Estimating Immanants of Special Unitary Matrices by Interferometry and Photon Counting

Associated People:

Barry Sanders (Institute for Quantum Information Science - University of Calgary)

Si-Hui Tan (Data Storage Institute - Singapore)

Hubert de Guise (Lakehead University - Thunder Bay)

Associated Sites:
PIMS University of Calgary
Associated PIMS Programs:

Mathematics of Quantum Information

Predicting photon-coincidence probabilities for multi-channel interferometers with single photons entering each input port is computationally hard. The problem can be turned around by using the interferometer as a computational tool to compute these distributions. We show how photon coincidence rates as functions of delay times between input photons reveal immanants (with determinants and permanents as special cases) of the interferometer transformation matrix. Interferometers could serve as a natural purpose-built (non-universal) quantum computer for solving non-trivial computational problems. We show that the famous Hong-Ou-Mandel two-photon dip is a special case of this result.

References
  • SI-HUI TAN, YVONNE Y. GAO, HUBERT DE GUISE, BARRY C. SANDERS, SU(3) Quantum Interferometry with single-photon input pulses, arxiv.org/abs/1208.5677