Diagrammatic approach to quantum search
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We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theory’s effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with \(N\).
KeywordsQuantum search Quantum walks Quantum algorithms Perturbation theory Grover’s algorithm
Thanks to David Meyer for useful discussions. This work was partially supported by the European Union Seventh Framework Programme (FP7/2007-2013) under the QALGO (Grant Agreement No. 600700) project, and the ERC Advanced Grant MQC.
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