Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding

Quantum resource theories are a powerful framework for characterizing and quantifying relevant quantum phenomena and identifying processes that optimize their use for different tasks. Here, 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. Particularly, we use the Gottesman-Kitaev-Preskill code to represent multiqubit states and consider the resource theory for the Wigner negativity. Our techniques are useful in finding resource lower bounds for different applications as state conversion and gate synthesis. 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.