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This study establishes a definitive upper bound for fermionic non-Gaussianity, a critical resource known as "magic" required for universal fault-tolerant quantum computation. By identifying this limit within Sachdev-Ye-Kitaev Hamiltonian models, the research clarifies the theoretical capacity of many-body systems to generate computational power beyond standard thermodynamic predictions. These findings provide essential benchmarks for characterizing complex quantum states and optimizing the performance of future quantum processors.
Tokyo Team Bounds Fermionic Non-Gaussianity at Ln(4/3)

A distinct phase transition emerges during quantum interactions, revealed by changes in fermionic non-Gaussianity undetectable through standard thermodynamic calculations. Calculations demonstrate typical states achieve a maximal magic Rényi entropy (MRE) density of ln(4/3) per Majorana, a quantifiable upper bound previously unknown. This shift signifies an unexpected complexity within many-body systems as they evolve under specific Hamiltonian dynamics.
A new understanding of how to quantify non-Gaussianity has been established, representing a key resource enabling universal quantum computation. Typical states attain a maximal magic Rényi entropy density of natural logarithm of four thirds per Majorana fermion in large systems. This allows for improved characterisation of complex many-body interactions and their potential within quantum technologies, revealing subtle changes not detectable through conventional thermal analysis. The ultimate limit to ‘fermionic non-Gaussianity’, a vital resource underpinning powerful quantum computers, is…
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