Fermionic Independent Set and Laplacian of an independence complex are QMA-hard
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918045058859008 |
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| author | Rayudu, Chaithanya |
| author_facet | Rayudu, Chaithanya |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fermionic Independent Set and Laplacian of an independence complex are QMA-hard Rayudu, Chaithanya Quantum Physics Computational Complexity 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. |
| title | Fermionic Independent Set and Laplacian of an independence complex are QMA-hard |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2411.03230 |