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Discriminating between quantum computing architectures that can providequantum advantage from those that cannot is of crucial importance. From thefundamental point of view, establishing such a boundary is akin to pinpointingthe resources for quantum advantage; from the technological point of view, itis essential for the design of non-trivial quantum computing architectures.Wigner negativity is known to be a necessary resource for computationaladvantage in several quantum-computing architectures, including those based oncontinuous variables (CVs). However, it is not a sufficient resource, and it isan open question under which conditions CV circuits displaying Wignernegativity offer the potential for quantum advantage. In this work we identifyvast families of circuits that display large, possibly unbounded, Wignernegativity, and yet are classically efficiently simulatable, although they arenot recognized as such by previously available theorems. These families ofcircuits employ bosonic codes based on either translational or rotationalsymmetries (e.g., Gottesman-Kitaev-Preskill or cat codes), and can include bothGaussian and non-Gaussian gates and measurements. Crucially, within theseencodings, the computational basis states are described by intrinsicallynegative Wigner functions, even though they are stabilizer states if consideredas codewords belonging to a finite-dimensional Hilbert space. We derive ourresults by establishing a link between the simulatability of high-dimensionaldiscrete-variable quantum circuits and bosonic codes.

Efficient simulatability of continuous-variable circuits with large Wigner negativity