Related papers: A discrete spacetime model for quantum mechanics
Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct…
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk…
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme…
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…
Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
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…
We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum walk experiments realized with neutral…
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
This study aims to address the nature of state change, measurement, and probabilistic outcomes in non-relativistic quantum mechanics. We consider a pair of particles that interact in a one-dimensional setting via a delta-function potential.…
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…
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the…
We formulate the lattice QCD simulation with background classical gravitational fields. This formulation enables us to study nonperturbative aspects of quantum phenomena in curved spacetimes from the first principles. As the first…
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…