Quantum walk search on johnson graphs
WebThe Johnson graph J ( n, k) is defined by n symbols, where vertices are k-element subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, both J ( n, 1), the complete graph K n , and J ( n, 2), the strongly regular triangular graph T n , support fast quantum spatial search. Wong showed that …
Quantum walk search on johnson graphs
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WebSep 7, 2024 · It has been shown that a lackadaisical quantum walk can improve spatial search on the complete graph, discrete torus, cycle, and regular complete bipartite graph. In this paper, we observe that these are all vertex-transitive graphs, and when there is a unique marked vertex, the optimal weight of the self-loop equals the degree of the loopless graph … WebMay 28, 2024 · Doubling the success of quantum walk search using internal-state measurements Kri jnis Prsis, Jevgnijs Vihrovs and Thomas G Wong-Grover search with lackadaisical quantum walks Thomas G Wong-Quantum walk search on Johnson graphs Thomas G Wong-This content was downloaded from IP address 207.46.13.110 on …
WebFeb 1, 2024 · The Johnson graph J(n, k) plays an important role in quantum walks because it is used in the element distinctness algorithm [27] and in many spatial search algorithms … Webmakes quantum walk algorithms faster than classical ones since we can design them in such a way that wrong answers quickly cancel out.[4]. There are two types of quantum walks: discrete-time quantum walks and continuous-time quantum walks. In this project, as we are dealing with graphs so we would explore discrete-time quantum walks which are
WebAbstract. This paper introduces a subset-sum algorithm with heuristic asymptotic cost exponent below 0.25. The new algorithm combines the 2010 Howgrave-Graham–Joux subset-sum algorithm with a new streamlined data structure for … WebJohnson graph J(4;2), which is the triangular graph T 4. algorithm for element distinctness was developed by Childs [7], which walks on a modi ed Johnson graph with additional …
WebIn this paper, a new continuous-time quantum walk formulation is developed to simulate stochastic drift-diffusion processes in two- or higher-dimensional spaces. The random drift-diffusion process is mod-eled as the dynamics of imaginary-time quantum systems. The new simulation algorithm combines continuous-time quantum walk on graphs with path
WebIn this work, we show that spatial search on Johnson graphs by continuous-time quantum walk achieves the Grover lower bound π N / 2 with success probability 1 asymptotically for every fixed diameter, where N is the number of vertices. The proof is mathematically rigorous and can be used for other graph classes. scratch butterscotch puddingWebAug 4, 2024 · In fact, there are some results in literature analyzing quantum walk search on a subclass of Johnson graphs. Wong Wong2016JPA showed that J ( n , 3 ) supports fast spatial search by continuous-time quantum walk, and Xue et al. XRL_19 also showed that J ( n , 3 ) supports fast spatial search using the scattering quantum walk, and they discussed … scratch by katWeb2 days ago · Here we propose an alternative approach; we use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation without … scratch by rusty nailWebJun 1, 2024 · In this work, we address the spatial search problem on Johnson graphs using the coined quantum walk model. Since Johnson graphs are vertex- and distance … scratch by a dogWebMay 13, 2024 · Continuous-time quantum walks [1,2,3,4,5,6] are used for a variety of applications.In some situations, it is necessary to acquire the transition probability from one vertex to another in the associated graph, such as for coherent transport on complex networks [7,8,9,10] and graph isomorphism (GI) problems [11, 12].However, for the spatial … scratch by a cat is it dangerousWebKeywords: Quantum algorithms, quantum walks, collision search, lattice siev-ing 1 Introduction Quantum walks are a powerful algorithmic tool which has been used to pro- ... nodes in a so-called Johnson graph [19] (or a product of Johnson graphs). When walking on this particular graph, the MNRS framework is somewhat rigid. scratch cacaWebHere the search space is confined to a low-dimensional subspace corresponding to the collapsed graph. Using matrix perturbation theory, we show that discrete-time quantum … scratch by stray cat