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This paper introduces a resource-efficient method for quantum-selected configuration interaction that reduces circuit complexity by identifying dominant fermionic excitation operators and constructing a compact Hamiltonian. By applying this framework to Group IIIA monofluorides, the authors achieve a near-quadratic improvement in Hamiltonian-term scaling, which significantly decreases computational overhead while maintaining high precision. The method successfully computes relativistic ground-state energies and permanent electric dipole moments, demonstrating over 98% reductions in circuit depth and gate counts on a 20-qubit TlF system executed on the IBM Marrakesh processor.
Achieving over 98% reduction in circuit complexity while retaining quantum precision could revolutionize resource management in quantum simulations.
The quantum-selected configuration interaction identifies important determinantal basis functions through real-time evolution of a reference wavefunction and diagonalizing the Hamiltonian matrix in the resulting selected subspace. However, implementing the full electronic Hamiltonian on noisy quantum devices leads to rapidly increasing circuit complexity, limiting its scalability. To address this issue, we identify the dominant fermionic excitation operators and perform reference-state fidelity loss analysis to construct a compact Hamiltonian, reducing computational overhead while retaining high precision. Applied to Group IIIA monofluorides (BF, AlF, GaF, InF, and TlF), the proposed framework achieves a near-quadratic improvement in Hamiltonian-term scaling, enabling resource-efficient simulations. We employ this framework to compute the relativistic ground-state energies and permanent electric dipole moments (PDMs) of the systems under consideration. After validating the framework via simulations, we demonstrate hardware execution for AlF and TlF on the IBM Marrakesh processor using active spaces of up to 20 qubits. For a 20-qubit TlF system, the reduced Hamiltonian yields a reduction of higher than $ 98\%$ in both circuit depth and two-qubit gate counts, with the resulting PDMs from quantum hardware matching complete active space configuration interaction values within $99.99\%$. These results demonstrate the scalability of this approach on noisy intermediate-scale quantum devices.
