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Pré-Publication, Document De Travail Année : 2024

Quantum State Synthesis: Relation with Decision Complexity Classes and Impossibility of Synthesis Error Reduction

Synthèse d'états quantiques : relation avec les classes de complexité de décision et impossibilité de réduire l'erreur de synthèse

Résumé

This work investigates the relationships between quantum state synthesis complexity classes (a recent concept in computational complexity that focuses on the complexity of preparing quantum states) and traditional decision complexity classes. We especially investigate the role of the synthesis error parameter, which characterizes the quality of the synthesis in quantum state synthesis complexity classes. We first show that in the high synthesis error regime, collapse of synthesis classes implies collapse of the equivalent decision classes. For more reasonable synthesis error, we then show a similar relationships for BQP and QCMA. Finally, we show that for quantum state synthesis classes it is in general impossible to improve the quality of the synthesis: unlike the completeness and soundness parameters (which can be improved via repetition), the synthesis error cannot be reduced, even with arbitrary computational power.
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Dates et versions

hal-04634958 , version 1 (04-07-2024)

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Hugo Delavenne, François Le Gall. Quantum State Synthesis: Relation with Decision Complexity Classes and Impossibility of Synthesis Error Reduction. 2024. ⟨hal-04634958⟩
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