Towards fault-tolerant quantum computation with universal continuous-variable gates

TL;DR

This paper provides evidence that universal continuous-variable quantum gates, when combined with GKP encoding, can generate high-quality states suitable for fault-tolerant quantum memory, advancing the prospects of scalable quantum computation.

Contribution

It demonstrates, through numerical optimization, that universal CV gates can produce GKP states with low error probabilities suitable for fault-tolerant quantum memory.

Findings

GKP states can be generated from vacuum using universal CV gates.

Generated GKP states exhibit error probabilities below fault-tolerance thresholds.

Supports the feasibility of fault-tolerant quantum computation with CV systems.

Abstract

Continuous-variable (CV) systems have shown remarkable potential for quantum computation, particularly excelling in scalability and error correction through bosonic encoding. Within this framework, the foundational notion of computational universality was introduced in [Phys. Rev. Lett. 82, 1784 (1999)], and has proven especially successful since it allows for the identification of finite sets of universal CV gates independent of the encoding scheme. However, achieving the critical objective of fault-tolerant computation requires some form of encoding, and to date there has been no proof that these universal CV gates can lead to encoded fault tolerance. We present compelling evidence in this direction by utilizing the Gottesman-Kitaev-Preskill (GKP) encoding. Specifically, we numerically optimize the generation of GKP states from vacua using circuits comprised solely of universal CV gates. We demonstrate that these states can be attained with sufficient quality to exhibit error probabilities lower than the threshold needed to achieve a fault-tolerant memory via concatenated GKP-stabilizer codes.