Optical implementations, oracle equivalence, and the bernstein–vazirani algorithm

We describe a new implementation of the Bernstein–Vazirani algorithm that 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. © 2007 Optical Society of America.