Related papers: Systematic Dimensionality Reduction for Quantum Wa…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
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…
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
Given the recent advances in quantum technology, the complexity of quantum states is an important notion. The idea of the Krylov spread complexity has come into focus recently with the goal of capturing this in a quantitative way. The…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
We present a Mathematica package, QSWalk, to simulate the time evaluation of Quantum Stochastic Walks (QSWs) on arbitrary directed and weighted graphs. QSWs are a generalization of continuous time quantum walks that incorporate both…