Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer

TL;DR

This work introduces Hamiltonian simulation-based QSCI (HSB-QSCI), a quantum-classical hybrid method that samples important Slater determinants from real-time evolution of an initial approximate wave function and then diagonalizes the resulting subspace on a classical computer. By mapping the electronic Hamiltonian to qubits, enforcing spin symmetry, correcting electron-number on noisy hardware, and optionally truncating Hamiltonian terms via locality, HSB-QSCI achieves chemical precision with relatively small determinant subspaces and short-time evolution. The approach is validated through classical simulations and hardware demonstrations up to 36 qubits, showing that HSB-QSCI can capture over 99% of correlation energy with about 1% of Slater determinants, and can handle strongly correlated and larger systems without requiring variational quantum optimization. The results demonstrate potential for scalable, hardware-lean quantum chemical calculations on near-term devices, with further improvements anticipated through more shots, refined initial states, and advanced quantum-classical feedback loops.

Abstract

Quantum-selected configuration interaction (QSCI) is an approach for quantum chemical calculations using current quantum computers. In conventional QSCI, Slater determinants used for the wave function expansion are sampled by iteratively performing approximate wave function preparation and subsequent measurement in the computational basis, and then the subspace Hamiltonian matrix is diagonalized on a classical computer. In this approach, preparation of a high-quality approximate wave function is necessary to accurately compute total energies. Here we propose a Hamiltonian simulation-based QSCI (HSB-QSCI) to avoid this difficulty, by sampling the Slater determinants from quantum states generated by the real-time evolution of approximate wave functions. We provide numerical simulations for the lowest spin-singlet and triplet states of oligoacenes (benzene, naphthalene, and anthracene), phenylene-1,4-dinitrene, and hexa-1,2,3,4,5-pentaene. We found that the HSB-QSCI is applicable not only to molecules where the Hartree--Fock provides a good approximation of the ground state, but also to strongly correlated systems where preparing a high-quality approximate wave function is hard. Hardware demonstrations of the HSB-QSCI are also reported for carbyne molecules expressed by up to 36 qubits, using an IBM Quantum processor. The HSB-QSCI captures more than 99.18\% of the correlation energies in the active space by considering about 1\% of all the Slater determinants in 36 qubit systems, illustrating the ability of the proposed method to efficiently consider important electronic configurations.

Figures (24)

• Figure 1: Schematic view of the HSB-QSCI algorithm.
• Figure 2: Target molecules being studied.
• Figure 3: Procedure of orbital transformations for the Hamiltonian term truncations based on the locality of the Pauli strings, in the case of 5 in its planar geometry. Red arrows indicate the electron occupancies in the RHF wave function.
• Figure 4: HSB-QSCI and random sampling-based QSCI results of the H$_2$O molecule.
• Figure 5: HSB-QSCI results of oligoacenes. The number of Slater determinants included in the Hamiltonian diagonalization is given in (a), (b), and (c) for 1, 2, and 3, respectively. Red and blue indicate the S$_0$ and T$_1$ states, respectively. Dotted lines represent the number of Slater determinants in the CAS-CI wave function. The difference of the HSB-QSCI energy from the CAS-CI values in units of kcal mol$^{-1}$ are given in (d), (e), and (f) on the logarithmic scale.