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In this article, we consider dynamic multiagent systems (MAS) for decentralized resource allocation. The MAS operate at a competitive equilibrium to ensure a balanced supply and demand for available resources. Example resources include energy in a microgrid and carbon permits in a carbon trading system. First, we investigate the MAS over a finite horizon, where the utility functions of agents are parameterized to incorporate individual preferences. We shape individual preferences through a set of utility functions to guarantee the resource price at a competitive equilibrium remains socially acceptable, i.e., the price is upper-bounded by an affordability threshold. We show this problem is solvable implicitly. Next, we consider quadratic MAS and formulate the social shaping problem as a multiagent linear quadratic regulator (LQR) problem. We propose explicit utility sets using quadratic programming and dynamic programming. Moreover, we propose a numerical algorithm for calculating a tight range of the preference function parameters that guarantee a socially accepted price. We then investigate the properties of a competitive equilibrium over an infinite horizon, and show cases where any competitive equilibrium maximizes the social welfare. We show that for initial conditions sufficiently close to the origin, the social welfare maximization solution constitutes a competitive equilibrium with zero price. We also show that for all feasible initial conditions, there exists a time instant after which the optimal price, corresponding to a competitive equilibrium, becomes zero.

The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as O1/N, where Nis the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using d-1observables, where dis the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.

In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Luré-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time.

A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.

In this article, we present necessary and sufficient conditions under which a linear time-invariant (LTI) system is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show that a minimal LTI strictly proper system can be rendered NI using full state feedback, if and only if it can be output transformed into a system, which has relative degree less than or equal to two and is weakly minimum phase. We also considered the problems of state feedback equivalence to output strictly negative imaginary systems and strongly strictly negative imaginary systems. Then, we apply the NI state feedback equivalence results to robustly stabilize an uncertain system with strictly negative imaginary uncertainty. A real-world example is provided to illustrate the proposed results, for the purpose of stabilizing an uncertain system.

In this article, we propose a new approach to address the control problem for negative imaginary (NI) systems by using hybrid integrator-gain systems (HIGSs). We investigate the single HIGS of its original form and its two variations, including a multi-HIGS and the serial cascade of two HIGSs. A single HIGS is shown to be a nonlinear NI system and so is the multi-HIGS and the cascade of two HIGSs. We show that these three types of HIGSs can be used as controllers to asymptotically stabilize linear NI systems. The results of this article are then illustrated in a real-world experiment where a 2-DOF microelectromechanical system (MEMS) nanopositioner is stabilized by a multi-HIGS.

Theoretical developments in the field of superconducting microwave circuits involving continuous measurement feedback control as well as coherent feedback control are essential for advances in the domain of quantum technology. The smallest structures that can be fabricated by lithographic technologies request the inevitable development of the quantum control theory in order for quantum systems to function reliably in an engineering sense. Within these perspectives, this paper develops the positive real properties for a class of quantum systems involving annihilation operators only and then relates them to the corresponding bounded real properties and consequently to physical realizability conditions developed earlier by the authors. Based on these positive real properties of the annihilation operators quantum systems, it is shown that it is possible to use the Brune algorithm in order to find electrical circuits that can physically implement the type of quantum systems involving annihilation operators only. This would involve Josephson junctions, microwave cavities, and voltage sources. This theory, illustrated for one-port circuits, is essential for the implementation of microwave circuits especially those related to quantum filters found in the field of quantum computing. [ABSTRACT FROM AUTHOR]

This paper is concerned with infinite-horizon growth rates of quadratic-exponential functionals (QEFs) for linear quantum stochastic systems driven by multichannel bosonic fields. Such risk-sensitive performance criteria impose an exponential penalty on the integral of a quadratic function of the system variables, and their minimization improves robustness properties of the system with respect to quantum statistical uncertainties and makes its behavior more conservative in terms of tail distributions. We use a frequency-domain representation of the QEF growth rate for the invariant Gaussian quantum state of the system with vacuum input fields in order to compute it in state space. The QEF rate is related to a similar functional for a classical stationary Gaussian random process generated by an infinite cascade of linear systems. A truncation of this shaping filter allows the QEF rate to be computed with any accuracy by solving a recurrent sequence of algebraic Lyapunov equations together with an algebraic Riccati equation. The state-space computation of the QEF rate and its comparison with the frequency-domain results are demonstrated by a numerical example for an open quantum harmonic oscillator. [ABSTRACT FROM AUTHOR]

In this paper, a robust H ∞ analysis method is presented for a class of uncertain quantum systems where uncertainties may exist in the system and interaction Hamiltonians, and the coupling operators. We provide a sufficient condition to guarantee this class of uncertain systems robust strictly bounded real with respect to a given disturbance attenuation. Moreover, we propose a robust H ∞ control method for quantum systems with uncertain system Hamiltonian and uncertain coupling operators. The controller and the quantum plant are connected via direct and indirect couplings. This robust H ∞ control problem is shown to have a connection with a scaled H ∞ problem. We propose a numerical procedure to find the corresponding coefficients of the desired H ∞ controller by using an LMI formulation and multi-step optimization. [ABSTRACT FROM AUTHOR]

This article provides a protocol to address the robust output feedback consensus problem for networked heterogeneous nonlinear negative-imaginary (NI) systems with free body dynamics. We extend the definition of nonlinear NI systems to allow for systems with free-body motion. A new stability result is developed for the interconnection of a nonlinear NI system and a nonlinear output strictly negative-imaginary (OSNI) system. Also, a class of networked nonlinear OSNI controllers is proposed to achieve output feedback consensus for heterogeneous networked nonlinear NI systems. We show that in this control framework, the system outputs converge to the same limit trajectory. This consensus protocol is illustrated by a numerical example.

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.

This article presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift terms. The controlled terms are assumed to take place between pairwise states. Such bilinear systems naturally induce two interaction graphs: one graph from the drift, and another from the controlled dynamics. As a result, the system controllability or accessibility becomes a property of the two graphs in view of the classical Lie algebra rank condition. We establish a systemic way of transforming the Lie bracket operations in the underlying Lie algebra, into specific operations of removing or creating links over the drift and controlled interaction graphs. As a result, we establish a series of graphical conditions for the controllability and accessibility of such bilinear systems, which rely only on the connectivity of the union of the drift and controlled interaction graphs. We present examples to illustrate the validity of the established results, and show that the proposed conditions are in fact considerably tight.

Quantum detector tomography is a fundamental technique for calibrating quantum devices and thus lay foundations for quantum information processing tasks. In this work, we propose a quantum detector tomography method that employs deep neural networks to reconstruct quantum detectors from a set of probe states with high efficiency. Numerical results demonstrate that the proposed method exhibits a significant potential to estimate phase-insensitive detectors.

In this paper, we present a strictly negative imaginary state feedback control methodology for relative degree two negative imaginary systems such as flexible structures with collocated sensors and actuators. We show that by augmenting a nominal model with a destabilising PID controller, we can apply state feedback control to the system, resulting in a strictly negative imaginary nominal closed loop system with a prescribed degree of stability. Moreover, the overall system is guaranteed to be internally stable in the face of unmodelled spillover dynamics.

In this paper, we investigate the necessary and sufficient conditions under which a class of nonlinear systems are state feedback equivalent to nonlinear negative imaginary (NI) systems with positive definite storage functions. The nonlinear systems of interest have a normal form of relative degree less than or equal to two. The nonlinearity of the system is restricted with respect to a subset of the state variables, which are the state variables that have external dynamics. Under mild assumptions, such systems are state feedback equivalent to nonlinear NI systems and nonlinear output strictly negative imaginary (OSNI) systems if and only if they are weakly minimum phase. Such a state feedback control approach can also asymptotically stabilize the systems in question against nonlinear OSNI system uncertainties. A numerical example is provided to show the process of the state feedback equivalence control and stabilization of uncertain systems.

In this paper, we investigate the properties of competitive equilibriums for dynamic multi-agent systems (MAS) over an infinite horizon. When there is no external resource supply, a group of dynamic agents with distributed resource allocations form a transactive market to share their resources at a specific price. Each agent makes decisions on the locally consumed resource and the traded resource. The system reaches a competitive equilibrium when each agent's payoff is maximized and the tradings are balanced. Firstly, we consider general utility functions and show that under feasibility assumptions, any competitive equilibrium maximizes the social welfare. Secondly, we prove that for sufficiently small initial conditions, the social welfare maximization solution constitutes a competitive equilibrium with zero price. We also prove for general feasible initial conditions, there exists a time instant after which the optimal price, corresponding to a competitive equilibrium, becomes zero. Finally, we specifically focus on quadratic MAS for which the system-level social welfare optimization becomes a classical constrained linear quadratic regulator (CLQR) problem. We construct explicitly a feasible set of initial conditions under which the price under a competitive equilibrium is zero for all time.

In this paper, we extend nonlinear negative imaginary (NI) systems theory to switched systems. Switched nonlinear NI systems and switched nonlinear output strictly negative imaginary (OSNI) systems are defined. We show that the interconnection of two switched nonlinear NI systems is still switched nonlinear NI. The interconnection of a switched nonlinear NI system and a switched nonlinear OSNI system is asymptotically stable under some assumptions. This stability result is then illustrated using a numerical example.

This paper is concerned with the coherent quantum linear-quadratic-Gaussian control problem of minimising an infinite-horizon mean square cost for a measurement-free field-mediated interconnection of a quantum plant with a stabilising quantum controller. The plant and the controller are multimode open quantum harmonic oscillators, governed by linear quantum stochastic differential equations and coupled to each other and the external multichannel bosonic fields in the vacuum state. We discuss an interplay between the quantum physical realizability conditions and the Luenberger structure associated with the classical separation principle. This leads to a quadratic constraint on the controller gain matrices, which is formulated in the framework of a swapping transformation for the conjugate positions and momenta in the canonical representation of the controller variables. For the class of coherent quantum controllers with the Luenberger dynamics, we obtain first-order necessary conditions of optimality in the form of algebraic equations, involving a matrix-valued Lagrange multiplier.

In this article, we study the recursion corresponding to the measurement outcomes for open quantum networks under sequential measurements. Open quantum networks are networked quantum subsystems (e.g., qubits) with the state evolutions described by a continuous Lindblad master equation. When measurements are performed sequentially along such continuous dynamics, the quantum network states undergo probabilistic jumps and the corresponding measurement outcomes can be described by a vector of probabilistic Boolean variables. The induced recursion of the Boolean vectors forms a probabilistic Boolean network. First of all, we show that the state transition of the induced Boolean network can be explicitly represented through a real version of the master equation. Next, when the open quantum dynamics are relaxing in the sense that they possess a unique equilibrium as a global attractor, structural properties including absorbing states, reducibility, and periodicity for the induced Boolean network are direct consequences of this relaxing property. Particularly, we show that generically, relaxing quantum dynamics leads to irreducible and aperiodic chains for the measurement outcomes. Finally, we show that for quantum consensus networks, which are a type of nonrelaxing open quantum network dynamics, the communication classes of the measurement-induced Boolean networks are encoded in the quantum Laplacian of the underlying interaction graph

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this article is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and $H^\infty$ disturbance attenuation performance. This article first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault-tolerant $H^\infty$ control problem to the dissipation properties and the solutions of Riccati differential equations, an $H^\infty$ controller for the quantum system is then designed by solving a set of linear matrix inequalities. In particular, an algorithm is employed to introduce additional quantum inputs and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. Also, we propose a real application of the developed fault-tolerant control strategy to quantum optical systems. A linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values due to the fault processes, can be modeled as a linear Markovian jumping system. It is demonstrated that a quantum $H^\infty$ controller can be designed and implemented using some basic optical components to achieve the desired control goal for this class of systems. [ABSTRACT FROM AUTHOR]

The purpose of this article is to synthesize a linear quantum system, which is strictly stable and has a steady thermal state. Specifically, we give a parameterization of a class of stable linear quantum systems that have $V=\tau I/2$ , $\tau > 1$ , as their steady covariance matrsices. This is physically important since the covariance matrix $\tau I/2$ , $\tau > 1$ , corresponds to a quantum thermal state. Hence, we can say that these systems will asymptotically evolve into a quantum thermal state. An extension to the case where $V=S\operatorname{diag}(\Lambda,\Lambda) S^{\top }/2$ with $\Lambda > I$ being a diagonal matrix and $S$ being a symplectic matrix will also be considered. Physically, a covariance matrix of the form $V=S\operatorname{diag}(\Lambda,\Lambda) S^{\top }/2$ , $\Lambda > I$ , corresponds to a mixed Gaussian quantum state. So, we can alternatively say that the corresponding linear quantum systems will asymptotically evolve into a mixed Gaussian quantum state. [ABSTRACT FROM AUTHOR]

In this article, we consider the dynamical modeling of a class of quantum network systems consisting of qubits, where information extraction is allowed by performing measurement on several selected qubits of the system. For a variety of applications, a state space model is a useful approach to modeling the system dynamics. To construct a state space model for a quantum network system, the major task is to find an accessible set containing all of the operators coupled to the measurement operators. This article focuses on the generation of a proper accessible set for a given system and measurement scheme. We provide analytic results on simplifying the process of generating accessible sets for systems with a time-independent Hamiltonian. Since the order of elements in the accessible set determines the form of state space matrices, guidance is provided to effectively arrange the ordering of elements in the state vector. Defining a system state according to the accessible set, one can develop a state space model with a special pattern inherited from the system structure. As a demonstration, we specifically consider a typical 1-D-chain system with several common measurements and employ the proposed method to determine its accessible set.

By virtue of the wide implementation of communication-based train control (CBTC) systems and moving-block signaling systems, cooperative control for trains shows great potential in improving line utilization, passenger comfort, and operation flexibility. However, the operation of train platoons faces great challenges induced by model uncertainties, unpredictable resistances, and time-varying disturbances. To address these problems, consensus-based robust cooperative control schemes are presented in this article for both homogeneous and heterogeneous train platoons. Taking the physical connection between carriages into consideration, each train in the platoon is modeled as a negative-imaginary (NI) system, and the NI property is rigorously proved in this article. In the foundation of cooperative control theories of NI systems, robust strictly NI controllers considering the network topology are utilized to track a predefined motion reference. The proposed controllers are robust to both mass uncertainties and external disturbances. Moreover, the line utilization for the railway system and the ride comfort for the passengers are improved using the proposed control schemes. Numerical simulations are given to showcase the effectiveness and robustness of the proposed controllers.

This paper is concerned with robust performance analysis of linear stochastic systems acting as an integral operator on a standard Wiener process at the input and producing a stationary Gaussian random process at the output. We propose a performance criterion which uses the trace of an analytic function of the spectral density of the output process. This class of "covariance-analytic" cost functionals includes the usual mean square and risk-sensitive criteria as particular cases. Due to the "cost-shaping" analytic function, the covariance-analytic performance criterion depends on higher-order Hardy-Schatten norms of the system transfer function. We discuss the links of these norms with the asymptotic behaviour of cumulants of finite-horizon quadratic functionals of the system output and their variational properties pertaining to system robustness to statistically uncertain inputs which differ from the standard Wiener process. In the case of strictly proper finite-dimensional systems, governed in state space by linear stochastic differential equations, we develop a method for recursively computing the Hardy-Schatten norms through a recently proposed technique of rearranging cascaded linear systems, which resembles the Wick ordering of mixed products of noncommuting annihilation and creation operators in quantum mechanics. This computational procedure, which is one of the main results of the paper, involves a recurrence sequence of solutions to algebraic Lyapunov equations and represents the covariance-analytic cost as the squared H 2 -norm of an auxiliary cascaded system. These results are also compared with an alternative approach, which uses higher-order derivatives of stabilising solutions of parameter-dependent algebraic Riccati equations, and illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI) controllers to all the nonlinear NI plants in positive feedback through the network topology. First, we extend the definition of nonlinear NI systems from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and also extend the definition of OSNI systems to nonlinear scenarios. Asymptotic stability is proved for the closed-loop interconnection of a nonlinear NI system and a nonlinear OSNI system under reasonable assumptions. Then, an NI property and an OSNI-like property are proved for networked identical nonlinear NI systems and networked identical linear OSNI systems, respectively. Output feedback consensus is proved for a network of identical nonlinear NI plants by investigating the stability of its closed-loop interconnection with a network of linear OSNI controllers. This closed-loop interconnection is proposed as a protocol to deal with the output consensus problem for networked identical nonlinear NI systems and is robust against uncertainty in the individual system’s model.

This paper is concerned with linear-quadratic-Gaussian (LQG) control for a field-mediated feedback connection of a plant and a coherent (measurement-free) controller. The plant and controller are multimode open quantum harmonic oscillators governed by linear quantum stochastic differential equations. The control objective is to make the closed-loop system internally stable and to minimize the infinite-horizon quadratic cost for the plant variables and the controller output subject to quantum physical realizability (PR) constraints. This coherent quantum LQG (CQLQG) control problem, which has been of active research interest for over ten years, does not admit a solution in the form of separation principle and independent Riccati equations known for its classical counterpart. We apply variational techniques to a family of discounted CQLQG control problems parameterized by an effective time horizon. This yields a homotopy algorithm, which is initialized with a PR (but not necessarily stabilizing) controller and aims at a locally optimal stabilizing controller for the original problem in the limit.

The identifiability of a system is concerned with whether the unknown parameters in the system can be uniquely determined with all the possible data generated by a certain experimental setting. A test of quantum Hamiltonian identifiability is an important tool to save time and cost when exploring the identification capability of quantum probes and experimentally implementing quantum identification schemes. In this article, we generalize the identifiability test based on the similarity transformation approach (STA) in classical control theory and extend it to the domain of quantum Hamiltonian identification. We employ the STA to prove the identifiability of spin-1/2 chain systems with arbitrary dimension assisted by single-qubit probes. We further extend the traditional STA method by proposing a structure preserving transformation (SPT) method for nonminimal systems. We use the SPT method to introduce an indicator for the existence of economic quantum Hamiltonian identification algorithms, whose computational complexity directly depends on the number of unknown parameters (which could be much smaller than the system dimension). Finally, we give an example of such an economic Hamiltonian identification algorithm and perform simulations to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

This article develops a quantum projection filtering approach to approximating the quantum filter equation based on It $\hat{\rm o}$ stochastic Taylor expansions and quantum information geometric techniques. The proposed approximation scheme is designed so that the truncated Taylor expansion of the difference between the true quantum trajectory, and its approximation on a lower dimensional differential submanifold is minimized, through an orthogonal projection operation in the quantum Fisher metric. In addition, a convenient design for a special class of open quantum systems is formulated. Simulation results from a numerical example demonstrate the approximation capability of the proposed quantum projection filter. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements. [ABSTRACT FROM AUTHOR]

This paper is concerned with a risk-sensitive optimal control problem for a feedback connection of a quantum plant with a measurement-based classical controller. The plant is a multimode open quantum harmonic oscillator driven by a multichannel quantum Wiener process, and the controller is a linear time invariant system governed by a stochastic differential equation. The control objective is to stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional (QEF) which penalizes the plant variables and the controller output. We combine a frequency-domain representation of the QEF growth rate, obtained recently, with variational techniques and establish first-order necessary conditions of optimality for the state-space matrices of the controller.

This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a bounded time interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its infinite-horizon asymptotic growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formula expresses the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide an illustrative numerical example with a two-mode open quantum harmonic oscillator.

The purpose of this paper is to design a coherent feedback controller for a Markovian jump linear quantum system suffering from a fault signal. The control objective is to bound the effect of the disturbance input on the output for the time-varying quantum system. We prove the relation between the H∞control problem, the dissipation properties, and the solutions of Riccati differential equations, by which the H∞controller of the Markovian jump linear quantum system is given by the solutions of Linear Matrix Inequalities (LMIs).

This paper provides a procedure for building a one port impedance quantization involving annihilation operators only for a class of linear quantum systems having a positive real impedance transfer function matrix. Based on the positive real properties of these quantum systems, it is shown that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, illustrated for one-port circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.

In this paper, we study the induced probabilistic Boolean dynamics for dynamical quantum networks subject to sequential quantum measurements. In this part of the paper, we focus on closed networks of quits whose states evolutions are described by a continuous Lindblad master equation. When measurements are performed sequentially along such continuous dynamics, the quantum network states undergo random jumps and the corresponding measurement outcomes can be described by a probabilistic Boolean network. First of all, we show that the state transition of the induced Boolean networks can be explicitly represented through realification of the master equation. Next, when the open quantum dynamics is relaxing in the sense that it possesses a unique equilibrium as a global attractor, structural properties including absorbing states, reducibility, and periodicity for the induced Boolean network are direct consequences of the relaxing property. Finally, we show that for quantum consensus networks as a type of non-relaxing open quantum network dynamics, the communication classes of the measurement-induced Boolean networks are encoded in the quantum Laplacian of the underlying interaction graph.

Theoretical developments in the field of quantum optics and quantum superconducting electrical circuits involving continuous measurement based feedback control as well as coherent control are an important prerequisites for advances in the domain of quantum technology. Within these perspectives, this paper considers positive real properties for a class of quantum systems whose quantum stochastic differential equation model involves annihilation operators only and then relates them to corresponding bounded real properties and consequently to physical realizability conditions developed earlier by the authors. Based on the positive real properties of these quantum systems, it is anticipated that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, in the case of one-port circuits, may be useful for the implementation of microwave circuits related to quantum filters found in the field of quantum computing.

Additional noise in a quantum system can be detrimental to the performance of a quantum coherent feedback control system. This paper proposes a Linear Matrix Inequality (LMI) approach to construct an optimal quantum realization of a given Linear Time Invariant (LTI) system. The quantum realization problem is useful in designing coherent quantum feedback controllers. An optimal method is proposed for solving this problem in terms of a finite horizon quadratic performance index, which is related to the amount of quantum noise appearing at the system’s output. This cost function provides a measure of how much the additional quantum noise in the coherent controller will alter the feedback control system.

Quantum sensing, utilizing quantum techniques to extract key information of a quantum (or classical) system, is a fundamental area in quantum science and technology. For quantum sensors, a basic capability is to uniquely infer unknown parameters in a system based on measurement data from the sensors. In this paper, we investigate the capability of a class of quantum sensors for a spin-12chain system with unknown parameters. The sensors are composed of qubits which are coupled to the object system and can be initialized and measured. We consider the capability of the single- and two-qubit sensors and show that the capability of single-qubit quantum sensors can be enhanced by adding an extra qubit into the sensor under a certain initialization and measurement setting.

This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices for finite-level systems. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. The fields are represented by quantum Wiener processes which drive the system dynamics according to a quasilinear Hudson-Parthasarathy quantum stochastic differential equation whose drift vector and dispersion matrix are affine and linear functions of the system variables. This setting includes the zero-Hamiltonian isolated system dynamics as a particular case, where the system variables are constant in time, which makes them potentially applicable as a quantum memory. In a more realistic case of nonvanishing system-field coupling, we define a memory decoherence time when a mean-square deviation of the system variables from their initial values becomes relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the decoherence time maximization over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution. This optimization problem is also discussed for a direct energy coupling interconnection of such systems.

Quantum Hamiltonian identification (QHI) 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) QHI algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are input 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 $O(\frac{d^3}{\sqrt{N}})$ 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

In this paper, we develop a direct method for the characterization of dark modes. The results can be used to construct a transformation that separates dark and bright modes, through the decomposition of system dynamics. We also study a synthesis problem by engineering the system–environment coupling and Hamiltonian engineering. We apply the theory to investigate an optomechanical dark mode. [ABSTRACT FROM AUTHOR]

This paper presents a survey of some new applications of algebraic Riccati equations. In particular, the paper surveys some recent results on the use of algebraic Riccati equations in testing whether a system is negative imaginary and in synthesizing state feedback controllers which make the closed loop system negative imaginary. The paper also surveys the use of Riccati equation methods in the control of quantum linear systems including coherent H∞control.

Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.

This paper proposes a direct coupling coherent quantum observer for a quantum plant which consists of a two level quantum system. The quantum observer, which is a quantum harmonic oscillator, includes homodyne detection measurements. It is shown that the observer can be designed so that it does not affect the quantum variable of interest in the quantum plant and that measured output converges in a given sense to the plant variable of interest. Also, the plant variable of interest-observer system can be described by a set of linear quantum stochastic differential equations. A minimum variance unbiased estimator form of the Kalman filter is derived for linear quantum systems and applied to the direct coupled coherent quantum observer.

In this paper, we present a H∞filter for estimating dynamics of a Lorentzian-noise-disturbed non-Markovian cavity system with disturbances. The non-Markovian cavity system can be represented by an augmented system, where the Lorentzian quantum noise is parameterized by an ancillary system. This ancillary system is directly coupled to a principal system of interest and induces the non-Markovian dynamics of the principal system. The noise channels in this augmented model carry disturbances. To reduce the effect of the disturbances on the estimation, we design a H∞filter which can be obtained by solving a H∞control problem.

Identification of the Hamiltonian is vital for characterizing the dynamical evolution of a quantum system. The dimension of a multi-qubit system increases exponentially with the qubit number, which usually leads to daunting computational complexity for general Hamiltonian identification algorithms. In this paper, we design an efficient quantum Hamiltonian identification method based on periodical sampling. The computational complexity is O(M2+ MN2), where Mis the number of unknown parameters to be identified in the Hamiltonian and N is the length of the sampling data. Numerical results with different data lengths demonstrate the effectiveness of the proposed identification algorithm.

A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation, is modeled by a quantum cavity model. Then the hybrid quantum-classical system is described by a combined quantum system consisting of two quantum cavity subsystems. Quantum filtering theory and a quantum extended Kalman filter method are employed to estimate the states of the combined quantum system. An estimate of the classical stochastic process is derived from the estimate of the combined quantum system.

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. [ABSTRACT FROM PUBLISHER]

We study consensus seeking of quantum networks under directed balanced interactions defined by a set of permutation operators among a network of qubits. The state evolution of the quantum network is described by a continuous-time master equation. We show that the network state always converges along the equation, and the convergence limit is determined by the generating subgroup of the permutation operators. We also give a tight graphical criterion regarding when such limit admits a reduced-state consensus. Quantum consensus conditions under switching interactions are also established with the help of cut-balanced consensus processes in the classical setting. [ABSTRACT FROM AUTHOR]

This technical note extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear quantum system and is subject to quadratic perturbations in the system Hamiltonian. Based on these two methods, coherent guaranteed cost controllers are designed for a given quantum system to achieve improved control performance. An illustrative example also shows that the quantum Popov approach can obtain less conservative results than the quantum small gain approach for the same uncertain quantum system. [ABSTRACT FROM AUTHOR]