A quantum walk based search algorithm, and its optical realisation

Phase Errors
Description
F({ϕ}) = ∑ e iϕ dx
|d, x〉〈d, x|
d,x
U({ϕ}) = U ′ F({ϕ})
Single runs
0.4
0.35
Average probability (n = 6)
Average probability of success
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
100
200 300
Number of steps (t)
∆ϕ = 3 o
∆ϕ = 6 o
∆ϕ = 9 o
∆ϕ = 12 o
400
500
Probability of success
0.3
0.25
0.2
0.15
0.1
0.05
0
0
20
40
60 80 100
Number of steps (t)
120
140
160
Stable phase in one run
|ψ t ({ϕ})〉 = U({ϕ}) t |ψ 0 〉
ϱ out = |ψ t ({ϕ})〉〈ψ t ({ϕ})| {ϕ}
Gaussian: 〈ϕ〉 = 0, ∆ϕ variance
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