports allow the simulation of a range of discrete-time Hamiltonian systems. Examples are described, including a case where both spatial and internal degrees of freedom are simulated. Because input ports also double as output ports, there is substantial savings of resources compared to feed-forward networks carrying out the same functions. The simulation is implemented in a scalable manner using only linear optics, and can be generalized to higher dimensional systems in a straightforward fashion, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.