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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13156 |
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| _version_ | 1866907782181027840 |
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| author | Adhikari, Bibhas Jha, Aryan |
| author_facet | Adhikari, Bibhas Jha, Aryan |
| contents | In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by finding $2$-sparse unitary matrices of order $2^n$ explicitly corresponding to any single-qubit and two-qubit control gates in an $n$-qubit system. Finally, we determine analytical expression of Hamiltonians for any such gate and consequently a local Hamiltonian decomposition of any PQC is obtained. All results are validated with numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits Adhikari, Bibhas Jha, Aryan Quantum Physics Symbolic Computation In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by finding $2$-sparse unitary matrices of order $2^n$ explicitly corresponding to any single-qubit and two-qubit control gates in an $n$-qubit system. Finally, we determine analytical expression of Hamiltonians for any such gate and consequently a local Hamiltonian decomposition of any PQC is obtained. All results are validated with numerical simulations. |
| title | Local Hamiltonian decomposition and classical simulation of parametrized quantum circuits |
| topic | Quantum Physics Symbolic Computation |
| url | https://arxiv.org/abs/2401.13156 |