Related papers: Feynman checkers: number-theoretic properties
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
Feynman contended that the double-slit experiment contained the `only mystery' in quantum mechanics. The mystery was that electrons traverse the interferometer as waves, but are detected as particles. This note was motivated by the question…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
At a fundamental level every measurement process relies on an interaction where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interaction. This results in a…
This essay gives a short, informal account of the development of digital logic from the Pleistocene to the Manhattan Project, the introduction of reversible circuits, and Richard Feynman's allied proposal for quantum computing. We argue…
Quantum Rings have been simulated so far in many ways, but in this work a new aproximation is deemed. We use particles without angular momentum and several spectra, for different geometric settings, are gotten. These spectra depends on K,…
We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin…
We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting…
We show that recent experiments in hybrid qubit-oscillator devices that measure the phase-space characteristic function of the oscillator via the qubit can be seen through the lens of functional calculus and path integrals, drawing a clear…
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a…
In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the…
The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
A derivation is given of the Feynman rules to be used in the perturbative computation of the Green's functions of a generic quantum many-body theory when the action which is being perturbed is not necessarily quadratic. Some applications…
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various…
The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement…
The aim of this article is to relate the discrete quantum walk on $\mathbb{Z}$ with the continuous Schr\"odinger operator on $\mathbb{R}$ in the scattering problem. Each point of $\mathbb{Z}$ is associated with a barrier of the potential,…
In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number…