Simulating the same physics with two distinct Hamiltonians

TL;DR

This paper presents a framework demonstrating how different Hamiltonians can simulate identical physical phenomena, including analog and digital quantum simulations, and introduces a method for generating entangled states with short-range interactions.

Contribution

It introduces a novel framework for using distinct Hamiltonians to simulate the same physics and provides practical examples for analog and digital quantum simulations.

Findings

Simulated infinite-range interactions with short-range models

Built an alternative digital quantum simulator

Created maximally entangled states using only short-range interactions

Abstract

We develop a framework and give an example for situations where two distinct Hamiltonians living in the same Hilbert space can be used to simulate the same physics. As an example of an analog simulation, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version of a digital quantum simulator. As a by-product, we present a method for creating many-body maximally entangled states using only short-range nearest-neighbor interactions.