No Arabic abstract
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 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 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.
In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of motion for the dynamics itself--rather than the state. Here we develop a Markovian master equation for the process matrix of an open system, which resembles the Lindblad Markovian master equation. We employ this equation to introduce a scheme for optimal local coherent process control at target times, and extend the Krotov technique to obtain optimal control. We illustrate utility of this framework through several quantum coherent control scenarios, such as optimal decoherence suppression, gate simulation, and passive control of the environment, in all of which we aim to simulate a given terminal process at a given final time.
This paper considers the application of integral Linear Quadratic Gaussian (LQG) optimal control theory to a problem of cavity locking in quantum optics. The cavity locking problem involves controlling the error between the laser frequency and the resonant frequency of the cavity. A model for the cavity system, which comprises a piezo-electric actuator and an optical cavity is experimentally determined using a subspace identification method. An LQG controller which includes integral action is synthesized to stabilize the frequency of the cavity to the laser frequency and to reject low frequency noise. The controller is successfully implemented in the laboratory using a dSpace DSP board.
We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed.
We present a Heisenberg operator based formulation of coherent quantum feedback and Pyragas control. This model is easy to implement and allows for an efficient and fast calculation of the dynamics of feedback-driven observables as the number of contributing correlations grows in systems with a fixed number of excitations only linearly in time. Furthermore, our model unravels the quantum kinetics of entanglement growth in the system by explicitly calculating non-Markovian multi-time correlations, e.g., how the emission of a photon is correlated with an absorption process in the past. Therefore, the time-delayed differential equations are expressed in terms of insightful physical quantities. Another considerate advantage of this method is its compatibility to typical approximation schemes, such as factorization techniques and the semi-classical treatment of coherent fields. This allows the application on a variety of setups, ranging from closed quantum systems in the few excitation regimes to open systems and Pyragas control in general.