# Quantum annealing with longitudinal bias fields

## TL;DR

This paper proposes using inhomogeneous longitudinal magnetic fields in quantum annealing to improve solution efficiency by biasing the dynamics or filtering unwanted states, demonstrated through numerical simulations.

## Contribution

It introduces a novel approach of applying longitudinal bias fields in quantum annealing to enhance problem-solving capabilities, especially for difficult instances.

## Key findings

- Bias fields can steer annealing towards solutions.
- Antibias fields filter out undesired states.
- Numerical results show improved performance for complex problems.

## Abstract

Quantum annealing aims at solving hard computational problems through adiabatic state preparation. Here, I propose to use inhomogeneous longitudinal magnetic fields to enhance the efficiency of the annealing. Such fields are able to bias the annealing dynamics into the desired solution, and in many cases, suitable field configurations can be found iteratively. Alternatively, the longitudinal fields can also be applied as an antibias which filters out unwanted contributions from the final state. This strategy is particularly well suited for instances which are difficult to solve within the standard quantum annealing approach. By numerically simulating the dynamics for small instances of the exact cover problem, the performance of these different strategies is investigated.