Boosting photonic quantum computation with moderate nonlinearity

• Published in: arXiv.org 2021-03
• Main Authors: Pick, Adi, Siddiqui-Matekole, Elisha, Aqua, Ziv, Guendelman, Gabriel, Firstenberg, Ofer, Dowling, Jonathan P, Dayan, Barak
• Format: Article
• Language: English
• Subjects: Fault tolerance; Nonlinearity; Photonics; Quantum computing; Statistical analysis; Wave packets
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2011.06454

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.