Compressed quantum simulation of the Ising model

TL;DR

This paper demonstrates how to simulate the 1D Ising model using a compressed quantum circuit on a logarithmically smaller quantum computer, enabling efficient analysis of quantum phase transitions.

Contribution

It introduces a method to simulate the 1D Ising model via circuit compression, reducing the required qubits from n to log(n) for universal quantum computation.

Findings

Successful simulation of the Ising interaction on a log(n)-qubit system.

Implementation of adiabatic evolution to observe quantum phase transition.

Measurement of magnetization in the compressed quantum system.

Abstract

In [R. Jozsa, B. Kraus, A. Miyake, J. Watrous, Proc. R. Soc. A {\bf 466}, 809-830 (2010)] it has been shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on \log(n)+3 qubits. Here, we show how this compression can be employed to simulate the Ising interaction of a 1D--chain consisting out of n qubits using a universal quantum computer running on log(n) qubits. We demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which shows a quantum phase transition, can be measured.