Efficient simulatability of continuous-variable circuits with large Wigner negativity
Journal article, 2020

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 nontrivial 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.

continuous variables

quantum computing

quantum advantage


Laura García Álvarez

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Cameron Calcluth

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Alessandro Ferraro

Queen's University Belfast

Giulia Ferrini

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Physical review research

2643-1564 (ISSN) 2643-1564 (eISSN)

Vol. 2 4 043322-

Areas of Advance

Nanoscience and Nanotechnology (SO 2010-2017, EI 2018-)

Subject Categories

Atom and Molecular Physics and Optics



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