Sufficient condition for the mode mismatch of single photons for scalability of the boson-sampling computer
V. S. Shchesnovich · Physical Review A · 2014
The boson sampler proposed by Aaronson and Arkhipov is a nonuniversal quantum computer, which can serve as evidence against the extended Church-Turing thesis. It samples the probability distribution at the output of a linear unitary optical network with indistinguishable single photons at the input. Four experimental groups have already tested their small-scale prototypes with up to four photons. A boson sampler with a few dozens of single photons is believed to be hard to simulate on a classical computer. For scalability of a realistic boson sampler with current technology it is necessary to know the effect of the photon mode mismatch on its operation. Here a nondeterministic model of the boson sampler is analyzed, which employs partially indistinguishable single photons emitted by identical sources. A sufficient condition on the average mutual fidelity $\ensuremath{\langle}\mathcal{F}\ensuremath{\rangle}$ of the single photons is found, which guarantees that the realistic boson sampler outperforms the classical computer. Moreover, the boson-sampler computer with partially indistinguishable single photons is scalable and has more power than classical computers when the single-photon mode mismatch $1\ensuremath{-}\ensuremath{\langle}\mathcal{F}\ensuremath{\rangle}$ scales as $O({N}^{\ensuremath{-}3/2})$ with the total number of photons $N$.