Related papers: Quantum walk for SU(1,1)
We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is…
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…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a…
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…
In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory 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…
We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate…
We investigate the properties of a quantum walk which can simulate the behavior of a spin $1/2$ particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup…
In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…
It is shown that a standard one-dimensional coined discrete-time quantum walk can generate operationally admissible post-quantum correlations in a coin-position Bell scenario, without any modification of its unitary nearest-neighbor…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…
Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information…
In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems.…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new…
We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin…
We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z…