Quantum control theory and applications: A survey

This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective, some references are added, published versio

A scalable hardware and software control apparatus for experiments with hybrid quantum systems

Modern experiments with fundamental quantum systems - like ultracold atoms, trapped ions, single photons - are managed by a control system formed by a number of input/output electronic channels governed by a computer. In hybrid quantum systems, where two or more quantum systems are combined and made to interact, establishing an efficient control system is particularly challenging due to the higher complexity, especially when each single quantum system is characterized by a different timescale. Here we present a new control apparatus specifically designed to efficiently manage hybrid quantum systems. The apparatus is formed by a network of fast communicating Field Programmable Gate Arrays (FPGAs), the action of which is administrated by a software. Both hardware and software share the same tree-like structure, which ensures a full scalability of the control apparatus. In the hardware, a master board acts on a number of slave boards, each of which is equipped with an FPGA that locally drives analog and digital input/output channels and radiofrequency (RF) outputs up to 400 MHz. The software is designed to be a general platform for managing both commercial and home-made instruments in a user-friendly and intuitive Graphical User Interface (GUI). The architecture ensures that complex control protocols can be carried out, such as performing of concurrent commands loops by acting on different channels, the generation of multi-variable error functions and the implementation of self-optimization procedures. Although designed for managing experiments with hybrid quantum systems, in particular with atom-ion mixtures, this control apparatus can in principle be used in any experiment in atomic, molecular, and optical physics.Comment: 10 pages, 12 figure

Quantum Information with Continuous Variable systems

This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its structural mathematical description makes them much more amenable than any other CV system. Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control. Nevertheless, it is known that in spite of their exceptional role within the space of all Continuous Variable states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus non-Gaussian states emerge as potentially good candidates for communication and computation purposes.Comment: PhD Thesis in Universitat Autonoma de Barcelona. Published by the Lambert Academic Publishing (LAP) on March 18, 2011. ISBN-13: 978-3-8443-1948-

Geometrical versus time-series representation of data in quantum control learning

Recently machine learning techniques have become popular for analysing physical systems and solving problems occurring in quantum computing. In this paper we focus on using such techniques for finding the sequence of physical operations implementing the given quantum logical operation. In this context we analyse the flexibility of the data representation and compare the applicability of two machine learning approaches based on different representations of data. We demonstrate that the utilization of the geometrical structure of control pulses is sufficient for achieving high-fidelity of the implemented evolution. We also demonstrate that artificial neural networks, unlike geometrical methods, posses the generalization abilities enabling them to generate control pulses for the systems with variable strength of the disturbance. The presented results suggest that in some quantum control scenarios, geometrical data representation and processing is competitive to more complex methods.Comment: 12 pages, 14 figures, Python code available upon the reques

Spatially dependent electromagnetically induced transparency

Recent years have seen vast progress in the generation and detection of structured light, with potential applications in high capacity optical data storage and continuous variable quantum technologies. Here we measure the transmission of structured light through cold rubidium atoms and observe regions of electromagnetically induced transparency (EIT). We use q-plates to generate a probe beam with azimuthally varying phase and polarisation structure, and its right and left circular polarisation components provide the probe and control of an EIT transition. We observe an azimuthal modulation of the absorption profile that is dictated by the phase and polarisation structure of the probe laser. Conventional EIT systems do not exhibit phase sensitivity. We show, however, that a weak transverse magnetic field closes the EIT transitions, thereby generating phase dependent dark states which in turn lead to phase dependent transparency, in agreement with our measurements.Comment: 5 Pages, 5 Figure

Weak Markov Processes as Linear Systems

A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out systematically and some quantum mechanical interpretations are given. We introduce subprocesses and quotient processes and then the notion of a $\gamma$-extension for processes which leads to a complete classification of all the ways in which processes can be built from subprocesses and quotient processes. We show that within a $\gamma$-extension we have a cascade of noncommutative Fornasini-Marchesini systems. We study observability in this setting and as an application we gain new insights into stationary Markov chains where observability for the system is closely related to asymptotic completeness in a scattering theory for the chain.Comment: Expanded version v2 (43 pages) with substantial additions and improvements compared to v1. More details and examples, in particular in sections 3, 4 and 7. Also changes in terminology, compare Def. 3.1, 4.2, 6.4, page 33. To appear in the journal: Mathematics of Control, Signals, and Systems (MCSS

A Direct Coupling Coherent Quantum Observer for a Single Qubit Finite Level Quantum System

This paper considers the problem of constructing a direct coupling quantum observer for a single qubit finite level quantum system plant. The proposed observer is a single mode linear quantum system which is shown to be able to estimate one of the plant variables in a time averaged sense. A numerical example and simulations are included to illustrate the properties of the observer.Comment: A preliminary version of this paper has been accepted to appear in the 2014 Australian Control Conferenc

Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.Comment: 33 pages, 7 figures; accepted for publication in IEEE Transactions on Automatic Control, October 201

Quantum Control Landscapes

Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum systems despite the expense of solving the Schrodinger equation in simulations and the complicating effects of environmental decoherence in the laboratory. Recent work indicates that this simplicity originates in universal properties of the solution sets to quantum control problems that are fundamentally different from their classical counterparts. Here, we review studies that aim to systematically characterize these properties, enabling the classification of quantum control mechanisms and the design of globally efficient quantum control algorithms.Comment: 45 pages, 15 figures; International Reviews in Physical Chemistry, Vol. 26, Iss. 4, pp. 671-735 (2007