Boosting Photonic Quantum Computation with Moderate Nonlinearity
A. Pick, E.S. Matekole, Z. Aqua, G. Guendelman, O. Firstenberg, J.P. Dowling, B. Dayan · Physical Review Applied · 2021
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 $\ensuremath{\pi}$) 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 nonlinearities can result in a significant reduction in the required resources.