Gradient projection method for constrained quantum control

• URL: http://arxiv.org/abs/2411.19644v1
• Date: Fri, 29 Nov 2024 11:56:55 GMT
• Title: Gradient projection method for constrained quantum control
• Authors: Oleg Morzhin, Alexander Pechen,
• Abstract summary: We adopt the Gradient Projection Method (GPM) to problems of quantum control. The main advantage of the method is that it allows to exactly satisfy the bounds. We apply the GPM to several examples including generation of one- and two-qubit gates and two-qubit Bell and Werner states.
• Score: 50.24983453990065
• License:
• Abstract: In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-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.

Related papers

• Gate generation for open quantum systems via a monotonic algorithm with time optimization [0.0]
  We present a monotonic numerical algorithm for generating quantum gates for open systems. Preliminary implementations indicate that this algorithm is well suited for cat-qubit gates.
  arXiv  Detail & Related papers  (2024-03-29T07:43:29Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• Hamiltonian Switching Control of Noisy Bipartite Qubit Systems [7.094462708097975]
  We develop a Hamiltonian switching ansatz for bipartite control inspired by the Quantum Approximate Optimization Algorithm (QAOA) We demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols.
  arXiv  Detail & Related papers  (2023-04-11T20:12:57Z)
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls [77.34726150561087]
  State preparation is important for optimal control of two-qubit quantum systems. We exploit two physically different coherent control and optimize the Hilbert-Schmidt target density matrices.
  arXiv  Detail & Related papers  (2023-04-03T10:22:35Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls [77.34726150561087]
  The article considers a two-level open quantum system governed by the Gorini--Kossakowski--Lindblad--Sudarshan master equation. The system is analyzed using Bloch parametrization of the system's density matrix.
  arXiv  Detail & Related papers  (2021-06-18T14:23:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.