Related papers: Quantum Markov chains: recurrence, Schur functions…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
We introduce quantized bipartite walks, compute their spectra, generalize the algorithms of Grover \cite{g} and Ambainis \cite{amb03} and interpret them as quantum walks with memory. We compare the performance of walk based classical and…
Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…
The P\'olya number characterizes the recurrence of a random walk. We apply the generalization of this concept to quantum walks [M. \v{S}tefa\v{n}\'ak, I. Jex and T. Kiss, Phys. Rev. Lett. \textbf{100}, 020501 (2008)] which is based on a…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…
Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…
The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak…
We study the analogues of irreducibility, period, and communicating classes for open quantum random walks, as defined by Attal et al. (J. Stat. Phys., 2012). We recover results similar to the standard ones for Markov chains, in terms of…
We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory,…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
We give a list of equivalent conditions for reversibility of the adjoint of a unital Schwarz map with respect to a set of quantum states. A large class of such conditions is given by preservation of distinguishability measures:…
Distributed quantum computing (DQC) connects many small quantum processors into a single logical machine, offering a practical route to scalable quantum computation. However, most existing DQC paradigms are structure-agnostic. Circuit…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…
Although the security of quantum cryptography is provable based on the principles of quantum mechanics, it can be compromised by the flaws in the design of quantum protocols and the noise in their physical implementations. So, it is…
Quantum channels are not invertible in general. A quasi-inverse allows for a partial recovery of the input state, but its analytical results are found only in a restricted space of its parameters. This work explores the potential of neural…