Implementing Scalable Boson Sampling with Time-Bin Encoding: Analysis of Loss, Mode Mismatch, and Time Jitter

TL;DR

This paper analyzes how physical errors like loss and mode-mismatch impact the performance of scalable boson sampling using time-bin encoding, providing insights for improving experimental implementations.

Contribution

It offers a detailed error analysis of loss and mode-mismatch in time-bin encoded boson sampling, highlighting their effects on success probability and unitary bias.

Findings

Loss asymmetrically biases the implemented unitaries.

Loss limits the class of unitaries that can be realized.

Errors due to fiber-length mismatch and time-jitter affect fidelity.

Abstract

It was recently shown by Motes, Gilchrist, Dowling & Rohde [PRL 113, 120501 (2014)] that a time-bin encoded fiber-loop architecture can implement an arbitrary passive linear optics transformation. This was shown in the case of an ideal scheme whereby the architecture has no sources of error. In any realistic implementation, however, physical errors are present, which corrupt the output of the transformation. We investigate the dominant sources of error in this architecture --- loss and mode-mismatch --- and consider how it affects the BosonSampling protocol, a key application for passive linear optics. For our loss analysis we consider two major components that contribute to loss --- fiber and switches --- and calculate how this affects the success probability and fidelity of the device. Interestingly, we find that errors due to loss are not uniform (unique to time-bin encoding), which asymmetrically biases the implemented unitary. Thus, loss necessarily limits the class of unitaries that may be implemented, and therefore future implementations must prioritise minimising loss rates if arbitrary unitaries are to be implemented. Our formalism for mode-mismatch is generlized to account for various phenomenon that may cause mode-mismatch, but we focus on two --- errors in fiber-loop lengths, and time-jitter of the photon source. These results provide a guideline for how well future experimental implementations might perform in light of these error mechanisms.