Classical variational optimization of a PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians - Hayata Morisaki; Kosuke Mitarai; Keisuke Fujii; Yuya O. Nakagawa (Physical Review Research)
We propose a method for constructing 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 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 [18Shirakawa et al., Phys. Rev. Res. 6, 043008 (2024)10.1103/PhysRevResearch.6.043008] to construct PREPARE circuits, which requires classical simulations of quantum circuits of O(logN) qubits with N being the number of qubits of the Hamiltonian. The generated PREPARE circuits do not need any ancillary qubit. We demonstrate our method by investigating the number of T-gates of the obtained 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.