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Optical implementations, oracle equivalence, and the Bernstein-Vazirani algorithm

Arvind·Gurpreet Kaur·Geetu Narang
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Abstract

We describe a new implementation of the Bernstein-Vazirani algorithm which relies on the fact that the polarization states of classical light beams can be cloned. We explore the possibility of computing with waves and discuss a classical optical model capable of implementing any algorithm (on $n$ qubits) that does not involve entanglement. The Bernstein-Vazirani algorithm (with a suitably modified oracle), wherein a hidden $n$ bit vector is discovered by one oracle query as against $n$ oracle queries required classically, belongs to this category. In our scheme, the modified oracle is also capable of computing $f(x)$ for a given $x$, which is not possible with earlier versions used in recent NMR and optics implementations of the algorithm.

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Arvind, Gurpreet Kaur, Geetu Narang. 2006-05-10. Optical implementations, oracle equivalence, and the Bernstein-Vazirani algorithm. https://doi.org/10.1364/josab.24.000221

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