Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states: The quantum-classical divide and computational-complexity transitions in linear optics

Kaushik P. Seshadreesan, Jonathan P. Olson, Keith R. Motes, Peter P. Rohde, Jonathan P. Dowling

    Research output: Contribution to journalArticlepeer-review

    28 Citations (Scopus)

    Abstract

    Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes.

    Original languageEnglish
    Article number022334
    Pages (from-to)022334-1-022334-6
    Number of pages6
    JournalPhysical Review A - Atomic, Molecular, and Optical Physics
    Volume91
    Issue number2
    DOIs
    Publication statusPublished - 27 Feb 2015

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