ar X iv : 0 71 1 . 25 51 v 1 [ qu an t - ph ] 1 6 N ov 2 00 7 Coherent Quantum LQG Control ∗ Hendra
نویسندگان
چکیده
Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum. Such a control scheme is often referred to in the quantum control literature as “coherent control.” It distinguishes the present work from previous works on the quantum LQG problem where measurement is performed on the plant and the measurement signals are used as input to a fully classical controller with no quantum degrees of freedom. The difference in our formulation is the presence of additional non-linear and linear constraints on the coefficients of the sought after controller, rendering the problem as a type of constrained controller design problem. Due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard LQG problem. We propose a numerical procedure for solving this problem based on an alternating projections algorithm and, as initial demonstration of the feasibility of this approach, we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained. For comparison, we also consider the case of classical controllers which use direct or indirect measurements, and show that fully quantum controllers can offer an improvement in performance over the classical ones.
منابع مشابه
ar X iv : 0 71 0 . 34 25 v 2 [ qu an t - ph ] 1 4 N ov 2 00 7 Properties of the residual entanglement for n - qubits 1
X iv :0 71 0. 34 25 v2 [ qu an tph ] 1 4 N ov 2 00 7 Properties of the residual entanglement for n-qubits Dafa Li, Xiangrong Li, Hongtao Huang, Xinxin Li a Dept of mathematical sciences, Tsinghua University, Beijing 100084 CHINA b Department of Mathematics, University of California, Irvine, CA 92697-3875, USA c Electrical Engineering and Computer Science Department University of Michigan, Ann A...
متن کاملar X iv : 0 71 1 . 35 78 v 1 [ qu an t - ph ] 2 2 N ov 2 00 7 A formula for the spectral projection of the time operator
In this paper, we study the one-level Friedrichs model with using the quantum time super-operator that predicts the excited state decay inside the continuum. Its survival probability in long time limit is an algebraically decreasing function and an exponentially decreasing multiplied by the oscillating functions.
متن کاملar X iv : 0 71 0 . 18 02 v 2 [ qu an t - ph ] 1 2 N ov 2 00 7 A complex periodic QES potential and exceptional points
We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 3, it may lead to exceptional points depending upon the strength of the coupling parameter ξ. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of...
متن کاملar X iv : 0 71 1 . 41 28 v 1 [ m at h - ph ] 2 6 N ov 2 00 7 Mean field limit for bosons and infinite dimensional phase - space analysis
This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007