Interplay of resources for universal continuous-variable quantum computing

TL;DR

This paper introduces symplectic coherence as a key resource in continuous-variable quantum computing, demonstrating its necessity for universality and its interplay with non-Gaussianity and entanglement, supported by a classical simulation algorithm.

Contribution

It uncovers symplectic coherence as a new resource and analyzes its role alongside other resources, providing a resource-theoretic framework for continuous-variable quantum computing.

Findings

Symplectic coherence is necessary for universal continuous-variable quantum computation.

An efficient classical simulation algorithm is developed for low symplectic coherence circuits.

The resource interplay mirrors the discrete-variable coherence, magic, and entanglement relationship.

Abstract

Quantum resource theories identify the features of quantum computers that provide their computational advantage over classical systems. We investigate the resources driving the complexity of classical simulation in the standard model of continuous-variable quantum computing, and their interplay enabling computational universality. Specifically, we uncover a new property in continuous-variable circuits, analogous to coherence in discrete-variable systems, termed symplectic coherence. Using quadrature propagation across multiple computational paths, we develop an efficient classical simulation algorithm for continuous-variable computations with low symplectic coherence. This establishes symplectic coherence as a necessary resource for universality in continuous-variable quantum computing, alongside non-Gaussianity and entanglement. Via the Gottesman--Kitaev--Preskill encoding, we show that the interplay of these three continuous-variable quantum resources mirrors the discrete-variable relationship between coherence, magic, and entanglement.