### Abstract

Science, medicine and engineering demand efficient information processing. It is a long-standing goal to use quantum mechanics to significantly improve such computations. The processing routinely involves examining data as a function of complementary variables, e.g., time and frequency. This is done by the Fourier transform approximations which accurately compute inputs of $2^n$ samples in $O(n 2^n)$ steps. In the quantum domain, an analogous process exists, namely a Fourier transform of quantum amplitudes, which requires exponentially fewer $O(n \log n)$ quantum gates. Here, we report a quantum fractional Kravchuk-Fourier transform, a related process suited to finite string processing. Unlike previous demonstrations, our architecture involves only one gate, resulting in constant-time processing of quantum information. The gate exploits a generalized Hong--Ou--Mandel effect, the basis for quantum-photonic information applications. We perform a proof-of-concept experiment by creation of large photon number states, interfering them on a beam splitter and using photon-counting detection. Existing quantum technologies may scale it up towards diverse applications.

Original language | English |
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Publisher | arXiv.org |

Number of pages | 44 |

Publication status | Published - 11 Jul 2018 |

### Publication series

Name | Arxiv.org |
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### Keywords

- quant-ph

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## Cite this

Stobińska, M., Buraczewski, A., Moore, M., Clements, W. R., Renema, J. J., Nam, S. W., ... Walmsley, I. A. (2018).

*Quantum interference enables constant-time quantum information processing*. (Arxiv.org). arXiv.org.