Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians

• URL: http://arxiv.org/abs/2308.13770v1
• Date: Sat, 26 Aug 2023 05:32:38 GMT
• Title: Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians
• Authors: Hayata Morisaki, Kosuke Mitarai, Keisuke Fujii, Yuya O. Nakagawa
• Abstract summary: We propose a method for constructing $textttPREPARE$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry. The $textttPREPARE$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes.
• Score: 0.8009842832476994
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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