NISQ Security and Complexity via Simple Classical Reasoning
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909783500521472 |
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| author | Cojocaru, Alexandru Garay, Juan Liu, Qipeng Song, Fang |
| author_facet | Cojocaru, Alexandru Garay, Juan Liu, Qipeng Song, Fang |
| contents | We give novel lifting theorems for security games in the quantum random oracle model (QROM) in Noisy Intermediate-Scale Quantum (NISQ) settings such as the hybrid query model, the noisy oracle and the bounded-depth models. We provide, for the first time, a hybrid lifting theorem for hybrid algorithms that can perform both quantum and classical queries, as well as a lifting theorem for quantum algorithms with access to noisy oracles or bounded quantum depth.
At the core of our results lies a novel measure-and-reprogram framework, called hybrid coherent measure-and-reprogramming, tailored specifically for hybrid algorithms. Equipped with the lifting theorem, we are able to prove directly NISQ security and complexity results by calculating a single combinatorial quantity, relying solely on classical reasoning.
As applications, we derive the first direct product theorems in the average case, in the hybrid setting-i.e., an enabling tool to determine the hybrid hardness of solving multi-instance security games. This allows us to derive in a straightforward manner the NISQ hardness of various security games, such as (i) the non-uniform hardness of salted games, (ii) the hardness of specific cryptographic tasks such as the multiple instance version of one-wayness and collision-resistance, and (iii) uniform or non-uniform hardness of many other games. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | NISQ Security and Complexity via Simple Classical Reasoning Cojocaru, Alexandru Garay, Juan Liu, Qipeng Song, Fang Quantum Physics Computational Complexity Cryptography and Security We give novel lifting theorems for security games in the quantum random oracle model (QROM) in Noisy Intermediate-Scale Quantum (NISQ) settings such as the hybrid query model, the noisy oracle and the bounded-depth models. We provide, for the first time, a hybrid lifting theorem for hybrid algorithms that can perform both quantum and classical queries, as well as a lifting theorem for quantum algorithms with access to noisy oracles or bounded quantum depth. At the core of our results lies a novel measure-and-reprogram framework, called hybrid coherent measure-and-reprogramming, tailored specifically for hybrid algorithms. Equipped with the lifting theorem, we are able to prove directly NISQ security and complexity results by calculating a single combinatorial quantity, relying solely on classical reasoning. As applications, we derive the first direct product theorems in the average case, in the hybrid setting-i.e., an enabling tool to determine the hybrid hardness of solving multi-instance security games. This allows us to derive in a straightforward manner the NISQ hardness of various security games, such as (i) the non-uniform hardness of salted games, (ii) the hardness of specific cryptographic tasks such as the multiple instance version of one-wayness and collision-resistance, and (iii) uniform or non-uniform hardness of many other games. |
| title | NISQ Security and Complexity via Simple Classical Reasoning |
| topic | Quantum Physics Computational Complexity Cryptography and Security |
| url | https://arxiv.org/abs/2509.09900 |