Boson-sampling with photons of arbitrary spectral structure

TL;DR

This paper investigates how the spectral properties of photons affect boson-sampling, revealing the relationship between photon distinguishability and computational complexity in linear optical quantum computing.

Contribution

It introduces a general framework for analyzing boson-sampling with photons of arbitrary spectral structure, extending understanding of partial distinguishability effects.

Findings

Sampling statistics relate to matrix permanents.

Spectral distinguishability impacts computational complexity.

Results apply to both spectrally resolving and non-resolving detectors.

Abstract

Boson-sampling has attracted much interest as a simplified approach to implementing a subset of optical quantum computing. Boson-sampling requires indistinguishable photons, but far fewer of them than universal optical quantum computing architectures. In reality, photons are never indistinguishable, and exhibit a rich spectral structure. Here we consider the operation of boson-sampling with photons of arbitrary spectral structure and relate the sampling statistics of the device to matrix permanents. This sheds light on the computational complexity of different regimes of the photons' spectral characteristics, and provides very general results for the operation of linear optics interferometers in the presence of partially distinguishable photons. Our results apply to both the cases of spectrally resolving and non-spectrally resolving detectors.