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 expression 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 timedependent Hamiltonian, which mimics the procedure of quantum annealing.

Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems

“…Thus, we conclude that SB finds lower minima among many minima harnessing the ergodicity. [Very recently, a new approach to the Ising problem using a classical Hamiltonian system with “classical spins” mimicking quantum annealing has been proposed ( 42 ), where a fixed point is tracked by the technique called shortcut to adiabaticity. Although this approach uses classical Hamiltonian dynamics as well, it is quite different from SB, because it will not exploit the ergodic search but just track a fixed point.…”

Rapid counter-diabatic sweeps in lattice gauge adiabatic quantum computing

“…Shortcuts to adiabaticity (STA) make use of quantum coherence during the protocol and allow one to prepare the ground state or at least states that are close to the ground state in finite time. A variety of methods to engineer such protocols including invariant-based inverse engineering [16][17][18][19], fast-forward techniques [20][21][22][23][24][25][26], transitionless counter-diabatic driving [27][28][29][30][31] and optimal control theory [32][33][34] have been developed and applied to various fields such as quantum heat engines [35][36][37], atomic physics [38,16,39,40], open quantum systems [41][42][43][44][45], Ising spin models [46][47][48][49][50][51][52], adiabatic quantum computation [53,54] as well as experiments with spins and ions [55][56][57][58][59]…”

Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing

“…for infinitesimal step size), it is known that a physical interpretation of our approach is possible [39]: namely, as a dynamical evolution of a system in a viscous medium in which the momentum parameter plays the role of mass. This evolution is not equivalent to that of [32,38] due to the effects of damping implied by the viscosity. Furthermore, since our parameter updates are done at the level of the variables w and not θ, the variables on which this physical evolution is understood are not the same.…”

“…Our method is reminiscent of but different to the approaches suggested in [32,38], which use a similar product state ansatz and Hamiltonian to mimik the effects of quantum annealing. These approaches are based on a dynamical (physical) evolution of the parameters θ under the Hamiltonian (6).…”