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We propose a method for constructing $\texttt{PREPARE}$ circuits for quantumphase estimation of a molecular Hamiltonian in quantum chemistry by usingvariational optimization of quantum circuits solely on classical computers. The$\texttt{PREPARE}$ circuit generates a quantum state which encodes thecoefficients of the terms in the Hamiltonian as probability amplitudes andplays a crucial role in the state-of-the-art efficient implementations ofquantum phase estimation. We employ the automatic quantum circuit encodingalgorithm [Shirakawa $\textit{et al.}$, arXiv:2112.14524] to construct$\texttt{PREPARE}$ circuits, which requires classical simulations of quantumcircuits of $O(\log N)$ qubits with $N$ being the number of qubits of theHamiltonian. The generated $\texttt{PREPARE}$ circuits do not need anyancillary qubit. We demonstrate our method by investigating the number of$T$-gates of the obtained $\texttt{PREPARE}$ circuits for quantum chemistryHamiltonians of various molecules, which shows a constant-factor reductioncompared to previous approaches that do not use ancillary qubits. Since thenumber of available logical qubits and $T$ gates will be limited at the earlystage of the fault-tolerant quantum computing, the proposed method isparticularly of use for performing the quantum phase estimation with suchlimited capability.

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