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A quantum walk based search algorithm, and its optical realisation

A quantum walk based search algorithm, and its optical realisation

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Discrete time <strong>quantum</strong> <strong>walk</strong> (coined QW)<br />

Focussing generalization on:<br />

Stochastic process → Unitary process<br />

Simple example<br />

Galton’s board (quincunx)<br />

at each pin: 50%-50% probability<br />

→ tossing a coin<br />

Resolution<br />

Replace classical coin by <strong>quantum</strong> coin!<br />

{|j〉 |v j 〉 : j = 1, . . . , degree(v j )}<br />

additional degree of freedom<br />

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