Two-parameter counter-diabatic driving in quantum annealing

Abstract

We introduce a two-parameter approximate counter-diabatic term into the Hamiltonian of the transverse-field Ising model for quantum annealing to accelerate convergence to the solution, generalizing an existing single-parameter approach. The protocol is equivalent to unconventional diabatic control of the longitudinal and transverse fields in the transverse-field Ising model and thus makes it more feasible for experimental realization than an introduction of new terms such as non-stoquastic catalysts toward the same goal of performance enhancement. We test the idea for the $p$-spin model with $p=3$, which has a first-order quantum phase transition, and show that our two-parameter approach leads to significantly larger ground-state fidelity and lower residual energy than those by traditional quantum annealing as well as by the single-parameter method. We also find a scaling advantage in terms of the time to solution as a function of the system size in a certain range of parameters as compared to the traditional methods.

14 pages, 6 figures

References in corpus (14)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Mathematical Foundation of Quantum Annealing
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Quantum annealing with antiferromagnetic fluctuations
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Focus on Shortcuts to Adiabaticity
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• Shortcuts to adiabaticity for quantum annealing
• Counterdiabatic driving of the quantum Ising model
• Controlling quantum critical dynamics of isolated systems
• Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian