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

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.