Quantum annealing in spin-boson model: from a perturbative to a ultrastrong mediated coupling

TL;DR

This paper investigates how boson-mediated interactions influence the efficiency of quantum annealing in spin systems, revealing conditions under which excited states can enhance performance.

Contribution

It introduces a comparative analysis of direct and mediated couplings in quantum annealing, highlighting the role of excited solutions and their impact on annealing efficiency.

Findings

Boson-mediated interactions can improve quantum annealing performance.

Excited solutions with higher bosonic occupancy influence state populations.

Optimal conditions depend on the interplay between excited states and local errors.

Abstract

We study a quantum annealer where bosons mediate the Ising-type interactions between qubits. We compare the efficiency of ground state preparation for direct and mediated couplings, for which Ising and spin-boson Hamiltonian are employed respectively. This comparison is done numerically for a small frustrated antiferromagnet, with a careful choice of the optimal adiabatic passage that reveals the features of the boson-mediated interactions. Those features can be explained by taking into account what we called excited solutions: states with the same spin correlations as the ground-state but with a larger bosonic occupancy. For similar frequencies of the bosons and qubits, the performance of quantum annealing depends on how excited solutions interchange population with local spin errors. We report an enhancement of quantum annealing thanks to this interchange under certain circumstances.