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arXiv:0709.4314 · Physical Review A

Experimental demonstration of quantum leader election in linear optics

Yuta Okubo, Xiang‐Bin Wang, Yun-Kun Jiang, Seiichiro Tani, Akihisa Tomita

Published Mar 27, 2008• 5 citations
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Abstract

Linear optics is a promising candidate to enable the construction of quantum computers. A number of quantum protocols gates based on linear optics have been demonstrated. However, it is well known that these gates are nondeterministic and that higher order nonlinearity is necessary for deterministic operations. We found the quantum leader election protocol can be operated deterministically only with linear optics, and we have demonstrated the nearly deterministic operation which overcomes classical limit.

DOI
10.1103/physreva.77.032343

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Linear optics is a promising candidate to enable the construction of quantum computers. A number of quantum protocols gates based on linear optics have been demonstrated. However, it is well known that these gates are nondeterministic and that higher order nonlinearity is necessary for deterministic operations. We found the quantum leader election protocol can be operated deterministically only with linear optics, and we have demonstrated the nearly deterministic operation which overcomes classical limit.
Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (nondestructive) CNOT that succeeds with a probability of 1/4.
Non-deterministic polynomial (NP)-complete problems are collections of intractable problems for classical computers, but they may be easier to solve for quantum computers. Considering that practical quantum computers and networks are still under development, it is necessary to find alternatives to solve these problems. Simulations with linear optics offer a good choice since much of the research on quantum information is executed with this approach. In this work, based on Aaronson's protocol (Theory Comput, 5, 1, 2009) ad Arrazola et. al.'s linear optics scheme (npj Quantum Inf, 78, 022310, 2018), we present a demonstration of the NP-complete 2-out-of-4 SAT problem for 4 variables. The experimental results show that NP-complete problems can be well simulated through linear optical systems.
In order for quantum communications systems to become widely used, it will probably be necessary to develop quantum repeaters that can extend the range of quantum key distribution systems and correct for errors in the transmission of quantum information. Quantum logic gates based on linear optical techniques appear to be a promising approach for the development of quantum repeaters, and they may have applications in quantum computing as well. Here we describe the basic principles of logic gates based on linear optics, along with the results from several experimental demonstrations of devices of this kind. A prototype source of single photons and a quantum memory device for photons are also discussed. These devices can be combined with a four-qubit encoding to implement a quantum repeater.
Leader election between n parties is known to be impossible classically. This work gives a simple algorithm that does it, based on the weak coin flipping protocol with arbitrarily small bias derived by Mochon in 2007, and recently published and simplified in Aharonov et al in 2016. A protocol with linear number of coin flipping rounds is quite simple to achieve; We further provide an improvement to logarithmic number of coin flipping rounds. This is a much improved journal version of a preprint posted in 2009: many typos are corrected, proofs are more rigorous and accurate, and the analysis of complexity is significantly tightened which gives a stronger result in terms of efficiency; The first protocol with linear number of rounds, was achieved independently also by Aharon and Silman in 2010.