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 (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.

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Cited by in corpus (10)

• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Addressing the Non-perturbative Regime of the Quantum Anharmonic Oscillator by Physics-Informed Neural Networks
• Using a Feedback-Based Quantum Algorithm to Analyze the Critical Properties of the ANNNI Model Without Classical Optimization
• Counterdiabatic Route to Entanglement Steering and Dynamical Freezing in the Floquet Lipkin-Meshkov-Glick Model
• Counterdiabatic Driving with Performance Guarantees
• A spectrum-based shortcut method for topological systems
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Digitized counterdiabatic quantum critical dynamics
• Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes