Tensor decomposition technique for qubit encoding of maximal-fidelity Lorentzian orbitals in real-space quantum chemistry

• URL: http://arxiv.org/abs/2501.07211v1
• Date: Mon, 13 Jan 2025 11:08:20 GMT
• Title: Tensor decomposition technique for qubit encoding of maximal-fidelity Lorentzian orbitals in real-space quantum chemistry
• Authors: Taichi Kosugi, Xinchi Huang, Hirofumi Nishi, Yu-ichiro Matsushita,
• Abstract summary: We propose an efficient scheme for encoding an MO as a many-qubit state from a Gaussian-type solution. We demonstrate via numerical simulations that the proposed scheme is a powerful tool for encoding MOs of various quantum chemical systems.
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• Abstract: To simulate the real- and imaginary-time evolution of a many-electron system on a quantum computer based on the first-quantized formalism, we need to encode molecular orbitals (MOs) into qubit states for typical initial-state preparation. We propose an efficient scheme for encoding an MO as a many-qubit state from a Gaussian-type solution that can be obtained from a tractable solver on a classical computer. We employ the discrete Lorentzian functions (LFs) as a fitting basis set, for which we maximize the fidelity to find the optimal Tucker-form state to represent a target MO. For $n_{\mathrm{prod}}$ three-dimensional LFs, we provide the explicit circuit construction for the state preparation involving $\mathcal{O} (n_{\mathrm{prod}})$ CNOT gates. Furthermore, we introduce a tensor decomposition technique to construct a canonical-form state to approximate the Tucker-form state with controllable accuracy. Rank-$R$ decomposition reduces the CNOT gate count to $\mathcal{O} (R n_{\mathrm{prod}}^{1/3}).$ We demonstrate via numerical simulations that the proposed scheme is a powerful tool for encoding MOs of various quantum chemical systems, paving the way for first-quantized calculations using hundreds or more logical qubits.

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