Counterdiabatic optimized driving in quantum phase sensitive models

TL;DR

This paper develops and benchmarks counterdiabatic driving protocols for quantum state preparation in spin models with phase transitions, demonstrating significant performance improvements and potential for higher-dimensional applications.

Contribution

It introduces an optimized control protocol using Bayesian methods for various spin models, outperforming standard annealing and showing generalization to larger systems.

Findings

Performance improvements of several orders of magnitude over standard annealing

Achievable fidelities exceeding 0.5 in the ANNNI model

Limitations observed in XXZ and Haldane-Shastry models outside ferromagnetic phases

Abstract

State preparation plays a pivotal role in numerous quantum algorithms, including quantum phase estimation. This paper extends and benchmarks counterdiabatic driving protocols across three one-dimensional spin systems characterized by phase transitions: the axial next-nearest neighbor Ising (ANNNI), XXZ, and Haldane-Shastry (HS) models. We perform quantum optimal control protocols by optimizing the energy cost function, which can always be evaluated as opposed to the fidelity one requiring the exact state. Moreover, we incorporate Bayesian optimization within a code package for computing various adiabatic gauge potentials. This protocol consistently surpasses standard annealing schedules, often achieving performance improvements of several orders of magnitude. Notably, the ANNNI model stands out as a notable example, where fidelities exceeding 0.5 are attainable in most cases. Furthermore, the optimized paths exhibits promising generalization capabilities to higher-dimensional systems, allowing for the extension of parameters from smaller models. This opens up possibilities for applying the protocol to higher-dimensional systems. However, our investigations reveal limitations in the case of the XXZ and HS models, particularly when transitioning away from the ferromagnetic phase. This suggests that finding optimal diabatic gauge potentials for specific systems remains an important research direction.