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arXiv:1009.3081 · Physical Review A

Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer

Pei Zhang, Ruifeng Liu, Yun‐Feng Huang, Hong Gao, Fuli Li

Published Dec 23, 2010• 20 citations
arXivHTMLPDF

Abstract

We report an experimental demonstration of quantum Deutsch's algorithm using a linear-optical system. By employing photon polarization and spatial modes, we implement all balanced and constant functions for a quantum computer. The experimental system is very stable, and the experimental data are in excellent accordance with the theoretical results.

DOI
10.1103/physreva.82.064302

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We report an experimental demonstration of quantum Deutsch's algorithm using a linear-optical system. By employing photon polarization and spatial modes, we implement all balanced and constant functions for a quantum computer. The experimental system is very stable, and the experimental data are in excellent accordance with the theoretical results.
We propose multiple implementations of linear-optical processing of Deutsch algorithm using entangled state. Recently Oliveira {\\it et al.} [ J. Opt. B \\textbf{7}, 288 (2005) ] experimentally demonstrated the use of polarization and transverse spatial modes of the electromagnetic field as qubits for Deutsch algorithm, in which three Hadamard gates and a function are used. In our new implementations, the answer to the Deutsch problem is successfully determined even without the use of Hadamard gates. Instead, we use a polarization-momentum entangled bi-photon state. Coincidence measurements of photon arrivals coupled with polarization state analyzers identify answers to Deutsch problem. The entanglement-witness analysis is applied to validate the fidelity or the performance of the schemes.
A quantum computation algorithm is demonstrated using single photons and linear optics. Quantum registers are realized by modes and polarization of photons, and the unitary transformations for them are implemented with linear optics. For each quantum computation, the answer to the Deutsch Jozsa problem for any 4 bit digit is given by a single-photon detection signal with a small error rate. The origin of the error is also studied and categorized according to the sources: systematic errors of quantum gates, phase relaxation, amplitude dumping, and misreadout. It is suspected that a demonstration of 11 qubits using linear optics anda single photon with less than a 20 % error rate is achievable by the technique used in the experiment. As a further objective, an idea to construct controlled-NOT gate using quantum phase gate (QPG) given by Chuang et. al., is introduced and experiments on the QPGs are also reviewed.
We report an experiment to demonstrate a quantum permutation determining algorithm with linear optical system. By employing photon's polarization and spatial mode, we realize the quantum ququart states and all the essential permutation transformations. The quantum permutation determining algorithm displays the speedup of quantum algorithm by determining the parity of the permutation in only one step of evaluation compared with two for classical algorithm. This experiment is accomplished in single photon level and the method exhibits universality in high-dimensional quantum computation.