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.
Highlights
Quantum annealing is a metaheuristic for combinatorial optimization problems [1,2,3,4,5,6,7] and has often been analyzed theoretically in the framework of adiabatic quantum computing [8,9,10]
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 and by the single-parameter method
We have proposed and tested a method to find an efficient local CD Hamiltonian that outperforms its traditional quantum annealing and single-parameter approximate CD counterparts with respect to enhanced final ground-state fidelity and reduced residual energy as well as time-to-solution
Summary
Quantum annealing is a metaheuristic for combinatorial optimization problems [1,2,3,4,5,6,7] and has often been analyzed theoretically in the framework of adiabatic quantum computing [8,9,10]. There have been attempts to design protocols to control the system variables based on this idea [11], and shortcuts to adiabaticity [12,13,14,15] present strong candidates, providing a systematic way toward this goal. Among these shortcuts-to-adiabaticity methods [16,17,18,19,20,21,22], counter-diabatic (CD) driving [21,23,24,25,26,27] is one of the most promising approaches. The price to pay is that the enhancement of performance is often limited
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