Counterdiabatic driving in the quantum annealing of the $p$-spin model: a variational approach

TL;DR

This paper develops a variational method to approximate counterdiabatic potentials in quantum annealing of the p-spin model, achieving high fidelity in short times and comparing different ansatz approaches.

Contribution

It introduces a new cyclic ansatz for the counterdiabatic potential in the p=3 spin model, enhancing quantum annealing efficiency.

Findings

Achieves optimal fidelity with short dynamics regardless of system size.

Introduces a novel cyclic ansatz for p=3 case.

Provides comparative analysis with nested commutator ansatz.

Abstract

Finding the exact counterdiabatic potential is, in principle, particularly demanding. Following recent progresses about variational strategies to approximate the counterdiabatic operator, in this paper we apply this technique to the quantum annealing of the $p$-spin model. In particular, for $ p = 3 $ we find a new form of the counterdiabatic potential originating from a cyclic ansatz, that allows us to have optimal fidelity even for extremely short dynamics, independently of the size of the system. We compare our results with a nested commutator ansatz, recently proposed in P. W. Claeys, M. Pandey, D. Sels, and A. Polkovnikov, Phys. Rev. Lett. 123, 090602 (2019), for $ p = 1 $ and $ p = 3 $. We also analyze generalized $ p $-spin models to get a further insight into our ansatz.