Error suppression in adiabatic quantum computing with qubit ensembles

TL;DR

This paper proposes an error suppression method for adiabatic quantum computing using qubit ensembles, which simplifies implementation and enhances robustness against decoherence, especially in neutral atomic gases.

Contribution

It introduces an ensemble-based encoding for AQC Hamiltonians, enabling error protection and improved performance with larger ensembles.

Findings

Critical ensemble size $N_c$ where the first excited state changes nature.

Mean-field theory accurately predicts the energy gap for large ensembles.

Error protection improves as ensemble size increases beyond $N_c$.

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 $N_{\mathrm{c}}$ 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 $N_{\mathrm{c}}$, 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.