Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4

Search results for: quantum systems

4 Stability of Stochastic Model Predictive Control for Schrödinger Equation with Finite Approximation

Authors: Tomoaki Hashimoto

Abstract:

Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: Optimal control, stochastic systems, quantum systems, stabilization.

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3 Open Problems on Zeros of Analytic Functions in Finite Quantum Systems

Authors: Muna Tabuni

Abstract:

The paper contains an investigation on basic problems about the zeros of analytic theta functions. A brief introduction to analytic representation of finite quantum systems is given. The zeros of this function and there evolution time are discussed. Two open problems are introduced. The first problem discusses the cases when the zeros follow the same path. As the basis change the quantum state |f transforms into different quantum state. The second problem is to define a map between two toruses where the domain and the range of this map are the analytic functions on toruses.

Keywords: open problems, constraint, change of basis.

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2 Winding Numbers of Paths of Analytic Functions Zeros in Finite Quantum Systems

Authors: Muna Tabuni

Abstract:

The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

Keywords: Winding numbers, period, paths of zeros.

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1 Entanglement-based Quantum Computing by Diagrams of States

Authors: Sara Felloni, Giuliano Strini

Abstract:

We explore entanglement in composite quantum systems and how its peculiar properties are exploited in quantum information and communication protocols by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for Bell states generation, measurements and projections, for dense coding and quantum teleportation, for probabilistic quantum machines designed to perform approximate quantum cloning and universal NOT and, finally, for quantum privacy amplification based on entanglement purification. Diagrams of states prove to be a useful approach to analyze quantum computations, by offering an intuitive graphic representation of the processing of quantum information. They also help in conceiving novel quantum computations, from describing the desired information processing to deriving the final implementation by quantum gate arrays.

Keywords: Diagrams of states, entanglement, quantum circuits, quantum information.

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