Effect of Quantum Statistics on Computational Power of Atomic Quantum Annealers

TL;DR

This paper investigates how quantum particle statistics influence the computational capabilities of atomic quantum annealers, revealing that bosonic systems outperform fermionic ones due to larger excitation gaps and more efficient Hilbert space exploration.

Contribution

It introduces a comparative study of spinless fermions and hard-core bosons in quantum annealing, highlighting the advantages of bosonic systems for optimization tasks.

Findings

Bosonic quantum annealers outperform fermionic ones.

Larger excitation gaps in bosons lead to smoother adiabatic evolution.

Bosons explore the Hilbert space more efficiently during annealing.

Abstract

Quantum particle statistics fundamentally controls the way particles interact, and plays an essential role in determining the properties of the system at low temperature. Here we study how the quantum statistics affects the computational power of quantum annealing. We propose an annealing Hamiltonian describing quantum particles moving on a square lattice and compare the computational performance of the atomic quantum annealers between two statistically-different components: spinless fermions and hard-core bosons. In addition, we take an Ising quantum annealer driven by traditional transverse-field quantum fluctuations as a baseline. The potential of our quantum annealers to solve combinatorial optimization problems is demonstrated on random 3-regular graph partitioning. We find that the bosonic quantum annealer outperforms the fermionic case. The superior performance of the bosonic quantum annealer is attributed to larger excitation gaps and the consequent smoother adiabatic transformation of its instantaneous quantum ground states. Along our annealing schedule, the bosonic quantum annealer is less affected by the glass order and explores the Hilbert space more efficiently. Our theoretical finding could shed light on constructing atomic quantum annealers using Rydberg atoms in optical lattices.