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

@article{Arvind2007OpticalIO, title={Optical implementations, oracle equivalence, and the Bernstein-Vazirani algorithm}, author={Arvind and Gurpreet Kaur and Geetu Narang}, journal={Journal of The Optical Society of America B-optical Physics}, year={2007}, volume={24}, pages={221-225} }

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…

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## References

SHOWING 1-10 OF 29 REFERENCES

Implementation of a quantum algorithm to solve the Bernstein-Vazirani parity problem without entanglement on an ensemble quantum computer

- Physics
- 2001

Bernstein and Varizani have given the first quantum algorithm to solve the parity problem in which a strong violation of the classical information theoretic bound comes about. In this paper we refine…

Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm

- Physics
- 2001

A scheme to execute an n-bit Deutsch-Jozsa (DJ) algorithm using n qubits has been implemented for up to three qubits on an NMR quantum computer. For the one- and the two-bit Deutsch problem, the…

On the role of entanglement in quantum-computational speed-up

- Mathematics, PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2003

For any quantum algorithm operating on pure states, we prove that the presence of multi‐partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the…

Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits.

- Physics, MedicinePhysical review letters
- 2003

We report on a fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms for 8-point functions. The measured visibility of the 8-path interferometer is about 97.5%.…

Two-bit gates are universal for quantum computation.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1995

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The…

Elementary gates for quantum computation.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1995

U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.

Quantum Computation and Shor's Factoring Algorithm

- Physics
- 1996

Current technology is beginning to allow us to manipulate rather than just observe individual quantum phenomena. This opens up the possibility of exploiting quantum effects to perform computations…

Sophisticated quantum search without entanglement

- Computer Science, MedicinePhysical review letters
- 2000

There is a quantum algorithm which searches a "sophisticated" database with a single query, but which it is shown does not require entanglement even for multiparticle implementations.

Quantum advantage without entanglement

- Computer Science, MathematicsSPIE Optics + Photonics
- 2005

The Deutsch-Jozsa algorithm is presented, and it is shown that the maximal subproblem is of greater significance, by proving that it contains all the Boolean functions whose quantum phase-oracle is non-entangling.

Quantum entanglement and quantum computational algorithms

- Physics
- 2001

The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We…