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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Implementation of Deutsch and Deutsch-Jozsa algorithms with classical light

Benjamin Perez-García, Jason Francis, Melanie G. McLaren, Sandeep K. Goyal, Raúl I. Hernández-Aranda, Andrew Forbes, Thomas Konrad

Published Sep 27, 2016• 0 citations
Publisher

Abstract

We study the realization of quantum algorithms using classical optical elements and a coherent laser source. The encoded qubits are present in form of path qubits, polarization and orbital angular momentum. In particular, we propose an implementation for the Deutsch Algorithm in a Sagnac interferometer and the Deutsch-Jozsa Algorithm in a ring cavity.

DOI
10.1117/12.2238271

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We study the realization of quantum algorithms using classical optical elements and a coherent laser source. The encoded qubits are present in form of path qubits, polarization and orbital angular momentum. In particular, we propose an implementation for the Deutsch Algorithm in a Sagnac interferometer and the Deutsch-Jozsa Algorithm in a ring cavity.
The first optical proposal for the realization of the two-bit version of the Deutsch-Jozsa algorithm [D. Deutsch and R. Jozsa, Proc. R. Soc. London A {\bf 493}, 553 (1992)] is presented. The proposal uses Stark shifts in an ensemble of atoms and degenerate sources of photons. The photons interact dispersively with an atomic ensemble, leading to an effective Hamiltonian in atom-field basis, which is useful for performing the required two-qubit operations. Combining these with a set of one-qubit operations, the algorithm can be implemented. A discussion of the experimental feasibility of the proposal is given.
We propose two physical schemes for implementing the simplest version of Deutsch-Jozsa algorithm(D-J) based on cavity QED technique.One is a perfect scheme,which can be generalized to multi-qubit inputs Deutsch-Jozsa algorithm.It can be realized with the help of controlled-NOT gates and single-qubit operations.The detailed process in cavity QED is discussed in the scheme.The other is a simpler scheme without controlled-NOT gates,which is only suit for the simplest version of Deutsch-Jozsa algorithm.The scheme only requires single-qubit operation.Thus the scheme can be realized easier than the former one.Our schemes would be an important step for quantum computer.
We present an optical scheme to implement the Deutsch-Jozsa algorithm using ac Stark shifts. The scheme uses an atomic ensemble consisting of four-level atoms interacting dispersively with a field. This leads to a Hamiltonian in the atom-field basis which is quite suitable for quantum computation. We show how one can implement the algorithm by performing proper one- and two-qubit operations. We emphasize that in our model the decoherence is expected to be minimal due to our usage of atomic ground states and freely propagating photon.