Quantum-Classical Auxiliary-Field Quantum Monte Carlo at the Edge of Practicability

We introduce algorithmic improvements to quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) that reduce the dominant per-step classical scaling from {mathcal{O}}\(N^5.5\) to {mathcal{O}}\(N^4.5\) as a function of the number of molecular spin-orbitals N. Central to this improvement is the application of Aitken's block transformation to handle singular Pfaffians arising in the estimation of overlaps between a quantum trial state and classical Slater-determinant walkers. Together with the use of algorithmic differentiation for the computation of the force bias, this yields a 248times estimated runtime improvement for a system of 100 molecular orbitals. Using our workflow, we demonstrate a ground-state energy calculation for H₈ from quantum data collected on IQM Emerald and post-processed with a tensor-network-based error-mitigation technique. We further validate the method's scalability through noiseless simulation of hydrogen chains up to H₁₂, and on the lithium-air battery related rearrangement pathway of the Li_2O4 lithium superoxide dimer in a (26e, 20o) active space. We estimate both quantum and classical runtimes for a potential fault-tolerant implementation of QC-AFQMC, showing that the method holds promise for the early fault-tolerant era. These results move QC-AFQMC a step closer to treating chemically relevant systems.