Simon's problem is of great importance in quantum algorithm design as it provides a clear gap between the classical and quantum times required to perform a calculation. However, it has never been experimentally realized in any physical system. Now, Mark Tame and co-workers in South Africa and the UK have demonstrated a one-way quantum algorithm for solving Simon's problem using a multipartite entangled state of photons. A Ti:sapphire laser with a wavelength of 724.5 nm pumped two birefringent photonic-crystal fibres (PCFs) to generate correlated photons with wavelengths of 626 nm and 860 nm through spontaneous four-wave mixing. Each PCF was arranged in a Sagnac loop closed using a polarization beam splitter to generate the five-qubit entangled cluster state plus an additional qubit. The algorithm was executed by measuring the relative populations and the polarization states. The team repeated the algorithm for the two-qubit version of Simon's Problem a number of times to obtain the success probabilities. The average runtime was around 2 iterations, whereas it was 8/3 iterations on average for the classical analogue, thus experimentally demonstrating the existence of a runtime gap.
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Horiuchi, N. One-way quantum computer. Nature Photon 9, 7 (2015). https://doi.org/10.1038/nphoton.2014.315
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DOI: https://doi.org/10.1038/nphoton.2014.315