Error suppression in adiabatic quantum computing with qubit ensembles

Naeimeh Mohseni,Tim Byrnes,Jonathan P Dowling,Marek Narozniak,Valentin Ivannikov,Alexey N Pyrkov

doi:10.1038/s41534-021-00405-2

Abstract

Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.

Highlights

Adiabatic quantum computing (AQC) is an alternative approach to traditional gate-based quantum computing where quantum adiabatic evolution is performed in order to achieve a computation[1,2,3,4]
We examine the dependence of the logical errors at the end of the AQC with the ensemble size N
We find generally the same behavior of the success probability is defined to be the total probability of all error with N when decoherence is introduced, but with a higher states that are logically equivalent to the ground state

Summary

INTRODUCTION

Adiabatic quantum computing (AQC) is an alternative approach to traditional gate-based quantum computing where quantum adiabatic evolution is performed in order to achieve a computation[1,2,3,4]. The aim is to find the ground state of a Hamiltonian HZ which encodes the problem to be solved and can be considered an instance of quantum annealing[5,6,7,8]. We characterize the nature of the ground and excited states of the ensemble Hamiltonian and assess the performance of AQC in comparison to the original qubit problem. The use of an ensemble duplicates the quantum information since the N qubits within an ensemble are in the same state at the start and at the end of the adiabatic evolution Such error-suppression strategies have been already investigated in the context of AQC. Farhi, and Shor[49] introduced an encoding capable of detecting the presence of single-qubit errors, which are suppressed by an additional energy penalty term in the total Hamiltonian.

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