Related papers: Implementation of multi-walker quantum walks with …
We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…
Quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QW with the…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
Quantum walks of correlated particles offer the possibility to study large-scale quantum interference, simulate biological, chemical and physical systems, and a route to universal quantum computation. Here we demonstrate quantum walks of…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position…
We show that the standard quantum-walk quantum-to-classical transition, characterized by ballistic-to-diffusive spreading of the walker's position, can be controlled by externally modulating the coin state. We illustrate by showing an…
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…
The concept of lackadaisical quantum walk -- quantum walk with self loops -- was first introduced for discrete-time quantum walk on one-dimensional line. Later it was successfully applied to improve the running time of the spacial search on…
Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of…
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
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…
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 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…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…