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This paper is concerned with the feasibility of the classical nearest-neighbor interpolation based on flexible representation of quantum images (FRQI) and novel enhanced quantum representation (NEQR). Firstly, the feasibility of the classical image nearest-neighbor interpolation for quantum images of FRQI and NEQR is proven. Then, by defining the halving operation and by making use of quantum rotation gates, the concrete quantum circuit of the nearest-neighbor interpolation for FRQI is designed for the first time. Furthermore, quantum circuit of the nearest-neighbor interpolation for NEQR is given. The merit of the proposed NEQR circuit lies in their low complexity, which is achieved by utilizing the halving operation and the quantum oracle operator. Finally, in order to further improve the performance of the former circuits, new interpolation circuits for FRQI and NEQR are presented by using Control-NOT gates instead of a halving operation. Simulation results show the effectiveness of the proposed circuits. [ABSTRACT FROM AUTHOR]

Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain models and is also supported by numerical studies of a variety of examples. In this paper we analyze the long-time behavior of a particular class of decoherent quantum walks, which, to the best of our knowledge, was only studied at the level of numerical simulations before. We consider a local coin operation which is randomly and independently chosen for each time step and each lattice site and prove that, under rather mild conditions, this leads to classical behavior: With the same scaling as needed for a classical diffusion the position distribution converges to a Gaussian, which is independent of the initial state. Our method is based on non-degenerate perturbation theory and yields an explicit expression for the covariance matrix of the asymptotic Gaussian in terms of the randomness parameters. [ABSTRACT FROM AUTHOR]

We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness (as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac), but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application–QL modeling of brain’s functioning. The brain is modeled as a QL-computer. [ABSTRACT FROM AUTHOR]

In this paper, we develop a theory of learning nonlinear input–output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory identifies the properties required for a class of dissipative quantum systems to be universal, in that any input–output map with fading memory can be approximated arbitrarily closely by an element of this class. We then introduce an example class of dissipative quantum systems that is provably universal. Numerical experiments illustrate that with a small number of qubits, this class can achieve comparable performance to classical learning schemes with a large number of tunable parameters. Further numerical analysis suggests that the exponentially increasing Hilbert space presents a potential resource for dissipative quantum systems to surpass classical learning schemes for input–output maps. [ABSTRACT FROM AUTHOR]