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

• URL: http://arxiv.org/abs/2606.19239v1
• Date: Wed, 17 Jun 2026 16:19:25 GMT
• Title: Quantum-Classical Auxiliary-Field Quantum Monte Carlo at the Edge of Practicability
• Abstract summary: We introduce algorithmic improvements to quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC)<n>These improvements reduce the dominant per-step classical scaling from $tildemathcalO(N5.5)$ to $tildemathcalO(N4.5)$.<n>We estimate both quantum and classical runtimes for a potential fault-tolerant implementation of QC-AFQMC.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce algorithmic improvements to quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) that reduce the dominant per-step classical scaling from $\tilde{\mathcal{O}}(N^{5.5})$ to $\tilde{\mathcal{O}}(N^{4.5})$ 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 $248\times$ estimated runtime improvement for a system of 100 molecular orbitals. Using our workflow, we demonstrate a ground-state energy calculation for $H_8$ 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 $H_{12}$, and on the lithium-air battery related rearrangement pathway of the $Li_2O_4$ 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.

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