Quantum State Transfer Optimization: Balancing Fidelity and Energy Consumption using Pontryagin Maximum Principle

We address a control-constrained optimal control problem pertaining to the transformation of quantum states. Our objective is to steer a quantum system from an initial state to a desired target state while adhering to the principles of the Liouville-von Neumann equation. To achieve this, we introduc...

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Veröffentlicht in:International Conference on Systems and Control (Print) S. 94 - 99
Hauptverfasser: Dehaghani, Nahid Binandeh, Aguiar, A. Pedro
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 18.12.2023
Schlagworte:
Energy consumption
Mathematical models
Optimal control
Quantum state
Quantum system
Trajectory
Vectors
ISSN:2379-0067
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Zusammenfassung:We address a control-constrained optimal control problem pertaining to the transformation of quantum states. Our objective is to steer a quantum system from an initial state to a desired target state while adhering to the principles of the Liouville-von Neumann equation. To achieve this, we introduce a cost functional that balances the dual goals of fidelity maximization and energy consumption minimization. We derive optimality conditions in the form of the Pontryagin Maximum Principle (PMP) for the matrix-valued dynamics associated with this problem. Subsequently, we present a time discretized computational scheme designed to solve the optimal control problem. This computational scheme is rooted in an indirect method grounded in the PMP, showcasing its versatility and efficacy. To illustrate the practicality and applicability of our methodology, we employ it to address the case of a spin ½ particle subjected to interaction with a magnetic field. Our findings shed light on the potential of this approach to tackle complex quantum control scenarios and contribute to the broader field of quantum state transformations.
ISSN:2379-0067
DOI:10.1109/ICSC58660.2023.10449792