Efficient simulatability of continuous-variable circuits with large Wigner negativity

TL;DR

This paper demonstrates that certain continuous-variable quantum circuits with large Wigner negativity can still be efficiently simulated classically, challenging previous assumptions about negativity as a resource for quantum advantage.

Contribution

It identifies families of CV circuits with large Wigner negativity that are classically efficiently simulatable, using a novel link to discrete-variable quantum circuit simulatability.

Findings

Large Wigner negativity does not imply quantum advantage.

Classical simulation methods extend to certain bosonic codes with negativity.

New criteria for quantum circuit simulatability based on bosonic code properties.

Abstract

Discriminating between quantum computing architectures that can provide quantum advantage from those that cannot is of crucial importance. From the fundamental point of view, establishing such a boundary is akin to pinpointing the resources for quantum advantage; from the technological point of view, it is essential for the design of non-trivial quantum computing architectures. Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures, including those based on continuous variables (CVs). However, it is not a sufficient resource, and it is an open question under which conditions CV circuits displaying Wigner negativity offer the potential for quantum advantage. In this work we identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable, although they are not recognized as such by previously available theorems. These families of circuits employ bosonic codes based on either translational or rotational symmetries (e.g., Gottesman-Kitaev-Preskill or cat codes), and can include both Gaussian and non-Gaussian gates and measurements. Crucially, within these encodings, the computational basis states are described by intrinsically negative Wigner functions, even though they are stabilizer states if considered as codewords belonging to a finite-dimensional Hilbert space. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.