Quantum phases with differing computational power

Jian Cui,Leong Chuan Kwek,Heng Fan,Vlatko Vedral,Mile Gu,Marcelo França Santos

doi:10.1038/ncomms1809

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.

Highlights

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
Adiabatic quantum computation (AQC) involves the adiabatic evolution of the ground state of some Hamiltonian, which features a parameter that varies with time[26,27]
This is instantly reminiscent of our study, which observes what computational processes are required to simulate the adiabatic evolution of the ground state under variance of an external parameter in different quantum phases

Summary

Introduction

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. 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. For example, that the extremum points of entanglement and other related correlations coincide with phase transition points[3,4,5,6,7], and that different phases may feature differing fidelity between neighbouring states[8,9,10,11,12,13] These observations have helped pioneer many alternative indicators of phase transitions, allowing the tools of quantum information science to be harnessed in the analysis of quantum many-body systems[1,2]. Is the Rényi entropy with parameter α, ρA(g) is the reduced density the matrix of |G(g)〉AB with respect to eigenvalues of ρA(g) in decreasing

Methods

Results

Conclusion