Orbital-Rotation Shadow Tomography Reduces the Classical Cost of Quantum-Classical Auxiliary-Field Quantum Monte Carlo

arXiv:2610.03103v1 Announce Type: new Abstract: Quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) is a promising route to using quantum computers for strongly correlated electronic structure problems, but its scalability is limited by a classical post-processing bottleneck: the measured quantum trial state must be used to evaluate overlaps, force biases, and local energies for many walkers throughout the AFQMC propagation. Existing matchgate-shadow approaches avoid the exponential cost of generic classical shadows, but their post-processing remains expensive for large systems. In this work, we show that particle-number-preserving fermionic shadows, implemented as orbital-rotation shadows, are able to drastically reduce QC-AFQMC post-processing costs. We derive efficient estimators for overlaps and their derivatives, giving $O(N^3)$ scaling for overlaps and force biases and $O(N^4)$ scaling for local energies per shadow and walker and with $O(N)$ Cholesky vector. For fixed normalized target determinants, we also prove that the overlap estimator is unbiased with variance upper bounded by $O(\eta)$, where $\eta$ is the particle number, yielding a sufficient budget of $O(\eta/\epsilon^2)$ ideal independent measurements for additive overlap error $\epsilon$. We combine these estimators with a novel virtual-correlation-energy treatment and a GPU implementation and demonstrate QC-AFQMC using orbital-rotation shadows. Performance projections for $\pi$-conjugated molecules up to pentacene with a (22e, 22o) active space and 356 total orbitals show that the full classical post-processing workflow can be completed in slightly more than two days on 8$\times$A100 graphics processing units (GPUs). These results significantly reduce classical post-processing costs for QC-AFQMC and motivate further improvements in preparation and measurement of the trial state on quantum hardware.

Abstract:Quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) is a promising route to using quantum computers for strongly correlated electronic structure problems, but its scalability is limited by a classical post-processing bottleneck: the measured quantum trial state must be used to evaluate overlaps, force biases, and local energies for many walkers throughout the AFQMC propagation. Existing matchgate-shadow approaches avoid the exponential cost of generic classical shadows, but their post-processing remains expensive for large systems. In this work, we show that particle-number-preserving fermionic shadows, implemented as orbital-rotation shadows, are able to drastically reduce QC-AFQMC post-processing costs. We derive efficient estimators for overlaps and their derivatives, giving $O(N^3)$ scaling for overlaps and force biases and $O(N^4)$ scaling for local energies per shadow and walker and with $O(N)$ Cholesky vector. For fixed normalized target determinants, we also prove that the overlap estimator is unbiased with variance upper bounded by $O(\eta)$, where $\eta$ is the particle number, yielding a sufficient budget of $O(\eta/\epsilon^2)$ ideal independent measurements for additive overlap error $\epsilon$. We combine these estimators with a novel virtual-correlation-energy treatment and a GPU implementation and demonstrate QC-AFQMC using orbital-rotation shadows. Performance projections for $\pi$-conjugated molecules up to pentacene with a (22e, 22o) active space and 356 total orbitals show that the full classical post-processing workflow can be completed in slightly more than two days on 8$\times$A100 graphics processing units (GPUs). These results significantly reduce classical post-processing costs for QC-AFQMC and motivate further improvements in preparation and measurement of the trial state on quantum hardware.

Quantum Physics (quant-ph); Classical Physics (physics.class-ph)

arXiv:2610.03103 [quant-ph]

(or arXiv:2610.03103v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.03103 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Orbital-Rotation Shadow Tomography Reduces the Classical Cost of Quantum-Classical Auxiliary-Field Quantum Monte Carlo

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