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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.03230 |
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Table of Contents:
- The Independent Set is a well known NP-hard optimization problem. In this work, we define a fermionic generalization of the Independent Set problem and prove that the optimization problem is QMA-hard in a $k$-particle subspace using perturbative gadgets. We discuss how the Fermionic Independent Set is related to the problem of computing the minimum eigenvalue of the $k^{\text{th}}$-Laplacian of an independence complex of a vertex weighted graph. Consequently, we use the same perturbative gadget to prove QMA-hardness of the later problem resolving an open conjecture from arXiv:2311.17234 and give the first example of a natural topological data analysis problem that is QMA-hard.