NISQ Security and Complexity via Simple Classical Reasoning

• URL: http://arxiv.org/abs/2509.09900v1
• Date: Thu, 11 Sep 2025 23:31:39 GMT
• Title: NISQ Security and Complexity via Simple Classical Reasoning
• Authors: Alexandru Cojocaru, Juan Garay, Qipeng Liu, Fang Song,
• Abstract summary: We give novel lifting theorems for security games in the quantum random oracle model (QROM) in Noisy Intermediate-Scale Quantum (NISQ) settings.<n>We provide, for the first time, a hybrid lifting theorem for hybrid algorithms that can perform both quantum and classical queries.<n>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.
• Score: 41.17296890645859
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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