A quantum walk based search algorithm, and its optical realisation

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Direction dependent loss η 0 η 1 η n−1 η 0 , η 1 , . . . , η n−1 can be different Warning: original symmetry of hypercube broken! Walk cannot be collapsed onto a line 21 / 26
Direction dependent loss Description starting with pure state: D = n−1 ∑ d=0 η d |d〉〈d|, {η} = {η d | d = 0, . . . , n − 1} a lower bound: p({η}, t) ≥ ¯η 2t { √ pi (t) − (η max /¯η) [ (η max /¯η) t − 1 ] } 2 ¯η = η max + η min 2 21 / 26
Page 1 and 2: A quantum walk based search algorit
Page 3 and 4: Quantum walks on graphs Graph G = (
Page 5 and 6: Discrete quantum walk G = (V, E) n-
Page 7 and 8: Applications of QWs Designing effic
Page 9 and 10: Quantum walk on a hypercube hypercu
Page 11 and 12: Spectrum of Grover walk on a hyperc
Page 13 and 14: Proof of principle (sketch) Collaps
Page 15 and 16: Proof of principle (sketch) 2 Treat
Page 17 and 18: Quantum optical realization of SKW
Page 19 and 20: Quantum optical realization of SKW
Page 21 and 22: QRW search in linear optical networ
Page 23 and 24: QRW search in linear optical networ
Page 25 and 26: Uniform loss Loss model D(ϱ) = η
Page 27: Comparison with numerical results M
Page 31 and 32: Direction dependent loss Descriptio
Page 33 and 34: Numerical results Second order Tayl
Page 35 and 36: Phase Errors Description F({ϕ}) =
Page 37 and 38: Phase Errors 0.4 Description 0.35 F
Page 39: Conclusions Quantum walks Interesti

A quantum walk based search algorithm, and its optical realisation

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