A quantum walk based search algorithm, and its optical realisation
A quantum walk based search algorithm, and its optical realisation
A quantum walk based search algorithm, and its optical realisation
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Quantum <strong>optical</strong> realization of SKW <strong>algorithm</strong><br />
n − n multiport<br />
0<br />
1<br />
n<br />
n − 1<br />
Scattering r<strong>and</strong>om <strong>walk</strong><br />
x = 0<br />
t<br />
t + 1<br />
n − 1<br />
1<br />
n 0<br />
transformation:<br />
n−1 ∑<br />
d=0<br />
a d |d〉 → n−1 ∑<br />
→ coin operator<br />
d,k=0<br />
C dk a k |d〉<br />
x = 1<br />
x = 2<br />
x = 3<br />
x = 4<br />
|d, x〉 → |d, x ⊕ e d 〉<br />
S(C 0 ⊗ 1) ∑ a dx |d, x〉 = ∑ C dk a kx |d, x ⊕ e d 〉<br />
dx<br />
dxk<br />
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