Fine-Grained Complexity via Quantum Natural Proofs
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911156060291072 |
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| author | Chen, Yanlin Chen, Yilei Kumar, Rajendra Patro, Subhasree Speelman, Florian |
| author_facet | Chen, Yanlin Chen, Yilei Kumar, Rajendra Patro, Subhasree Speelman, Florian |
| contents | Buhrman, Patro, and Speelman presented a framework of conjectures that together form a quantum analogue of the strong exponential-time hypothesis and its variants. They called it the QSETH framework. In this paper, using a notion of quantum natural proofs (built from natural proofs introduced by Razborov and Rudich), we show how part of the QSETH conjecture that requires properties to be `compression oblivious' can in many cases be replaced by assuming the existence of quantum-secure pseudorandom functions, a standard hardness assumption. Combined with techniques from Fourier analysis of Boolean functions, we show that properties such as PARITY and MAJORITY are compression oblivious for certain circuit class $Λ$ if subexponentially secure quantum pseudorandom functions exist in $Λ$, answering an open question in [Buhrman-Patro-Speelman 2021]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fine-Grained Complexity via Quantum Natural Proofs Chen, Yanlin Chen, Yilei Kumar, Rajendra Patro, Subhasree Speelman, Florian Quantum Physics Computational Complexity Buhrman, Patro, and Speelman presented a framework of conjectures that together form a quantum analogue of the strong exponential-time hypothesis and its variants. They called it the QSETH framework. In this paper, using a notion of quantum natural proofs (built from natural proofs introduced by Razborov and Rudich), we show how part of the QSETH conjecture that requires properties to be `compression oblivious' can in many cases be replaced by assuming the existence of quantum-secure pseudorandom functions, a standard hardness assumption. Combined with techniques from Fourier analysis of Boolean functions, we show that properties such as PARITY and MAJORITY are compression oblivious for certain circuit class $Λ$ if subexponentially secure quantum pseudorandom functions exist in $Λ$, answering an open question in [Buhrman-Patro-Speelman 2021]. |
| title | Fine-Grained Complexity via Quantum Natural Proofs |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2504.10363 |