Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding

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.

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• Nonstabilizerness determining the hardness of direct fidelity estimation
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Quantifying non-stabilizerness via information scrambling
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Handbook for Quantifying Robustness of Magic
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Sufficient condition for universal quantum computation using bosonic circuits
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Maximal Magic for Two-qubit States
• Clifford operations and homological codes for rotors and oscillators
• Classical simulation and quantum resource theory of non-Gaussian optics
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
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• Invested and Potential Magic Resources in Measurement-Based Quantum Computation
• Grand Unification of All Discrete Wigner Functions on $d\times d$ Phase Space
• Tessellation codes: encoded quantum gates by geometric rotation
• High-expressibility Quantum Neural Networks using only classical resources