Shortcuts to Adiabatic Classical Spin Dynamics Mimicking Quantum Annealing

Abstract

We propose a simple construction of shortcuts to adiabaticity tracking instantaneous stationary states in classical spin systems without knowing tracked stationary states. In our construction, control fields of counter-diabatic driving are constituted by state-dependent magnetic fields, which can be easily determined with an aid of numerical calculations. Easiness of our construction is a remarkable feature since it is usually a hard task to determine explicit form of required counter-diabatic terms in many-body systems. We also argue that our method can be applied to solve combinatorial optimization problems by considering classical spin dynamics under a time-dependent Hamiltonian, which mimics the procedure of quantum annealing.

arXiv commentAccepted for publication in PRE

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• Implementation of a Hybrid Classical-Quantum Annealing Algorithm for Logistic Network Design
• Hamiltonian engineering for adiabatic quantum computation: Lessons from shortcuts to adiabaticity
• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• General bound on the performance of counter-diabatic driving acting on dissipative spin systems
• Counterdiabatic Reverse Annealing
• Geometric Floquet theory
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• Iterative classical superadiabatic algorithm for combinatorial optimization
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Variational matrix product states for combinatorial optimization