Compressed Simulation of evolutions of the XY-model

TL;DR

This paper introduces a method for simulating the 1D XY-model using exponentially fewer qubits through compressed quantum circuits, enabling efficient analysis of quantum phase transitions and dynamical processes.

Contribution

It extends compressed quantum simulation techniques to the XY-model, deriving circuits that simulate large systems with logarithmic qubits and demonstrating their application to phase transitions and dynamics.

Findings

Successfully simulates XY-model with log(n) qubits

Realizes adiabatic evolution on compressed systems

Analyzes quantum quenching and finite-time dynamics

Abstract

We extend the notion of compressed quantum simulation to the XY-model. We derive a quantum circuit processing log(n) qubits which simulates the 1D XY-model describing n qubits. In particular, we demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which witnesses a quantum phase transition can be observed. Furthermore, we analyze several dynamical processes, like quantum quenching and finite time evolution and derive the corresponding compressed quantum circuit.