Quantum chemistry with provable convergence via randomized sample-based quantum diagonalization

Sample-based quantum diagonalization (SQD) approximates many-body ground states by classically diagonalizing Hamiltonians in subspaces generated from samples produced on a quantum processor. Building on the Sample-based Krylov Quantum Diagonalization (SKQD) variant — which constructs Krylov subspaces from time-evolution circuits and guarantees convergence under the assumption of a concentrated ground-state wave function — we address a key limitation: the large circuit depth required to generate Krylov states for realistic chemical Hamiltonians.

We introduce SqDRIFT, a randomized version of SKQD that replaces coherent time evolution with a qDRIFT-style stochastic compilation of the propagator. This approach preserves the convergence guarantees of SKQD while substantially reducing circuit depth and mitigating hardware noise. We apply SqDRIFT to compute the electronic ground-state energies of polycyclic aromatic hydrocarbons, achieving accurate results for molecular sizes beyond the reach of exact diagonalization. These findings highlight SqDRIFT as an efficient and robust approach for quantum-enhanced electronic structure calculations.