Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912356490018816 |
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| author | Morisaki, Hayata Mitarai, Kosuke Fujii, Keisuke Nakagawa, Yuya O. |
| author_facet | Morisaki, Hayata Mitarai, Kosuke Fujii, Keisuke Nakagawa, Yuya O. |
| contents | We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The $\texttt{PREPARE}$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes and plays a crucial role in the state-of-the-art efficient implementations of quantum phase estimation. We employ the automatic quantum circuit encoding algorithm [Shirakawa $\textit{et al.}$, arXiv:2112.14524] to construct $\texttt{PREPARE}$ circuits, which requires classical simulations of quantum circuits of $O(\log N)$ qubits with $N$ being the number of qubits of the Hamiltonian. The generated $\texttt{PREPARE}$ circuits do not need any ancillary qubit. We demonstrate our method by investigating the number of $T$-gates of the obtained $\texttt{PREPARE}$ circuits for quantum chemistry Hamiltonians of various molecules, which shows a constant-factor reduction compared to previous approaches that do not use ancillary qubits. Since the number of available logical qubits and $T$ gates will be limited at the early stage of the fault-tolerant quantum computing, the proposed method is particularly of use for performing the quantum phase estimation with such limited capability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians Morisaki, Hayata Mitarai, Kosuke Fujii, Keisuke Nakagawa, Yuya O. Quantum Physics We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The $\texttt{PREPARE}$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes and plays a crucial role in the state-of-the-art efficient implementations of quantum phase estimation. We employ the automatic quantum circuit encoding algorithm [Shirakawa $\textit{et al.}$, arXiv:2112.14524] to construct $\texttt{PREPARE}$ circuits, which requires classical simulations of quantum circuits of $O(\log N)$ qubits with $N$ being the number of qubits of the Hamiltonian. The generated $\texttt{PREPARE}$ circuits do not need any ancillary qubit. We demonstrate our method by investigating the number of $T$-gates of the obtained $\texttt{PREPARE}$ circuits for quantum chemistry Hamiltonians of various molecules, which shows a constant-factor reduction compared to previous approaches that do not use ancillary qubits. Since the number of available logical qubits and $T$ gates will be limited at the early stage of the fault-tolerant quantum computing, the proposed method is particularly of use for performing the quantum phase estimation with such limited capability. |
| title | Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.13770 |