ADAPT-QSCI: Adaptive Construction of an Input State\nfor Quantum-Selected Configuration Interaction

We\npresent a quantum-classical hybrid algorithm for calculating\nthe ground state and its energy of the quantum many-body Hamiltonian\nby proposing an adaptive construction of a quantum state for the quantum-selected\nconfiguration interaction (QSCI) method. QSCI allows us to select\nimportant electronic configurations in the system to perform configuration\ninteraction (CI) calculation (subspace diagonalization of the Hamiltonian)\nby sampling measurement for a proper input quantum state on a quantum\ncomputer, but how we prepare a desirable input state remains a challenge.\nWe propose an adaptive construction of the input state for QSCI in\nwhich we run QSCI repeatedly to grow the input state iteratively.\nWe numerically illustrate that our method, dubbed <i>ADAPT-QSCI</i>, can yield accurate ground-state energies for small molecules, including\na noisy situation for eight qubits where error rates of two-qubit\ngates and the measurement are both as large as 1%. ADAPT-QSCI serves\nas a promising method to take advantage of current noisy quantum devices\nand pushes forward its application to quantum chemistry.