Related papers: Matrix valued Szego polynomials and quantum random…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
It is shown in this paper that the quantum master equation can be mapped to a modified continuous time random walk (CTRW) if the relaxation term is composed of transitions over a set of states. When the Hamiltonian is time-independent and…
The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by…
Quantum walks (QWs) have a property that classical random walks (RWs) do not possess -- the coexistence of linear spreading and localization -- and this property is utilized to implement various kinds of applications. This paper proposes…
Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach,…
A new family of discrete-time quantum walks (DTQWs) propagating on a regular $(1+2)$D spacetime lattice is introduced. The continuous limit of these DTQWs is shown to coincide with the dynamics of a Dirac fermion interacting with an…
In this work we study certain aspects of Open Quantum Random Walks (OQRWs), a class of quantum channels described by S. Attal et al. \cite{attal}. As a first objective we consider processes which are nonhomogeneous in time, i.e., at each…
We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…
In this paper, we study a family of lattice walks which are related to the Hadamard conjecture. There is a bijection between paths of these walks which originate and terminate at the origin and equivalence classes of partial Hadamard…
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…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form…
A quantum master equation of the Lindblad form is obtained in this paper by considering the spontaneous wave-packet reduction. Different classical equations can be derived after exactly mapping such a quantum master equation to a continuous…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
As cloud services continue to expand, the security of private data stored and processed in these environments has become paramount. This work delves into quantum homomorphic encryption (QHE), an emerging technology that facilitates secure…
Szegedy's quantization of a reversible Markov chain provides a quantum walk whose spectral gap is quadratically larger than that of the classical walk. Quantum computers are therefore expected to provide a speedup of Metropolis-Hastings…
This work is motivated by the study of some two-dimensional random walks in random environment (RWRE) with transition probabilities independent of one coordinate of the walk. These are non-reversible models and can not be treated by…
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical…