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arXiv · 2409.20028

A Quantum Unique Games Conjecture

Hamoon Mousavi·Taro Spirig
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Abstract

After the NP-hardness of computational problems such as 3SAT and MaxCut was established, a natural next step was to explore whether these problems remain hard to approximate. While the quantum extensions of some of these problems are known to be hard-indeed undecidable-their inapproximability remains largely unresolved. In this work, we introduce definitions for the quantum extensions of Label-Cover and Unique-Label-Cover. We show that these problems play a similarly crucial role in studying the inapproximability of quantum constraint satisfaction problems as they do in the classical setting.

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Hamoon Mousavi, Taro Spirig. 2024-09-30. A Quantum Unique Games Conjecture. https://arxiv.org/abs/2409.20028

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