Related papers: Quantum Pascal's Triangle and Sierpinski's carpet
We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…
We present a novel application of the HHL (Harrow-Hassidim-Lloyd) algorithm -- a quantum algorithm solving systems of linear equations -- in solving an open problem about quantum random walks, namely computing hitting (or absorption)…
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on…
Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a time-periodic field. While there is ample theoretical work…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is…
We introduce a minimal set of physically motivated postulates that the Hamiltonian H of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
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…
In this article we present an effective Hamiltonian approach for Discrete Time Quantum Random Walk. A form of the Hamiltonian for one dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are the generators of…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
The Pascal matrix, which is related to Pascal's triangle, appears in many places in the theory of uniform distribution and in many other areas of mathematics. Examples are the construction of low-discrepancy sequences as well as normal…
Random walks behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the…
The weak convergence theorems of the one- and two-dimensional simple quantum walks, SQW$^{(d)}, d=1,2$, show a striking contrast to the classical counterparts, the simple random walks, SRW$^{(d)}$. The limit distributions have novel…
The pursuit of quantum advantage in simulating many-body quantum systems on quantum computers has gained momentum with advancements in quantum hardware. This work focuses on leveraging the symmetry properties of these systems, particularly…
Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schr\"{o}dinger, massive Dirac, and Klein-Gordon equations. Here, two different types of Fibonacci discrete-time…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its…
By defining the dimension of natural numbers as the number of prime factors, all natural numbers smaller than 2^(n+1) (n is a natural number) can be classified by their dimensions, and the count of numbers of each dimension gives a…