Quantifying Qubit Magic with Gottesman-Kitaev-Preskill Encoding

Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify processes that optimize their use for different tasks. In this work [1], we define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. In contrast to previous literature, our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation. With this new methodology, we are able to prove its properties and connect it to the st-norm, a quantity previously only known to be a one-sided magic witness in qubit systems. In particular, we use the Gottesman-Kitaev-Preskill code to represent multi-qubit states and employ the resource theory of Wigner negativity. The analytical expression of our magic measure allows us to extend current analysis limited to small dimensions, easily addressing systems of up to 12 qubits.

Our work opens the way to link other resources in CV with qubit systems and study their implications for discrete-variable properties.

[1] O. Hahn, A. Ferraro, L. Hultquist, G. Ferrini, and L. García-Álvarez, Quantifying qubit magic with gottesman-kitaev-preskill encoding (2021), arXiv:2109.13018 .