Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity

Thi Ha Kyaw,Leong-Chuan Kwek

doi:10.1088/1367-2630/aab315

Abstract

We propose a mean to obtain computationally useful resource states also known as cluster states, for measurement-based quantum computation, via transitionless quantum driving algorithm. The idea is to cool the system to its unique ground state and tune some control parameters to arrive at computationally useful resource state, which is in one of the degenerate ground states. Even though there is set of conserved quantities already present in the model Hamiltonian, which prevents the instantaneous state to go to any other eigenstate subspaces, one cannot quench the control parameters to get the desired state. In that case, the state will not evolve. With involvement of the shortcut Hamiltonian, we obtain cluster states in fast-forward manner. We elaborate our proposal in the one-dimensional Kitaev honeycomb model, and show that the auxiliary Hamiltonian needed for the counterdiabatic driving is of M-body interaction.

Highlights

A quantum computer promises efficient processing capability for certain computational problems in contrast to current classical computer [1,2,3]
There exists an alternative paradigm, where the desired quantum gate operations are obtained through single-particle projective measurements on some highly entangled resource states or cluster states [6]
This is known as the measurementbased quantum computation (MBQC) [7,8,9]

Summary

Introduction

A quantum computer promises efficient processing capability for certain computational problems in contrast to current classical computer [1,2,3]. There exists an alternative paradigm, where the desired quantum gate operations are obtained through single-particle projective measurements on some highly entangled resource states or cluster states [6] This is known as the measurementbased quantum computation (MBQC) [7,8,9]. A preferred way to prepare and obtain these resources is to consider physical systems whose ground states are precisely these entangled resources and obtaining the states through cooling the system to its ground state One such resource for the MBQC is the cluster state [10] which is the ground state of spin-1/2 particles with k-body interactions where k 3 [11, 12].

General setup

The model

Conclusion