Pdf quantum feedback for measurement and control semantic. We showed that it is possible to harness measurement backaction as a form of actuation in quantum control, and thus we describe a valuable tool for quantum information science. However, two key points distinguish quantum feedback control. We explain how feedback in quantum systems differs from that in traditional classical systems, and how. Experimental feedback control of quantum systems using weak. Femtosecond pulses tailored by a computercontrolled acoustooptic pulse shaper excite fluorescence from laser dye molecules in solution. In this paper we consider the problem of feedback control at the quantum limit. Finally, we combine the theoretical focus on quantum feedback with the experimental capabilities of superconducting circuits to implement a feedback controlled quantum amplifier. It is widely believed that quantum physics is a fundamental theory describing the universe. Quantum feedback for quantum technology white rose.
Just as in the classical case, feedback occurs when outputs from the system are used as inputs that control the dynamics e. Quantum systems are dynamical systems in this sense control theory applies directly to quantum systems however, two key points distinguish quantum feedback control 1. The eigenstates of the quantum system are defined by the spin model. Feedback loops are central to most classical control procedures. The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. Quantum coherent feedback control for generation system of. Our scheme bath control system source system bath control. Error correction of quantum system dynamics via measurement. Quantum feedback in cavity qed workshop on quantum control, 2010. In reality however, no physical process can occur over a truly infinitesimal time interval.
Quantum feedback for quantum technology white rose etheses. As such, one would expect to be able to see how classical physics that is observed in the macroscopic world emerges from quantum theory. As of the time of this writing, there are no textbooks available on this important subject of closed loop quantum control. We describe the application of stateobserverbased control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a. Quantum feedback or quantum feedback control is a class of methods to prepare and. Thus, the problem of optimal quantum feedback control was separated into quantum ltering which provides optimal estimates of.
Circuit qed is a promising solidstate quantum computing architecture. We will look at the formulation of quantum feedback control theory for continuously observed open quantum systems in a manner that highlights both the similarities and di. Entanglementassisted quantum feedback control springerlink. The low quality of this measurement makes the implementation of. The resulting system is capable of adaptive measurement, which we use to perform the first canonical phase measurement. Realtime quantum feedback control 1 often involves timecontinuous measurements of a quantum state followed by control of a physical system with.
Measurement induces noisy and nonlinear dynamics these differences also lead to new applications whats different about. We aim to teach the reader the fundamental theory in quantum measurement and control. In recent years, quantum control theory has been widely used in various protocols of quantum optics research. The random quantum backaction of adaptive measurements can be used to control a quantum system two purely quantum effects the dynamics introduced by quantum measurements the quantum backaction leads to some remarkable effects. Hopkins and hideo mabuchi, quantum filter reduction for measurementfeedback control via unsupervised manifold learning, new j. Since belavkin had derived quantum continuous measurements as an extension of the theory of classical continuous measurements, where the latter are used heavily in control theory, it was natural for him to consider the application of continuous measurements to feedback control of quantum systems, and to consider adapting the techniques from. Sorensen et alcomparison of squashing and selfconsistent. Nondemolition measurement and control in quantum dynamical systems. This thesis aims to show how open quantum systems naturally contain correlations from their quantum nature. This has so far largely eluded physicists, due to the inherent linear nature of quantum physics and the nonlinear behaviour of classical physics. Information, disturbance and hamiltonian quantum feedback control.
Quantum feedback control qfc plant controll control er laws measurem ent informat ion measurementbased qfc controll er control actions informat ion classical existing models are not applicable to nonmarkovian open quantum systems. Applications of feedback control in quantum systems. Phd tutorial using feedback for coherent control of quantum. Quantum feedback for rsp in the presence of control imperfections joshua combes and howard m wisemanrecent citations spontaneous symmetry breaking induced by quantum monitoring luis pedro garciapintos et alquantum control with measurements and quantum zeno dynamics j. In a fully quantum mechanical feedback control theory the quantum dynamics of the system and the backaction of measurements must both be taken into account. Introduction a major goal in chemical physics since the invention of the laser has been to move from observing to controlling. First, a gradientbased control law is computed using schroodingers description. This paper will discuss both measurement feedback and coherent feedback control for quantum systems. We introduce and discuss the problem of quantum feedback control in the.
Indeed, developments in quantum technology provide strong motivation for the feedback control of quantum systems. Pdf highfidelity measurement and quantum feedback control. Feedback can be used to increase the speed at which the. Quantum feedback or quantum feedback control is a class of methods to prepare and manipulate a quantum system in which that systems quantum state or trajectory is used to evolve the system towards some desired outcome.
The principles of quantum optimal control introduced in part i are extended to the derivation of closed loop control laws in part ii. The nonmeasurement based coherent feedback control cfc is a control. The system considered is a general linear dynamical quantum system, where the control goal can be. Generalizing this approach to quantum states is complicated by the fact that sensor measurements of. We then consider quantum filtering and measurement feedback optimal control for a twolevel quantum system. Realtime feedback performed during a quantum nondemolition measurement of atomic spinangular momentum allowed us to influence the quantum statistics of the measurement outcome. Pdf feedback control of quantum state reduction hideo. Arc centre for quantum computation and communication technology.
Quantum feedback in optics has been proposed and studied earliersee, e. In a fully quantum mechanical feedback control theory the quantum dynamics of the system andthe backactionofmeasurementsmust bothbe taken into account. Pdf quantum feedback control and classical control theory. Moreover, even seemingly simple open quantum systems can behave far more complexly than expected upon the introduction of quantum feedback. The sp ectr al the or em for a self a dj o in t op erat or a sa y s tha t. The classical measurement results are used by the controller e. Quantum feedback control of a solidstate twolevel system rusko ruskov. In this paper, we will study the operation of a feedback loop proposed in ref. The major theoretical challenge of extending feedback control to the quantum mechanical regime is to describe. Introduction in quantum feedback control qfc, an observer continuously monitors a quantum system 1,2, and uses the information from this measurement, as it is obtained, to control the system by continually modifying the hamiltonian andor the observable.
Information, disturbance and hamiltonian quantum feedback. Pdf quantum feedback control and classical control. Circuitqed and quantum feedback control by hanhan li doctor of philosophy in physics university of california, berkeley professor birgitta whaley, cochair associate professor irfan siddiqi, cochair quantum computation and quantum information are an emerging research eld that involves both physics, computer science, and engineering. Before we examine such examples however, it is worth presenting the general equations which describe feedback control in quantum systems, in analogy to those for classical systems. Feedback control is invaluable in macroscopic applications, and as a consequence there is a vast body of literature devoted to classical feedback control. A gradientbased approach to feedback control of quantum. This procedure is used even if the information is not realized in a measurement 12, but is passed directly to a. Cavity qed quantum feedback scheme state injection goal. A tutorial introduction to quantum feedback control ieee xplore. Bayesian quantum feedback control of a qubit qubit h e detector bayesian equations it control stage barrier height. It also has excellent potential as a platform for quantum control especially quantum feedback control experiments. Feedback quantum control of molecular electronic population. A more subtle investigation of open quantum systems lead to the theory of continuous. Classical feedback control the classical dynamical system to be controlled has a set of input variables, which are processed by the system dynamics into a set of output variables.
In this sense control theory applies directly to quantum systems. The control of individual quantum systems promises a new technology for the 21st century quantum technology. Coherent control, feedback, ultrafast, quantum state preparation, learning algorithm some. Realtime quantum feedback prepares and stabilizes photon. An introduction to quantum control anu college of engineering. In this paper, we propose an analogous method utilizing entanglement for the purpose of feedback control. No quantum measurement can give full information on the state of a quantum system.
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. Next, an estimate of state of the quantum system is obtained using lindblads differential. Recent theoretical and experimental advances mean that it is now possible to control physical systems at the quantum level. The major theoretical challenge of extending feedback. Feedback control is traditionally realized by applying deterministic forces to a system for example, by modifying the hamiltonian in response to information obtained. To sidestep such restrictions, one can always combine measurement with feedback for quantum system control 4755. Stabilizing feedback controls for quantum systems siam. However, they are not the only way in which correlations are created in quantum systems.
Applications of feedback control in quantum systems arxiv. Continuous quantum error correction via quantum feedback. Quantum feedback control of a solidstate twolevel system. Quantum feedback for preparation and protection of quantum. Experimental feedback control of quantum systems using. Phd tutorial using feedback for coherent control of.
Laur996719 quantum feedback control and classical control. In information complexity and control in quantum systems 3129, springerverlag, wien 1987. Quantum enhanced feedback cooling of a mechanical oscillator. Quantum control has already led to significant improvements in technologies ranging from magnetic resonance to prototype quantum computers, from quantum highprecision sensors to quantum logic clocks, from single atom transistors to quantum noise suppression in gravitation wave detectors. Generalizing this approach to quantum states is complicated by the fact that sensor measurements of the output cause a random back.
In this paper, a gradientbased approach to the control of quantum systems will be examined. Nov 29, 2016 realtime quantum feedback control 1 often involves timecontinuous measurements of a quantum state followed by control of a physical system with the aim of steering that system into a desired. It also has excellent potential as a platform for quantum controlespecially quantum feedback controlexperiments. Steering the trapped microwave field harmonic oscillator to a desired quantum state preserving this state from decoherence elements of feedback loop quantum measurement. Microscopically justify classical feedback schemes. An introduction to control theory from classical to. Jun 27, 2012 the paper proposes a gradient method for feedback control and stabilization of quantum systems using schroodingers and lindblads descriptions. If we are to apply the concepts and methods of feedback control theory to quantum dynamical systems, we must not only extend classical control concepts to new. Quantum feedback control outputs feedback controller dynamical inputs system measurement errors external perturbations, parametric drifts, and uncertainties figure 1. Realtime quantum feedback control of atomic spinsqueezing. This paper presents a survey on quantum control theory and applications from a control systems perspective.
For instance, conceptual guidance is developed to maintain quantum. The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. Theory of the control of observable quantum systems. Quantum feedback control and classical control theory. Tw o imp orta n t typ es o f nor mal op erat ors are selfadjoint a a. However, the current scheme for measurement in circuit qed is low efficiency and has low signaltonoise ratio for singleshot measurements.
633 491 801 1486 1078 840 1142 675 966 233 755 589 1137 1347 1118 1015 939 882 99 551 486 322 981 595 1081 29 438 608 505 754 496 1233 148 1031 811 285 621 973 1437 588 1480 1055 955 417 1388 1248 840 974 540 1407