Shortcuts to adiabaticity for quantum annealing

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.

12 pages, 25 figures, revised for publication

References in corpus (10)

• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Decoherence in adiabatic quantum computation
• Adiabatic tracking of quantum many-body dynamics
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Quantum annealing with antiferromagnetic fluctuations
• Quantum Adiabatic Evolution Algorithms with Different Paths
• Counterdiabatic driving of the quantum Ising model
• Unitary deformations of counterdiabatic driving

Cited by in corpus (9)

• Focus on Shortcuts to Adiabaticity
• Two-parameter counter-diabatic driving in quantum annealing
• Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions
• Shortcuts to adiabaticity in the infinite-range Ising model by mean-field counter-diabatic driving
• Optimizing Counterdiabaticity by Variational Quantum Circuits
• Counterdiabatic Reverse Annealing
• Counterdiabatic Formalism of Shortcuts to Adiabaticity
• Dynamical invariant formalism of shortcuts to adiabaticity
• Assessing the performance of quantum annealing with nonlinear driving