Quantum annealing showing the exponentially small success probability despite a constant energy gap

Hayasaka, Hiroshi; Imoto, Takashi; Matsuzaki, Yuichiro; Kawabata, Shiro

doi:10.48550/arxiv.2212.09995

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“…Adiabatic processes are entirely reversible in their ideal form, making them theoretically robust. However, they usually require the system to be driven very slowly, which is a practical obstacle through most implementations [2].…”

Section: Introductionmentioning

confidence: 99%

Counterdiabatic optimized driving in quantum phase sensitive models

Barone,

Kiss,

Grossi

et al. 2024

New J. Phys.

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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.

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Section: Introductionmentioning

confidence: 99%