Steering random spin systems to speed up the quantum adiabatic algorithm

TL;DR

This paper introduces a modified quantum adiabatic algorithm using a steering term, which improves the likelihood of remaining in the ground state during evolution, especially in disordered systems.

Contribution

It develops a single-particle and cluster approximation to the steering term, enhancing the quantum adiabatic process for complex models like the disordered Ising chain.

Findings

Significantly increases ground state retention probability in strongly disordered systems.

Most probable states remain low-energy states even with stronger qubit interactions.

Applicable to various models, paving the way for improved quantum adiabatic algorithms.

Abstract

A general time-dependent quantum system can be driven fast from its initial ground state to its final ground state without generating transitions by adding a steering term to the Hamiltonian. We show how this technique can be modified to improve on the standard quantum adiabatic algorithm by making a single-particle and cluster approximation to the steering term. The method is applied to a one-dimensional Ising model in a random field. For the limit of strong disorder, the correction terms significantly enhance the probability for the whole system to remain in the ground state for the proposed non-stoquastic annealing protocol. We demonstrate that even when transitions occur for stronger interaction between qubits, the most probable quantum state is one of the lower energy states of the final Hamiltonian. Since the method can be applied to any model, and more sophisticated approximations to the steering term are possible, the new technique opens up an avenue for the improvement of the quantum adiabatic algorithm.