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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.19181 |
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| _version_ | 1866911332094181376 |
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| author | Ramezani, Mehdi Zargar, Sina Asadiyan Salami, Sadegh Bahrampour, Abolfazl Bahrampour, Alireza |
| author_facet | Ramezani, Mehdi Zargar, Sina Asadiyan Salami, Sadegh Bahrampour, Abolfazl Bahrampour, Alireza |
| contents | We propose a Hamiltonian-based quantum state preparation method implemented via a shallow parametrized quantum circuit. The approach learns the parameters of a diagonal Hamiltonian through a classical training phase, while the quantum circuit itself performs only fixed-depth Hamiltonian evolution and mixing operations. With oracle access to the learned Hamiltonian parameters, $N$ classical data values can be encoded into $n=\log_2{N}$ qubits using $O(1)$ quantum queries, shifting the overall computational cost to an $O(N\log{N})$ classical preprocessing stage. For structured datasets generated by an underlying function, oracle access can be avoided by expressing the Hamiltonian in the Walsh basis and retaining only a polynomial number of significant terms. In this regime, quantum state preparation is achieved in $\text{poly}(n)$ time using $\text{poly}(n)$ parameters, reaching infidelities on the order of $10^{-5}$. By restricting the Hamiltonian to one-local and two-local terms, the method naturally yields hardware-efficient circuits suitable for near-term quantum devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Hamiltonians for $O(1)$ Oracle-Query Quantum State Preparation Ramezani, Mehdi Zargar, Sina Asadiyan Salami, Sadegh Bahrampour, Abolfazl Bahrampour, Alireza Quantum Physics We propose a Hamiltonian-based quantum state preparation method implemented via a shallow parametrized quantum circuit. The approach learns the parameters of a diagonal Hamiltonian through a classical training phase, while the quantum circuit itself performs only fixed-depth Hamiltonian evolution and mixing operations. With oracle access to the learned Hamiltonian parameters, $N$ classical data values can be encoded into $n=\log_2{N}$ qubits using $O(1)$ quantum queries, shifting the overall computational cost to an $O(N\log{N})$ classical preprocessing stage. For structured datasets generated by an underlying function, oracle access can be avoided by expressing the Hamiltonian in the Walsh basis and retaining only a polynomial number of significant terms. In this regime, quantum state preparation is achieved in $\text{poly}(n)$ time using $\text{poly}(n)$ parameters, reaching infidelities on the order of $10^{-5}$. By restricting the Hamiltonian to one-local and two-local terms, the method naturally yields hardware-efficient circuits suitable for near-term quantum devices. |
| title | Learning Hamiltonians for $O(1)$ Oracle-Query Quantum State Preparation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.19181 |