  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.
