Shortcuts to adiabaticity for quantum annealing

TL;DR

This paper introduces shortcuts to adiabaticity in quantum annealing, enabling faster and more efficient quantum state evolution by designing Hamiltonian time dependence through inverse engineering and mean-field invariants.

Contribution

It develops a method to design Hamiltonian dynamics for quantum annealing using shortcuts to adiabaticity, improving control over quantum state evolution.

Findings

Magnetization dynamics are speed-independent in the infinite-range model.

Rotating transverse magnetic fields facilitate ideal quantum evolution.

The inverse engineering approach effectively implements shortcuts to adiabaticity.

Abstract

We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz, and the Hamiltonian is designed by the inverse engineering. We show that the time dependence of physical quantities such as the magnetization is independent of the speed of the Hamiltonian variation in the infinite-range model. We also show that rotating transverse magnetic fields are useful to achieve the ideal time evolution.