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

TL;DR

This paper introduces a method using shortcut to adiabaticity to efficiently generate cluster states in a one-dimensional Kitaev honeycomb model, enhancing quantum computation resources.

Contribution

It presents a novel application of transitionless quantum driving to produce cluster states in a specific quantum model, involving M-body interactions for fast state preparation.

Findings

Successfully generates cluster states via shortcut to adiabaticity.

Shows auxiliary Hamiltonian involves M-body interactions.

Demonstrates fast preparation of resource states for quantum computation.

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 auxillary Hamiltonian needed for the counterdiabatic driving is of M-body interaction.