Efficiently Computable Bounds for Magic State Distillation

Area of Science:

• Quantum Information Science
• Quantum Computation Theory
• Resource Theories

Background:

• Magic-state distillation is essential for scalable, fault-tolerant quantum computation.
• Characterizing and quantifying nonstabilizerness is a key goal in the resource theory of nonstabilizer states.

Purpose of the Study:

• Introduce the family of thauma measures to quantify nonstabilizerness.
• Address open questions in the resource theory of nonstabilizer states.
• Develop efficient benchmarks for magic-state distillation.

Main Methods:

• Introduced the family of thauma measures (min-thauma, max-thauma, hypothesis testing thauma).
• Utilized hypothesis testing thauma to benchmark one-shot distillable nonstabilizerness.
• Employed max-thauma for efficient benchmarking of magic-state distillation efficiency.
• Applied min-thauma to bound the regularized relative entropy of magic.

Main Results:

• Established hypothesis testing thauma as an efficiently computable benchmark for one-shot distillable nonstabilizerness.
• Demonstrated that max-thauma outperforms mana-based approaches for benchmarking distillation efficiency.
• Proved that two classes of states with maximal mana cannot be interconverted at a rate of one in the asymptotic regime.

Conclusions:

• Thauma measures offer efficient and powerful tools for analyzing nonstabilizerness in quantum states.
• The results provide new bounds on magic-state distillation overhead and rates.
• Resolved a fundamental question regarding state interconversion in the resource theory of nonstabilizer states, highlighting differences from other resource theories.