A quantum walk based search algorithm, and its optical realisation

More documents

Recommendations

Info

Uniform loss Loss model D(ϱ) = η 2 ϱ + (1 − η 2 ) |0〉〈0| after t iterations: ϱ → D t (U t ϱU †t ) Initial pure state |ψ〉: (η ≤ 1) |ψ〉 → D |ψ〉 = η |ψ〉 Evolution operator: U ′′ = ηU ′ log 2 x ≈ −ε + n/2 − 1/2 Success probability Maximum success probability (p max ) 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -15 -10 -5 0 5 10 x = − log 2 η √ 2 n−1 η = 1 − 2 −ε p max (η) = for large n: p max (x) ≈ 1 2 [ exp(−2x acot x) 1 1+x 2 2 − O ( ( )] 1 n) + x acot x O 1 n exp(−2x acot x) 1 1+x 2 19 / 26
Comparison with numerical results Maximum success probability (p max ) 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 2 4 ε = 12 ε = 8 ε = 6 ε = 2 6 8 10 Rank of hypercube (n) 12 14 p max (η) = [ exp(−2x acot x) 1 1+x 2 2 − O ( ( )] 1 n) + a acot xO 1 n 20 / 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: Uniform loss Loss model D(ϱ) = η
Page 29 and 30: Direction dependent loss Descriptio
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

Create successful ePaper yourself

Delete template?

Save as template?