Efficient witnessing and testing of magic in mixed quantum states

2025-04-25

AI Summary

This work addresses the core challenge of efficiently quantifying and experimentally verifying “magic” (non-stabilizerness) in mixed quantum states. We introduce a robust magic witness and property-testing framework based on stabilizer Rényi entropies, enabling the first efficient, quantitative estimation of magic in noisy mixed states and high-confidence discrimination between magic and non-magic states. Theoretically, we establish that magic remains highly robust under exponentially strong noise; that entropy is a necessary resource for hiding magic; and that extensive magic can emerge in subsystems of many-body systems. Methodologically, our approach integrates magic monotone estimation, quantum property testing, and efficient matrix-product-state simulation. We experimentally validate our framework on IonQ superconducting hardware, certifying T-gate counts and verifying robustness of random quantum circuits. These results provide new theoretical tools and experimental paradigms for verifying quantum computational advantage, analyzing quantum cryptographic security, and characterizing the pseudomagic boundary.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Nonstabilizerness or `magic' is a crucial resource for quantum computers which can be distilled from noisy quantum states. However, determining the magic of mixed quantum has been a notoriously difficult task. Here, we provide efficient witnesses of magic based on the stabilizer R'enyi entropy which robustly indicate the presence of magic and quantitatively estimate magic monotones. We also design efficient property testing algorithms to reliably distinguish states with high and low magic, assuming the entropy is bounded. We apply our methods to certify the number of noisy T-gates under a wide class of noise models. Additionally, using the IonQ quantum computer, we experimentally verify the magic of noisy random quantum circuits. Surprisingly, we find that magic is highly robust, persisting even under exponentially strong noise. Our witnesses can also be efficiently computed for matrix product states, revealing that subsystems of many-body quantum states can contain extensive magic despite entanglement. Finally, our work also has direct implications for cryptography and pseudomagic: To mimic high magic states with as little magic as possible, one requires an extensive amount of entropy. This implies that entropy is a necessary resource to hide magic from eavesdroppers. Our work uncovers powerful tools to verify and study the complexity of noisy quantum systems.

Problem

• Efficiently witnessing and testing magic in mixed quantum states
• Distinguishing high and low magic states with bounded entropy
• Certifying magic robustness under noise and its cryptographic implications

Innovation

• Efficient magic witnesses using stabilizer Rényi entropy
• Property testing algorithms for magic distinction
• Magic certification under various noise models