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We show that the class of quantum baker's maps defined by Schack and Caves have the proper classical limit provided the number of momentum bits approaches infinity. This is done by deriving a semi-classical approximation to the…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…
Controlling quantum systems under correlated non-Markovian noise, particularly when strongly coupled, poses significant challenges in the development of quantum technologies. Traditional quantum control strategies, heavily reliant on…
The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e., conditions under which it holds sup_{t in R} | (psi(t),H(t) psi(t))…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…
Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation…
Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition,…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Quantum Turing machines are discussed and reviewed in this paper. Most of the paper is concerned with processes defined by a step operator $T$ that is used to construct a Hamiltonian $H$ according to Feynman's prescription. Differences…
We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map…
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of…
We study transport properties of discrete quantum dynamical systems on the lattice, in particular Coined Quantum Walks and the Chalker--Coddington model. We prove existence of a non trivial charge transport and that the absolutely…
In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain desintegration. This is a desintegration with…
Quantum algorithmics with single spins poses serious technological challenges such as precision fabrication, rapid decoherence, atomic-scale addressing and readout. To circumvent atomic-scale challenges, we examine the case of fully…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Many results have been recently obtained regarding the power of hypothetical closed time-like curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way…
A crucial step towards the 6th generation (6G) of networks would be a shift in communication paradigm beyond the limits of Shannon's theory. In both classical and quantum Shannon's information theory, communication channels are generally…