Adapting O(Δτ^3) Zeno-error reduction to AFQMC without degrading computational scaling

Determine how to adapt the quantum-Zeno-based O(Δτ^3) error-reduction technique introduced for enlarged-basis quantum algorithms by Luo and Cirac (PRX Quantum, 2025) to auxiliary-field quantum Monte Carlo (AFQMC) implemented in an extended basis using isometric tensor hypercontraction (ITHC), so that the per-step propagation error improves from O(Δτ^2) to O(Δτ^3) while preserving the favorable AFQMC computational scaling for propagation and memory usage.

Background

The paper introduces an AFQMC method that operates in an extended basis using isometric tensor hypercontraction (ITHC) to diagonalize the two-electron interaction, enabling Hubbard-like propagation with reduced computational and memory costs. The imaginary-time evolution employs a Trotter–Suzuki decomposition together with repeated projections (quantum Zeno dynamics), leading to a per-step error dominated by a Zeno contribution that yields an overall O(Δτ^2) step error and linear-in-Δτ bias in equilibrium energies.

Prior work on quantum algorithms (Luo and Cirac, 2025) proposed a simple modification that reduces the Zeno-related error scaling from O(Δτ^2) to O(Δτ^3). While such an improvement would directly benefit AFQMC by reducing time-step bias and potentially obviating the need for aggressive extrapolation, the present work explicitly notes that it is not yet known how to incorporate that technique into AFQMC without sacrificing the method’s favorable complexity. Hence, devising an AFQMC-compatible adaptation that maintains the advantageous scaling constitutes an explicit open problem.