Related papers: Selected Open Problems in Continuous-Time Quantum …
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
Quantum walks are dynamic systems with a wide range of applications in quantum computation and quantum simulation of analog systems, therefore it is of common interest to understand what changes from an isolated process to one embedded in…
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph $G$ has perfect state transfer if and only if its quotient $G/\pi$, under any equitable partition $\pi$, has perfect state transfer, we…
We describe two BQP-complete problems concerning properties of sparse graphs having a certain symmetry. The graphs are specified by efficiently computable functions which output the adjacent vertices for each vertex. Let i and j be two…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
Quantum walks have emerged as an interesting candidate for the implementation of quantum information processing protocols. Optical implementations of quantum walks have been demonstrated by various groups and some have received high-profile…
Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
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…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
Open quantum walks (OQWs) describe a quantum walker on an underlying graph whose dynamics is purely driven by dissipation and decoherence. Mathematically, they are formulated as completely positive trace preserving (CPTP) maps on the space…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
Quantum computing, leveraging the principles of quantum mechanics, has been found to significantly enhance computational capabilities in principle, in some cases beyond classical computing limits. This paper explores quantum computing's…
Open quantum walks (OQWs) are a new type of quantum walks which are entirely driven by the dissipative interaction with external environments and are formulated as completely positive trace-preserving maps on graphs. A generalized quantum…
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more…
This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by using a new path integral approach based on an orthonormal…