
Quantum walkbased search algorithms with multiple marked vertices
The quantum walk is a powerful tool to develop quantum algorithms, which...
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Detecting quantum speedup by quantum walk with convolutional neural networks
Quantum walks are at the heart of modern quantum technologies. They allo...
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Quantum Walk Sampling by Growing Seed Sets
This work describes a new algorithm for creating a superposition over th...
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Upperbounds on the probability of finding marked connected components using quantum walks
Finding a marked vertex in a graph can be a complicated task when using ...
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Szegedy Walk Unitaries for Quantum Maps
Szegedy developed a generic method for quantizing classical algorithms b...
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QSW_MPI: a framework for parallel simulation of quantum stochastic walks
QSW_MPI is a python package developed for the modeling of quantum stocha...
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Random Walks: A Review of Algorithms and Applications
A random walk is known as a random process which describes a path includ...
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Quadratic speedup for finding marked vertices by quantum walks
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element quadratically faster than a classical random walk were only known for the special case when the marked set consists of just a single vertex, or in the case of some specific graphs. We present a new quantum algorithm for finding a marked vertex in any graph, with any set of marked vertices, that is (up to a log factor) quadratically faster than the corresponding classical random walk.
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