Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography. Utilizing a tensor structure, our algorithm exhibits a computational complexity of$O(MLd^{2})$where d is the dimension of the quantum system and$M, L~(M\geq d^{2}, L\geq d^{2})$represent the numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm.

Ensuring robust and precise tracking control in the presence of uncertain multi-input-multi-output (MIMO) system dynamics and environmental variations is a significant challenge in the field of robust and adaptive control theory. While fuzzy control strategies have demonstrated good tracking performance in normal conditions, designing and tuning fuzzy controllers can be a challenging task in highly uncertain environments. In this study, we investigate a novel approach that combines robust nonlinear negative-imaginary (NI) systems theory with a self-adaptive fuzzy control scheme and the Lyapunov synthesis to develop a robust adaptive negative-imaginary-fuzzy (RANIF) control scheme. We optimize the critical parameters of the proposed fuzzy system using a self-tuning technique with a proportional-derivative sliding manifold. Furthermore, unlike the existing adaptive fuzzy control methods, we propose a small number of membership functions and systematically derive the fuzzy rules by employing Lyapunov, nonlinear NI, and dissipativity theories, which simplify the tuning process, work out the matter of "explosion of complexity," and reduce computational complexity. We demonstrate the global stability of the closed-loop system using nonlinear NI theory. To evaluate the effectiveness of our proposed approach, we present simulation results for two examples involving uncertain MIMO second-order Euler-Lagrange systems. These systems, known for their capacity to represent a diverse range of practical physical systems, serve as suitable testbeds for our methodology. Our results show that RANIF outperforms other control methods, such as nonlinear strictly NI-Fuzzy, fuzzy-logic control, model predictive control, and conventional PID control, in terms of robustness to disturbances and inestimable faults, trajectory tracking performance, and computational complexity.

Quadrotors are one of the popular unmanned aerial vehicles (UAVs) due to their versatility and simple design. However, the tuning of gains for quadrotor flight controllers can be laborious, and accurately stable control of trajectories can be difficult to maintain under exogenous disturbances and uncertain system parameters. This article introduces a novel robust adaptive control synthesis methodology for a quadrotor robot's attitude and altitude stabilization. The proposed method is based on the fuzzy reinforcement learning and strictly negative imaginary (SNI) property. The first stage of our control approach is to transform a nonlinear quadrotor system into an equivalent negative-imaginary (NI) linear model by means of the feedback linearization (FL) technique. The second phase is to design a control scheme that adapts online the SNI controller gains via fuzzy Q -learning. The performance of the designed controller is compared with that of a fixed-gain SNI controller, a fuzzy-SNI controller, and a conventional PID controller in a series of numerical simulations. Furthermore, the proofs for the stability of the proposed controller and the adaptive laws are provided using the NI theorem.

A hybrid quantum-classical filtering problem, where a qubit system is disturbed by a classical stochastic process, is investigated. The strategy is to model the classical disturbance by using an optical cavity. The relations between classical disturbances and the cavity analog system are analyzed. The dynamics of the enlarged quantum network system, which includes a qubit system and a cavity system, are derived. A stochastic master equation for the qubit-cavity hybrid system is given, based on which estimates for the state of the cavity system and the classical signal are obtained. The quantum-extended Kalman filter is employed to achieve efficient computation. The numerical results are presented to illustrate the effectiveness of our methods.

This paper solves the problem of discrete-time fault-tolerant quantum filtering for a class of laser-atom open quantum systems subject to the stochastic faults. We show that by using the discrete-time quantum measurements, optimal estimates of both the atomic observables and the classical fault process can be simultaneously determined in terms of recursive quantum stochastic difference equations. A dispersive interaction quantum system example is used to demonstrate the proposed filtering approach.

Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, a novel quantum detector tomography method is proposed. First, a series of different probe states are used to generate measurement data. Then, using constrained linear regression estimation, a stage-1 estimation of the detector is obtained. Finally, the positive semidefinite requirement is added to guarantee a physical stage-2 estimation. This Two-stage Estimation (TSE) method has computational complexity O(nd2M), where n is the number of d-dimensional detector matrices and M is the number of different probe states. An error upper bound is established, and optimization on the coherent probe states is investigated. We perform simulation and a quantum optical experiment to testify the effectiveness of the TSE method.

This paper proposes a recursively adaptive tomography protocol to improve the precision of quantum process estimation for finite dimensional systems. The problem of quantum process tomography is firstly formulated as a parameter estimation problem which can then be solved by the linear regression estimation method. An adaptive algorithm is proposed for the selection of subsequent input states given the previous estimation results. Numerical results show that the proposed adaptive process tomography protocol can achieve an improved level of estimation performance.

Robustness in the face of uncertainties is an important aspect in designing high performance control systems. This paper addresses the problem of accurate trajectory tracking of a small quadcopter unmanned aerial vehicle in the face of uncertainties. Accommodating the worst-case scenario, we propose a hybrid feedback and feedforward autopilot that has the capability to eliminate the cross-coupling disturbance between the lateral and the longitudinal loops with respect to the vertical loop as well as external disturbances (e.g., wind gusts). The proposed control system leverages on the technical benefits of both the nonlinear model predictive control and the fuzzy feedforward compensator. We highlight the efficacy of our hybrid autopilot system with respect to the performance of the conventional PD control systems through rigorous comparative studies. We also present stability analysis of our hybrid control system.

This paper presents methods to find a positively invariant set (PIS) and derive conditions on the edge weights for a multirate Kuramoto oscillator network to achieve synchronization. These methods can be applied to a network with an arbitrary topology and nonidentical oscillators. The proposed methods are based on the construction of energy functions for this type of network. Two different conditions on the edge weights are provided by using graph spectral properties, or alternatively by analyzing a path set of a graph. These methods provide flexibility in checking the edge weight conditions. We further improve the estimate of the PIS for the multirate Kuramoto network when its damping coefficients are greater than a certain value. The effectiveness and conservativeness of the proposed methods are demonstrated by simulation studies. A comparison with another method from the existing literature shows that our method gives less conservative estimate of the PIS.

In this paper, we consider the filtering problem for a hybrid system where a quantum qubit system is disturbed by a classical signal. The quantum filtering theory, which is based on quantum probability theory, can not be directly applied to a hybrid system where a classical stochastic process is also needed in describing the system dynamics. An optical cavity system is employed to model the classical disturbance. By designing the parameters of the auxiliary cavity system, the expectation of the quadrature operator of the cavity shares the same dynamics with the classical signal. With this correspondence guaranteed, one can obtain the real time expectation of the classical signal. The quantum concatenation product is adopted to describe the quantum system which contains both the qubit subsystem and the cavity subsystem. A stochastic master equation, which provides estimates for the quantum state and the classical signal, is given. To reduce the computational complexity, the quantum extended Kalman filter is also applied to this system.

In this paper, we present a gradient algorithm to identify a damping rate function for a non-Markovian single qubit system. The dynamics of the single qubit system in a non-Markovian environment are assumed to obey a time convolutionless master equation, where all the non-Markovian effects of the environment are combined in the unknown damping rate function. To identify the damping rate function, we measure time trace observables of the qubit such that we can formulate the identification procedure as an optimization problem. Thus, we design a gradient algorithm to optimally reveal the damping rate function.

An optimal controller for high-precision spiral positioning of a piezoelectric tube scanner used in an atomic force microscope (AFM) is proposed in this paper. In the proposed control scheme, a second-order vibration compensator is incorporated with the piezoelectric tube scanner (PTS) to suppress the vibration of the PTS at the resonant frequency. An internal model of a reference sinusoidal signal is included with the augmented plant model and an integrator is introduced with a linear quadratic Gaussian controller which reduces the phase error between the input and output sinusoids. The proposed method allows a commercial AFM to scan at high scanning speeds as an alternative to the raster scanning approach. The performance of this controller is assessed with closed-loop frequency response, tracking accuracy, and a set of spiral scanned images. The raster scanned images obtained using the standard AFM PI controller is also presented for comparison with the spiral images. Experimental results prove the effectiveness of the proposed method.

Nanotechnology is the branch of science which deals with the manipulation of matters at an extremely high resolution down to the atomic level. In recent years, atomic force microscopy (AFM) has proven to be extremely versatile as an investigative tool in this field. The imaging performance of AFMs is hindered by: 1) the complex behavior of piezo materials, such as vibrations due to the lightly damped low-frequency resonant modes, inherent hysteresis, and creep nonlinearities; 2) the cross-coupling effect caused by the piezoelectric tube scanner (PTS); 3) the limited bandwidth of the probe; 4) the limitations of the conventional raster scanning method using a triangular reference signal; 5) the limited bandwidth of the proportional-integral controllers used in AFMs; 6) the offset, noise, and limited sensitivity of position sensors and photodetectors; and 7) the limited sampling rate of the AFM's measurement unit. Due to these limitations, an AFM has a high spatial but low temporal resolution, i.e., its imaging is slow, e.g., an image frame of a living cell takes up to 120 s, which means that rapid biological processes that occur in seconds cannot be studied using commercially available AFMs. There is a need to perform fast scans using an AFM with nanoscale accuracy. This paper presents a survey of the literature, presents an overview of a few emerging innovative solutions in AFM imaging, and proposes future research directions.

Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

An adaptive target scheme is implemented for learning control of population transfer between subspaces of quantum systems. In this control scheme, the target state is updated according to the renormalized yield in the desired subspace throughout the learning iterations, to obtain the desired laser control field. In the numerical experiments, we perform learning control simulations based on a V-type three-subspace quantum system. The field obtained by learning control can transfer the population to the target subspace with high probability. In comparison with a fixed target state, this adaptive target scheme proves to be more efficient for the quantum control problem under consideration.

Summary 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.

Quantum ensemble classification has significant applications in discrimination of atoms (or molecules), separation of isotopic molecules and quantum information extraction. In this paper, we recast quantum ensemble classification as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). Numerical results demonstrate the effectiveness of the proposed approach for the discrimination of two quantum systems and the binary classification of two-level quantum ensembles.

This paper presents a design of an internal reference model based optimal linear quadratic Gaussian controller (LQG) for a piezoelectric tube (PZT) actuator used in the atomic force microscope (AFM). This control scheme minimizes the steady-state error and provides improved closed-loop bandwidth and enables the controller to track reference triangular signal. The proposed scheme places the closed-loop poles in the left half of the s-plane such that significant damping of the resonant modes of the PZT actuator can be achieved. Experimental results with the AFM show that the proposed control approach is able to scan faster and improves the quality of images by minimizing blurring, tilting, and edge distortion of the image as compared to the existing PI controller of the AFM.

This paper presents the design of a model predictive control (MPC) scheme with a notch filter for reducing the tracking error of an atomic force microscope (AFM) by damping the resonant mode of the piezoelectric tube (PZT) scanner. The development of a controller for the AFM imaging and scanning speed is illustrated in this paper. Experimental results show that the proposed controller can increase the scanning speed significantly as compared with the existing PI controller.

In this correspondence, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of conditional relative entropy between conditional probability measures is introduced as an a posteriori probability distance which can be used to measure the discrepancy between hidden Markov models when a realized observation sequence is observed. Using a measure change technique, we derive a representation for conditional relative entropy in terms of the parameters of the HMMs and conditional expectations given measurements. With this representation, we show that this distance can be calculated using an information state approach

We study the decoding problem in an uncertain noise environment. If the receiver knows the noise probability density function (PDF) at each time slot or its a priori probability, the standard Viterbi (1967) algorithm (VA) or the a posteriori probability (APP) algorithm can achieve optimal performance. However, if the actual noise distribution differs from the noise model used to design the receiver, there can be significant performance degradation due to the model mismatch. The minimax concept is used to minimize the worst possible error performance over a family of possible channel noise PDFs. We show that the optimal robust scheme is difficult to derive; therefore, alternative, practically feasible, robust decoding schemes are presented and implemented on a VA decoder and two-way APP decoder. The performance analysis and numerical results show our robust decoders have a performance advantage over standard decoders in uncertain noise channels, with no or little computational overhead. Our robust decoding approach can also explain why for turbo decoding overestimating the noise variance gives better results than underestimating it.

We study and develop several robust decoding algorithms based on the minimax rule. The algorithms robust to estimation errors and channel variations. The decoding problem is studied when using a matched and mismatched decoder. Examples using robust the Viterbi algorithm (1967) and MAP algorithm are also presented.