Counterdiabatic optimized driving in quantum phase sensitive models

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, XXZ, and Haldane-Shastry models. We perform a shallow quantum optimal control over the counterdiabatic protocols by optimizing an energy cost function. Moreover, we provide a code package for computing symbolically various adiabatic gauge potentials. This protocol consistently surpasses standard annealing schedules, often achieving performance improvements of several orders of magnitude. The the axial next-nearest neighbor Ising model stands out as a notable example, where fidelities exceeding 0.5 are attainable in most cases. Furthermore, the optimized paths exhibit promising generalization capabilities to higher-dimensional systems, allowing for the extension of parameters from smaller models. Nevertheless, our investigations reveal limitations in the case of the XXZ and Haldane-Shastry 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.

Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations

“…Counterdiabatic optimized local driving was proposed as a combination of optimal control theory with local approximate counterdiabatic driving [110]. A benchmark test was performed using nontrivial spin systems [111]. The Pauli-Y matrix is known as the first-order counterdiabatic term in local approximate counterdiabatic driving of quantum annealing.…”

Physics-informed neural networks for an optimal counterdiabatic quantum computation

“…From an experimental standpoint, the amount of possible operations is often very limited and usually involves scenarios where the qubits are arranged in a certain specific manner only allowing a subset of the totality of the interactions (e.g. [45,63] where a certain ansatz for A CD is considered, or [64], where different graphs illustrating some connectivities are depicted). Consequently, trying to solve the entirety of the CD protocol in such situations would be impractical and unrealistic.…”