Gradient projection method for constrained quantum control
arXiv:2411.19644 · doi:10.1088/1751-8121/adbe1a
Abstract
In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general -level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and provide the projection versions of the Pontryagin maximum principle and the GPM, all directly in terms of quantum objects such as evolution operator, Hamiltonians, density matrices, etc. Various forms of the GPM, including one- and two-step, are provided and compared. We formulate the GPM both for closed and open quantum systems, latter for the general case with simultaneous coherent and incoherent controls. The GPM is designed to perform local gradient based optimization in the case when bounds are imposed on the controls. The main advantage of the method is that it allows to exactly satisfy the bounds, in difference to other approaches such as adding constraints as weight to objective. We apply the GPM to several examples including generation of one- and two-qubit gates and two-qubit Bell and Werner states for models of superconducting qubits under the constraint when controls are zero at the initial and final times, and steering an open quantum system state to a target density matrix for simulating action of the Werner-Holevo channel, etc.
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References in corpus (29)
- Control of quantum phenomena: Past, present, and future
- Generalized Simulated Annealing
- Optimal control technique for Many Body Quantum Systems dynamics
- Chopped random-basis quantum optimization
- Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
- Second order gradient ascent pulse engineering
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Counterexample to an additivity conjecture for output purity of quantum channels
- Optimal control of open quantum systems: cooperative effects of driving and dissipation
- Communication at the quantum speed limit along a spin chain
- Protocol for universal gates in optimally biased superconducting qubits
- Teaching the Environment to Control Quantum Systems
- Time-optimal control of SU(2) quantum operations
- Optimal control theory for a unitary operation under dissipative evolution
- Global optimization of quantum dynamics with AlphaZero deep exploration
- Protecting coherence in Optimal Control Theory: State dependent constraint approach
- Engineering arbitrary pure and mixed quantum states
- Hybrid Optimization Schemes for Quantum Control
- GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls
- Optimal control under spectral constraints: Enforcing multi-photon absorption pathways
- Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls
- Energy control in a quantum oscillator using coherent control and engineered environment
- Mitigating controller noise in quantum gates using optimal control theory
- The noisy Werner-Holevo channel and its properties
- Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives
- Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving
- Time-optimal state transfer for an open qubit
- Optimal solutions to quantum annealing using two independent control functions
- Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System