On quantum multi-Hamiltonian systems

Mich�le Irac-Astaud, Guy Rideau

Jincheng Zhang

Quantum multi-particle systems pose significant challenges in modeling and understanding complex phenomena. Traditional Hamiltonian approaches often struggle to accurately capture the dynamic behavior of such systems, particularly when interactions are variable. This paper introduces a novel approach, utilizing an adaptive Hamiltonian description, to address this challenge. We formulate a new framework for dynamically adjusting the Hamiltonian based on the relative strengths and directions of interactions, resulting in a more efficient and accurate representation of the system's dynamics. This design enhances our ability to predict and control the behavior of quantum multi-particle systems, offering a significant step towards improved simulation and analysis.

Shuang Cong, Fangfang Meng

In closed quantum systems, if controlled systems are not strongly regular or there exists at least one eigenstate that is directly uncoupled to the target state, then such systems control will become degenerate cases. This paper proposes a quantum control method designed by an implicit Lyapunov function to transfer states of the quantum systems in these two degenerate cases, especially the method proposed is suitable for multi-control Hamiltonian systems. The state distance is selected as the Lyapunov function in this paper. Numerical simulation experiments on a 4-level system are done, and the experiment results indicate the effectiveness of the implicit Lyapunov control method proposed for degenerate cases and multi-control Hamiltonians.

Sonia G. Schirmer

Valerij V. Kozlov, Oleg Georgievich Smolyanov

Haftu W. Fentaw, Steve Campbell, Simon Caton

We present a Multi-task Soft Actor-Critic (SAC) Reinforcement Learning framework designed for open-system quantum control across diverse Hamiltonians, which learns optimal pulse sequences while simultaneously discovering problem-specific evolution time T and number of control pulse segments N. Experimental results across 51 Hamiltonian variations demonstrate that the multi-task SAC model is able to generate control pulses that can drive a system, under environment noise, from its initial state to its target state with high fidelities, establishing essential foundations for universal quantum control applicable to realistic noisy quantum devices. Through progressive expansion of the training Hamiltonian set, we investigate if a single multi-task model trained using a given number of sample Hamiltonians can successfully accomplish state-transfer tasks for Hamiltonians drawn from the same Hamiltonian space but not encountered during training. In addition, our Robustness Infidelity Measure (RIM) analysis reveals that SAC trained policies exhibit superior robustness to pulse amplitude perturbations and decoherence rate variations compared to GRAPE-optimized controls.