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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.08466 |
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| _version_ | 1866915927593844736 |
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| author | Pham, N. C. Mai Santos, Raul A. |
| author_facet | Pham, N. C. Mai Santos, Raul A. |
| contents | Impurity Hamiltonians are systems of $N$ fermionic modes where $O(1)$ of them interact among themselves via quartic (or higher order) fermion terms, while coupling quadratically with $O(N)$ bath modes. Without the quartic interactions, these systems are classically simulable with $O(N^3)$ resources. It was proved that the time-dependent evolution of these systems can perform universal quantum computation. The question of whether or not this remains true for time-independent evolution remains open. Here, we prove that the time evolution of generic time-independent impurity Hamiltonians on $O(N)$ qubits is universal on $N$ qubits if the input state is a product state of fermions in any single particle basis. In our proof we find that for a computation of depth $S$, the size of the impurity scales as $O(S\log S)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08466 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Time evolution of impurity models and their universality for quantum computation Pham, N. C. Mai Santos, Raul A. Quantum Physics Impurity Hamiltonians are systems of $N$ fermionic modes where $O(1)$ of them interact among themselves via quartic (or higher order) fermion terms, while coupling quadratically with $O(N)$ bath modes. Without the quartic interactions, these systems are classically simulable with $O(N^3)$ resources. It was proved that the time-dependent evolution of these systems can perform universal quantum computation. The question of whether or not this remains true for time-independent evolution remains open. Here, we prove that the time evolution of generic time-independent impurity Hamiltonians on $O(N)$ qubits is universal on $N$ qubits if the input state is a product state of fermions in any single particle basis. In our proof we find that for a computation of depth $S$, the size of the impurity scales as $O(S\log S)$. |
| title | Time evolution of impurity models and their universality for quantum computation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.08466 |