Boosting photonic quantum computation with moderate nonlinearity

TL;DR

This paper proposes using moderate nonlinearity in photonic systems, specifically a nonlinear router, to enhance quantum computation efficiency and reduce resource overhead in measurement-based quantum computing.

Contribution

It introduces a nonlinear router scheme utilizing moderate nonlinearity, such as Rydberg blockade, to improve key quantum operations and decrease resource requirements in photonic MBQC.

Findings

Nonlinear router directs photons based on intensity, improving operation success rates.

Protocols for Bell measurement, GHZ-state prep, CNOT, and factorization are developed.

Moderate nonlinearity significantly reduces resource overhead in fault-tolerant MBQC.

Abstract

Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $\pi$) to boost photonic quantum computing and significantly reduce its resources overhead. The key element in our scheme is a nonlinear router that preferentially directs photonic wavepackets to different output ports depending on their intensity. As a relevant example, we analyze the nonlinearity provided by Rydberg blockade in atomic ensembles, in which the trade-off between the nonlinearity and the accompanying loss is well understood. We present protocols for efficient Bell measurement and GHZ-state preparation -- both key elements in the construction of cluster states, as well as for the CNOT gate and quantum factorization. Given the large number of entangling operations involved in fault-tolerant MBQC, the increase in success probability provided by our protocols already at moderate nonlinearity can result in a dramatic reduction in the required resources.