Year: 2025
Type: article
Abstract: We present a novel derivation of the Quantum Optimal Control Theory (QOCT). First, we identify the QOCT equations as the Euler-Lagrange equations of the functional associated to the control scheme considering a general window function that accounts for the measurement process. In this framework, we prove that the extremal functions found by Peirce et al. [Phys. Rev. A 37, 4950 (1988)], can be obtained using the well-established theory of variations with appropriately chosen boundary conditions. Second, we derive the QOCT canonical equations to maximize an observable at a given time T by taking the limit of an infinite narrow window function, that is, a delta distribution. We show that the costate is discontinuous and vanishes after the measurement time. Finally, we illustrate the convergence to the limiting case with numerical computations on a spin-chain Heisenberg model.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0266880
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416948377