Multi-channel linear photon interferometry for quantum information processing

Quantum information processing is possible via multi-channel linear (passive) interferometry with photon number states as some or all of the inputs and photon-coincidence detection at the output ports. The Knill-Laflamme-Milburn nonlinear sign gate on dual-rail photonic qubits and the Aaronson-Arkhipov BosonSampling scheme are salient examples of linear photonic quantum information processing. Implementations of quantum walks also make use of linear photon interferometry. The famous Hong-Ou-Mandel dip presents the heart of what makes linear photon interferometry "quantum" and furthermore serves as an indispensable characterization tool for sources and interferometers. Our aim is to advance linear photonic quantum interferometry to serve as a precise and accurate tool for optical quantum information processing. To this end we develop and experimentally test a theory for accurate and precise characterization of the Hong-Ou-Mandel dip setup, extend this theory for accurate and precise characterization of multi-channel interferometry based on photon coincidences, extend the Hong-Ou-Mandel dip concept beyond two-channel to multi-channel interferometry, develop theory and (classical) algorithms for computing irreducible representations of SU(m) whose elements represent all m-channel interferometers, and determine the effects of extraneous multi-photon contributions to the desired outputs. Our approach allows for non-simultaneous photon arrival times, which removes the typical symmetrization assumption in photon interferometry and leads to photon coincidence rates depending on immanants of SU(m) matrices or submatrices; immanants generalize the concepts of permanents and determinants to allow for partial symmetries. For linear photon interferometry to move beyond the proof-of-principle stage to solving computational problems, they need to be reliable, accurate and precise within known error. Furthermore their performance needs to be benchmarked against the best classical simulation algorithms. Our results are enabling the field to advance in this direction.