# Enhancing quantum annealing performance by a degenerate two-level system

## TL;DR

This paper proposes a degenerate two-level system to improve quantum annealing success probability by preventing energy gap closure, potentially enhancing the efficiency of solving combinatorial optimization problems.

## Contribution

It introduces a degenerate two-level system model that outperforms the conventional spin-1/ick model in quantum annealing success probability.

## Key findings

- Degenerate two-level system increases success probability in quantum annealing.
- Effective magnetic field opens energy gap, reducing tunneling leakage.
- Lambda-type system may further improve success probability.

## Abstract

Quantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem. Since the combinatorial optimization problems are ubiquitous, quantum annealing machine with high efficiency and scalability will give an immeasurable impact on many fields. However, the conventional quantum annealing machine may not have a high success probability for finding the solution because the energy gap closes exponentially as a function of the system size. To propose an idea for finding high success probability is one of the most important issues. Here we show that a degenerate two-level system provides the higher success probability than the conventional spin-1/2 model in a weak longitudinal magnetic field region. The physics behind this is that the quantum annealing in this model can be reduced into that in the spin-1/2 model, where the effective longitudinal magnetic field may open the energy gap, which suppresses the Landau--Zener tunneling providing leakage of the ground state. We also present the success probability of the $\Lambda$-type system, which may show the higher success probability than the conventional spin-1/2 model.