Related papers: Quantum simulations of classical random walks and …
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
A quantum computing algorithm for rhythm generation is presented, which aims to expand and explore quantum computing applications in the arts, particularly in music. The algorithm maps quantum random walk trajectories onto a rhythmspace --…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
One of the methods proposed in the last years for studying non-perturbative gauge theory physics is quantum simulation, where lattice gauge theories are mapped onto quantum devices which can be built in the laboratory, or quantum computers.…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk…
We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walker's direction. We implement a dephasing process…
Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
Quantum walks exhibit properties without classical analogues. One of those is the phenomenon of asymptotic trapping -- there can be non-zero probability of the quantum walker being localised in a finite part of the underlying graph…
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…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs,…
It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the…
We study the problem of approximately simulating a $t$-step random walk on a graph where the input edges come from a single-pass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this…
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are…