Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding

TL;DR

This paper introduces a new measure for quantifying quantum magic resources using Gottesman-Kitaev-Preskill encoding, enabling analysis of larger quantum systems in fault-tolerant quantum computing.

Contribution

It develops a bosonic code-based resource measure for magic, extending analysis to systems of up to 12 qubits, unlike previous methods.

Findings

Provides analytical expression for magic measure.

Enables resource bounds for state conversion and unitary synthesis.

Addresses systems of up to 12 qubits.

Abstract

Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify 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 multi-qubit states and consider the resource theory for the Wigner negativity. Our techniques are useful to find resource lower bounds for different applications as state conversion and general unitary synthesis, in which measurements, auxiliary states, and classical feed-forward are allowed. 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.