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Register a new userFault-Tolerant Control of Linear Quantum Stochastic Systems
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Added by
Daoyi Dong
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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In quantum engineering, faults may occur in a quantum control system, which will cause the quantum control system unstable or deteriorate other relevant performance of the system. This note presents an estimator-based fault-tolerant control design approach for a class of linear quantum stochastic systems subject to fault signals. In this approach, the fault signals and some commutative components of the quantum system observables are estimated, and a fault-tolerant controller is designed to compensate the effect of the fault signals. Numerical procedures are developed for controller design and an example is presented to demonstrate the proposed design approach.
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Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper 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-infinity disturbance attenuation performance. This paper 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-infinity control problem to the dissipation properties and the solutions of Riccati differential equations, an H-infinity controller for the quantum system is then designed by solving a set of linear matrix inequalities (LMIs). In particular, an algorithm is employed to introduce additional noises and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. For real applications of the developed fault-tolerant control strategy, we present a linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values. It is demonstrated that a quantum H-infinity controller can be designed and implemented using some basic optical components to achieve the desired control goal.
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of i.i.d. observations. We adopt a distributionally robust approach to compute a mean-square stabilizing feedback gain with a given probability. The larger the sample size, the less conservative the controller, yet our methodology gives stability guarantees with high probability, for any number of samples. Using tools from statistical learning theory, we estimate confidence regions for the unknown probability distributions (ambiguity sets) which have the shape of total variation balls centered around the empirical distribution. We use these confidence regions in the design of appropriate distributionally robust controllers and show that the associated stability conditions can be cast as a tractable linear matrix inequality (LMI) by using conjugate duality. The resulting design procedure scales gracefully with the size of the probability space and the system dimensions. Through a numerical example, we illustrate the superior sample complexity of the proposed methodology over the stochastic approach.
The scalability of photonic implementations of fault-tolerant quantum computing based on Gottesman-Kitaev-Preskill (GKP) qubits is injured by the requirements of inline squeezing and reconfigurability of the linear optical network. In this work we propose a topologically error-corrected architecture that does away with these elements at no cost - in fact, at an advantage - to state preparation overheads. Our computer consists of three modules: a 2D array of probabilistic sources of GKP states; a depth-four circuit of static beamsplitters, phase shifters, and single-time-step delay lines; and a 2D array of homodyne detectors. The symmetry of our proposed circuit allows us to combine the effects of finite squeezing and uniform photon loss within the noise model, resulting in more comprehensive threshold estimates. These jumps over both architectural and analytical hurdles considerably expedite the construction of a photonic quantum computer.
We present a fault-tolerant semi-global control strategy for universal quantum computers. We show that N-dimensional array of qubits where only (N-1)-dimensional addressing resolution is available is compatible with fault-tolerant universal quantum computation. What is more, we show that measurements and individual control of qubits are required only at the boundaries of the fault-tolerant computer, i.e. holographic fault-tolerant quantum computation. Our model alleviates the heavy physical conditions on current qubit candidates imposed by addressability requirements and represents an option to improve their scalability.
The purpose of this paper is to formulate and solve a H-infinity controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H-infinity control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.
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