Quantum phases with differing computational power

TL;DR

This paper explores how quantum phase transitions can alter the capacity of quantum systems to process information, highlighting differences in simulation capabilities across phases in the XY model.

Contribution

It demonstrates that certain quantum phases enable local simulation of perturbations, while others induce non-local interactions, impacting quantum computational potential.

Findings

In some phases, external field perturbations are locally simulatable.

Other phases exhibit emergent non-local, multi-body interactions.

Implications for adiabatic quantum computation and computational advantage.

Abstract

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited. Here We show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.