2015/02/01 by Arash Kh. Sichani, Sichani, Arash Kh., Igor G. Vladimirov +3 · 1 citation
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.1502.00274
This paper is concerned with the Coherent Quantum Linear Quadratic Gaussian\n(CQLQG) control problem of finding a stabilizing measurement-free quantum\ncontroller for a quantum plant so as to minimize an infinite-horizon mean\nsquare performance index for the fully quantum closed-loop system. In\ncomparison with the observation-actuation structure of classical controllers,\nthe coherent quantum feedback is less invasive to the quantum dynamics and\nquantum information. Both the plant and the controller are open quantum systems\nwhose dynamic variables satisfy the canonical commutation relations (CCRs) of a\nquantum harmonic oscillator and are governed by linear quantum stochastic\ndifferential equations (QSDEs). In order to correspond to such oscillators,\nthese QSDEs must satisfy physical realizability (PR) conditions, which are\norganised as quadratic constraints on the controller matrices and reflect the\npreservation of CCRs in time. The CQLQG problem is a constrained optimization\nproblem for the steady-state quantum covariance matrix of the plant-controller\nsystem satisfying an algebraic Lyapunov equation. We propose a gradient descent\nalgorithm equipped with adaptive stepsize selection for the numerical solution\nof the problem. The algorithm finds a local minimum of the LQG cost over the\nparameters of the Hamiltonian and coupling operators of a stabilizing PR\nquantum controller, thus taking the PR constraints into account. A convergence\nanalysis of the proposed algorithm is presented. A numerical example of a\nlocally optimal CQLQG controller design is provided to demonstrate the\nalgorithm performance.\n