Correction scheme for total energy obtained on fault-tolerant quantum computer via quantum dominant orbital selection and subspace dynamical correlation methods

We propose a practical method for accurately evaluating molecular energies using a hybrid approach that integrates fault-tolerant quantum computers with classical computing. Our scheme comprises two complementary methods: quantum dominant orbital selection (QDOS) and subspace dynamical correlation (SDC). The QDOS method extracts only the relevant active orbitals from the complete active space (CAS) configuration interaction (CI) state on a quantum computer, thereby defining a more compact active space suitable for subsequent classical CASCI calculations. The SDC method evaluate correction of dynamical correlation of the CASCI obtained by quantum computing by using the compact CASCI state, which can be handled by classical computing. To demonstrate that the CAS energy resulting from the quantum computation is post-corrected by the SDC method, we examine the two frameworks, multi-reference perturbation theory and tailored coupled-cluster theory, for the SDC method. Our scheme does not suffer from massive task to read out quantum data readout and demonstrates the potential to efficiently compute large, complex molecular systems by leveraging quantum-classical hybrid computation with reasonable computational resources.