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arXiv:1508.01188 · Physical Review A

Deterministic quantum computation with one photonic qubit

Malena O. Hor-Meyll, D. S. Tasca, Stephen Patrick Walborn, P. H. Souto Ribeiro, M. M. Santos, Eduardo I. Duzzioni

Published Jul 31, 2015• 23 citations
arXivHTMLPDF

Abstract

We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high-dimension matrix, being limited by the resolution of the modulator panel and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our setup is $1080\ifmmode\times\else\texttimes\fi{}1920$, which is able to represent a system with approximately 21 qubits.

DOI
10.1103/physreva.92.012337

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We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high-dimension matrix, being limited by the resolution of the modulator panel and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our setup is 1080\ifmmode×\else\texttimes\fi19201080\ifmmode\times\else\texttimes\fi{}19201080\ifmmode×\else\texttimes\fi1920, which is able to represent a system with approximately 21 qubits.
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We report an experimental implementation of the minimal Deutsch algorithm in an optical setting. In this version, a redundancy is removed from the most famous form of the algorithm. The original version involves manipulation of two qubits, while in its minimal version, only one qubit is used. Our qubit is encoded in the transversal spatial modes of a spontaneous parametric down-converted signal photon, with the aid of a double slit, with the idler photon playing a crucial role in creating a heralded single-photon source. A spatial light modulator (SLM) is programmed to physically generate one-bit functions necessary to implement the algorithm's minimal version, which shows that the SLM can be used in future implementations of quantum protocols.
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In this work we implement the Deutsch-Jozsa algorithm with one qubit by removing a redundancy on it, which reduces the size of the register and simpli es the function evaluation. In order to do this, we used a pair of photons produced by down convertion, where one of them is used as triguer and the other passes trougth a double slit; as result its output is in a superposition of paths, i.e., one qubit. Using a spatial light modulator (SLM) that puts phases on the paths of the photons, and detecting in coincidence, we demonstrate the Deutsch-Jozsa algorithm with photons, and using only one qubit.