Showing papers by "Ian R. Petersen published in 2016"
TL;DR: In this article, an online optimization process based on machine learning is applied to the production of Bose-Einstein condensates (BEC), which is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely suboptimal for real experiments.
Abstract: We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ‘learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.
165 citations
TL;DR: In this article, the authors present a survey of recent results on the theory of quantum linear systems and present them within a unified framework for coherent feedback control, referred to as coherent quantum feedback control.
Abstract: This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). Such sys- tems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or ap- proximated by linear QSDEs include interconnections of optical cavities, beam-spitters, phase-shifters, optical parametric am- plifiers, optical squeezers, and cavity quantum electrodynamic systems. With advances in quantum technology, the feedback control of such quantum systems is generating new challenges in the field of control theory. Potential applications of such quantum feedback control systems include quantum computing, quantum error correction, quantum communications, gravity wave detection, metrology, atom lasers, and superconducting quantum circuits. A recently emerging approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient imple- mentation. This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case. An important issue which arises both in the modelling of linear quantum systems and in the synthesis of linear coherent quantum controllers is the issue of physical realizability. This issue relates to the property of whether a given set of QSDEs corresponds to a physical quantum system satisfying the laws of quantum mechanics. The paper will cover recent results relating the question of physical realizability to notions occuring in linear systems theory such as lossless bounded real systems and dual J-J unitary systems.
97 citations
TL;DR: An effective two-step optimization (TSO) QHI algorithm is developed within the framework of quantum process tomography, and several numerical examples demonstrate the effectiveness of the proposed TSO Hamiltonian identification method.
Abstract: Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum Hamiltonian identification algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are inputted into quantum systems and the output states are estimated using the quantum state tomography protocol via linear regression estimation. The time-independent system Hamiltonian is reconstructed based on the experimental data for the output states. The Hamiltonian identification method has computational complexity O(d^6) where d is the dimension of the system Hamiltonian. An error upper bound O(d^3/N^(1/2))$ is also established, where N is the resource number for the tomography of each output state, and several numerical examples demonstrate the effectiveness of the proposed TSO Hamiltonian identification method.
70 citations
TL;DR: It is shown that the proposed Bayesian inference approach provides a convenient tool to simultaneously derive the fault tolerant quantum filter and the fault detection equation for this class of open quantum systems.
54 citations
TL;DR: In this paper, a master-equation based approach to drive a quantum network with $n$ qubits to a consensus (symmetric) state introduced by Mazzarella et al. is proposed.
Abstract: In this paper, we propose and study a master-equation based approach to drive a quantum network with $n$ qubits to a consensus (symmetric) state introduced by Mazzarella et al. The state evolution of the quantum network is described by a Lindblad master equation with the Lindblad terms generated by continuous-time swapping operators, which also introduce an underlying interaction graph. We establish a graphical method that bridges the proposed quantum consensus scheme and classical consensus dynamics by studying an induced graph (with $2^{2n}$ nodes) of the quantum interaction graph (with $n$ qubits). A fundamental connection is then shown that quantum consensus over the quantum graph is equivalent to componentwise classical consensus over the induced graph, which allows various existing works on classical consensus to be applicable to the quantum setting. Some basic scaling and structural properties of the quantum induced graph are established via combinatorial analysis. Necessary and sufficient conditions for exponential and asymptotic quantum consensus are obtained, respectively, for switching quantum interaction graphs. As a quantum analogue of classical synchronization of coupled oscillators, quantum synchronization conditions are also presented, in which the reduced states of all qubits tend to a common trajectory.
53 citations
TL;DR: The paper concentrates on the application of negative imaginary systems theory in the area of control of atomic force microscopes.
50 citations
TL;DR: Numerical results show that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gates.
Abstract: Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results show that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gates.
44 citations
TL;DR: This paper is concerned with the negative imaginary synthesis problem for linear time-invariant systems by output feedback control, and the separation principle is shown to be valid for the observer-based design.
43 citations
TL;DR: In this paper, a sampling-based learning method was employed to find robust control pulses for generating a set of universal quantum gates, and the results showed that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gate.
Abstract: Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results show that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gates.
34 citations
Posted Content•
TL;DR: This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case, and discusses the issue of physical realizability.
Abstract: This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). Such systems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or approximated by linear QSDEs include interconnections of optical cavities, beam-spitters, phase-shifters, optical parametric amplifiers, optical squeezers, and cavity quantum electrodynamic systems. With advances in quantum technology, the feedback control of such quantum systems is generating new challenges in the field of control theory. Potential applications of such quantum feedback control systems include quantum computing, quantum error correction, quantum communications, gravity wave detection, metrology, atom lasers, and superconducting quantum circuits.
A recently emerging approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case. An important issue which arises both in the modelling of linear quantum systems and in the synthesis of linear coherent quantum controllers is the issue of physical realizability. This issue relates to the property of whether a given set of QSDEs corresponds to a physical quantum system satisfying the laws of quantum mechanics.
31 citations
TL;DR: It is established that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, and it is shown that generic real square matrices of even dimension can be transformed into a lower 2×2 block triangular form by a symplectic similarity transformation.
TL;DR: This technical note studies the negative imaginary properties of descriptor linear systems based on state-space realizations using a multiple-input and multiple-output RLC circuit network as an illustrative example to validate the developed theory.
Abstract: This technical note studies the negative imaginary properties of descriptor linear systems based on state-space realizations. Under the assumption of a minimal realization, necessary and sufficient conditions are established to characterize the negative imaginary properties of descriptor systems in terms of linear matrix inequalities with equality constraints. In particular, a negative imaginary lemma, a strict negative imaginary lemma and a lossless negative imaginary lemma are developed. A multiple-input and multiple-output RLC circuit network is used as an illustrative example to validate the developed theory.
TL;DR: The purpose of this paper is to address the problem of physical realizability for $n$-level quantum systems by providing necessary and sufficient conditions for quantum stochastic differential equilibria.
Abstract: The purpose of this paper is to address the problem of physical realizability for $n$-level quantum systems. We provide necessary and sufficient conditions for quantum stochastic differential equat...
TL;DR: It is proved that there always exists such a coherent quantum observer described by quantum stochastic differential equations in the Heisenberg picture, and it is shown that considering a joint plant-observer Gaussian quantum system, entanglement can be generated under the condition that appropriate coefficients of the coherent Quantum observer are chosen.
TL;DR: The stability of linear threshold dynamic neural networks is studied, and a series of methods to obtain globally attractive sets is proposed, including a sufficient condition to judge whether an invariant set is a globally attractive set.
Abstract: The stability of linear threshold dynamic neural networks is studied, and a series of methods to obtain globally attractive sets is proposed. A sufficient condition to judge whether an invariant set is a globally attractive set is also proposed. This method requires only the solution to a class of linear matrix inequalities. Also, two direct methods to obtain globally attractive sets are given. The stability criteria presented are based on the proposed globally attractive sets. Some numerical examples are given to illustrate the effectiveness of the obtained results.
TL;DR: In this paper, the authors proposed a sampled data design method for robust control of open two-level quantum systems with operator errors, characterised using the concept of a sliding mode domain related to fidelity, coherence or purity.
Abstract: This study proposes a sampled-data design method for robust control of open two-level quantum systems with operator errors. The required control performance is characterised using the concept of a sliding mode domain related to fidelity, coherence or purity. The authors have designed a control law offline and then utilise it online for a two-level system subject to decoherence with operator errors in the system model. They analyse three cases of approximate amplitude damping decoherence, approximate phase damping decoherence and approximate depolarising decoherence. They design specific sampling periods for these cases that can guarantee the required control performance.
TL;DR: In this article, a phase-locked loop (PLL)-based proportional integral (PI) controller was proposed for compensating the phase error between motions from the lateral axes of a piezoelectric tube scanner (PTS) during spiral scanning for an atomic force microscope (AFM) is achieved by applying two sinusoidal signals with a 90 degree phase shift and of varying amplitudes to the X and Y-axes of the scanner.
Abstract: The design of a phase-locked loop (PLL)-based proportional integral (PI) controller for compensating the phase error between motions from the lateral axes of a piezoelectric tube scanner (PTS) during spiral scanning for an atomic force microscope (AFM) is proposed in this paper. Spiral motion of the PTS for scanning of material surfaces or biological samples using an AFM is achieved by applying two sinusoidal signals with a 90 degree phase-shift and of varying amplitudes to the X and Y-axes of the scanner. The phase error between the X and Y-axes positions and scanner’s vibration due to its mechanical properties increase with increasing scanning speeds which reduce the imaging performance of the AFM at high frequencies. In the proposed control scheme, a vibration compensator is used with the X and Y-PTS to damp the vibration of the PTS at its resonant frequency and the phase error between the displacements of the two lateral axes of the scanner is measured by a phase detector and a PI controller is used to reduce the error. Comparisons of experimental results for reference tracking and imaging performance with the AFM PI controller demonstrate the efficiency of the proposed control method.
TL;DR: This paper designs some novel features of minutiae triplets in addition to some commonly used features to constitute the local minutia triplet features to improve the performance of partial fingerprint indexing.
Abstract: Existing work on partial fingerprint indexing attempts to make full use of the extracted features from the partial segments, such as singular points, minutiae, orientation field, and ridge count. However, singular points may not exist in partial fingerprints, and none of these features can form a complete set of feature vectors that can be used for matching with those derived from the corresponding full fingerprints for indexing. Our former work on fingerprint orientation model based on two-dimensional Fourier expansion FOMFE coefficients-based fingerprint indexing and global orientation field reconstruction has demonstrated the possibility of reconstructing a global feature vector for partial fingerprint indexing. In this paper, we design some novel features of minutiae triplets in addition to some commonly used features to constitute the local minutiae triplet features. Experiments carried out on fingerprint verification competition FVC 2000 DB2a, FVC 2002 DB1a, and National Institute of Standards and Technology NIST SD 14 demonstrate the performance improvement after adding the new features to minutiae triplet feature set. We then propose to combine the reconstructed global feature and local minutiae triplet features to improve the performance of partial fingerprint indexing. Specifically, the minutiae triplet-based indexing scheme and the FOMFE coefficients-based indexing scheme are applied separately to generate two candidate lists; then, a fuzzy-based fusion scheme is designed to generate the final candidate list for matching. Experiments carried out on the public database NIST SD 14 show that the proposed approach can improve the performance that has been achieved by individual partial fingerprint indexing algorithms before fusion. Copyright © 2015 John Wiley & Sons, Ltd.
TL;DR: In this article, a data-driven controller synthesis methodology for negative imaginary (NI) systems is presented, where measured frequency response data of the plant is used to construct the controller frequency response at every frequency by minimising a cost function.
Abstract: The negative imaginary (NI) property occurs in many important applications. For instance, flexible structure systems with collocated force actuators and position sensors can be modelled as negative imaginary systems. In this study, a data-driven controller synthesis methodology for NI systems is presented. In this approach, measured frequency response data of the plant is used to construct the controller frequency response at every frequency by minimising a cost function. Then, this controller response is used to identify the controller transfer function using system identification methods.
TL;DR: A Green’s function-based root locus approach to realizing a Lorentzian-noise-disturbed non-Markovian quantum system by Markovian coupled oscillators in an extended Hilbert space is developed.
Abstract: In this paper, we develop a Green's function-based root locus approach to realizing a Lorentzian-noise-disturbed non-Markovian quantum system by Markovian coupled oscillators in an extended Hilbert space. By using a Green's function-based root locus method, we design an ancillary oscillator for Markovian coupled oscillators to be a Lorentzian noise generator. Thus a principal oscillator coupled to the ancillary oscillator via a direct interaction can capture the dynamics of a Lorentzian-noise-disturbed non-Markovian quantum system. By matching the root locus in the frequency domain, conditions for the realization are obtained and a critical transition in the non-Markovian quantum system can also be observed in the Markovian coupled oscillators.
Posted Content•
TL;DR: In this article, the problem of constructing a direct coupling quantum observer for a quantum harmonic oscillator system was considered and the proposed observer is shown to be able to estimate one but not both of the plant variables and produces a measureable output using homodyne detection.
Abstract: This paper considers the problem of constructing a direct coupling quantum observer for a quantum harmonic oscillator system. The proposed observer is shown to be able to estimate one but not both of the plant variables and produces a measureable output using homodyne detection.
TL;DR: In this article, a sampling-based method to achieve a desired charge transfer probability with limited sensitivity to the arrival time of the laser pulses was proposed. But the results showed that the robustness of the measured laser pulses is not as good as the expected.
Abstract: In laser-assisted collisions, a control field may fail if we cannot precisely synchronize the colliding particles and the laser pulse. In this paper, we show that laser pulses that are robust in this situation can be obtained by a sampling-based method to achieve a desired charge transfer probability with limited sensitivity to the arrival time of the laser pulses. The time-dependent wave packet method and an adaptive target scheme are used in optimal control calculations based on an adiabatic two-state model of a H + D+ collision system. Several samples with different pulse arrival times are selected to construct robust fields at two different collision energies and the validity of these fields are examined by tests with additional samples. Excellent performance was obtained with the robust fields in both cases.
13 Jul 2016
TL;DR: In this paper, a coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant.
Abstract: This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of second-order moments of the system variables. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant. The cost functional also involves a quadratic penalty on the plant-observer coupling matrix in order to mitigate the back-action of the observer on the covariance dynamics of the plant. For the discounted mean square optimal CQF problem with penalized back-action, we establish first-order necessary conditions of optimality in the form of algebraic matrix equations. By using the Hamiltonian structure of the Heisenberg dynamics and related Liealgebraic techniques, we represent this set of equations in a more explicit form in the case of equally dimensioned plant and observer.
TL;DR: In this paper, the authors considered a quantum harmonic oscillator chain with a central oscillator coupled to a single reservoir and completely parametrized the class of $(2\aleph+1)$-mode pure Gaussian states that can be prepared by this type of quantum harmonic OO chain.
Abstract: We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of $(2\aleph+1)$ quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of $(2\aleph+1)$-mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
TL;DR: In this article, a quantum extended Kalman filter (quantum EKF) was proposed for non-commutative quantum stochastic differential equations (QSDEs).
Abstract: A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic master equation (SME). For a linear quantum system subject to linear measurements and Gaussian noise, the quantum filter reduces to a quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to non-commutative quantum stochastic differential equations (QSDEs). We will show that there are conditions under which a filter similar to the classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problems with `state-dependent' covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems which involve multiple modes, nonlinear Hamiltonians and simultaneous jump-diffusive measurements.
TL;DR: In this paper, the authors solve the fault tolerant filtering and fault detection problem for a class of open quantum systems driven by a continuous-mode bosonic input field in single photon states when the systems are subject to stochastic faults.
Abstract: The purpose of this paper is to solve the fault tolerant filtering and fault detection problem for a class of open quantum systems driven by a continuous-mode bosonic input field in single photon states when the systems are subject to stochastic faults. Optimal estimates of both the system observables and the fault process are simultaneously calculated and characterized by a set of coupled recursive quantum stochastic differential equations.
TL;DR: In this article, the robust H∞ estimation for uncertain linear quantum systems is solved by converting it to a suitably scaled H ∞ control problem, and the solution is obtained in the form of two algebraic Riccati equations.
Abstract: Summary
We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust H∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H∞ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method. Copyright © 2016 John Wiley & Sons, Ltd.
TL;DR: In this article, the Kalman decomposition for linear quantum systems was studied and it was shown that the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws of quantum mechanics.
Abstract: This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws of quantum mechanics. We propose a construction method for such transformations that put the system in a Kalman canonical form. Furthermore, we uncover an interesting structure for the obtained decomposition. In the case of passive systems, it is shown that there exist only controllable/observable and uncontrollable/unobservable subsystems. In the general case, controllable/unobservable and uncontrollable/observable subsystems may also be present, but their respective system variables must be conjugate variables of each other. This decomposition naturally exposes decoherence-free modes, quantum-nondemolition modes, quantum-mechanics-free subsystems, and back-action evasion measurements in the quantum system, which are useful resources for quantum information processing, and quantum measurements. The theory developed is applied to physical examples.
01 Nov 2016
TL;DR: A robot localization algorithm, that uses an Extended Kalman Filter (EKF) to fuse data from optical wheel encoders, a gyroscope and an accelerometer for an indoor navigation and additionally from DGPS unit for an outdoor scenario is presented.
Abstract: This paper presents a robot localization algorithm, that uses an Extended Kalman Filter (EKF) to fuse data from optical wheel encoders, a gyroscope and an accelerometer for an indoor navigation and additionally from DGPS unit for an outdoor scenario. The algorithm's performance is experimentally evaluated using a skid-steered SeekurJr mobile robot. Experimental results are provided to compare the localization accuracy achieved using the proposed algorithm with those using pure odometry readings and pure DGPS readings.
Posted Content•
TL;DR: In this paper, a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems was proposed and proved to be equivalent to the unitarity of the input-output transfer function and orthogonality of the feedthrough matrix of the system.
Abstract: This note is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR conditions. We provide a relatively simple proof that the PR condition is equivalent to the frequency domain $(J,J)$-unitarity of the input-output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.