Quantum State Transfer Optimization: Balancing Fidelity and Energy Consumption using Pontryagin Maximum Principle
- Resource Type
- Conference
- Authors
- Dehaghani, Nahid Binandeh; Aguiar, A. Pedro
- Source
- 2023 IEEE 11th International Conference on Systems and Control (ICSC) Systems and Control (ICSC), 2023 IEEE 11th International Conference on. :94-99 Dec, 2023
- Subject
- Aerospace
Bioengineering
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Computing and Processing
Engineering Profession
General Topics for Engineers
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Quantum system
Energy consumption
Optimal control
Quantum state
Mathematical models
Vectors
Trajectory
- Language
- ISSN
- 2379-0067
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.