Coherent quantum LQG control

By Hendra Ishwara Nurdin, Matthew R. James, Ian R. Petersen. at - Automatisierungstechnik, 2007

302 citations recorded by the source corpus.

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 feedback 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 the 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 an 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 linear controllers that use direct or indirect measurements, and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9b630608e7f5918e763c3a0e4407ff35310b5824

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Franco Nori
2. Yu-xi Liu
3. Jing Zhang
4. Kurt Jacobs
5. C. Bian
6. Guofeng Zhang
7. Re-Bing Wu
8. Sahel Ashhab

In Atomic and Molecular Physics, and Optics

1. Yu-xi Liu
2. Franco Nori
3. Jing Zhang
4. Re-Bing Wu
5. Kurt Jacobs
6. C. Bian
7. Guofeng Zhang
8. Sahel Ashhab

Citations in the corpus

• Quantum control theory and applications: A survey (2009, unknown): “The controller may be a classical controller [162] or a quantum controller [158], [159].”
• LQG/H∞ control of linear quantum stochastic systems (2015, methodology): “Theorem 2 (Quantum LQG control [5]): There exists a proper, real-rational controller K which solves Problem 1 for given ΘK and γl > 0 if and only if there exist AK , BK1, BK2, BK3, CK , symmetric matrix PL = S−1 L and Q such that the equality constraints (14) and inequality constraints (15) hold.”
• Quantum feedback: theory, experiments, and applications (2014, background): “ze the eect of a set of inputs on a set of outputs. For linear networks, this problem has been studied by a number of authors. James, Nurdin, and Petersen developed linear-quadratic-Gaussian control [90] and H-infinity (H 1) control [84]. Control of linear systems with squeezers and phase-shifters ha”