Hardware Robustness of Sample-Based Quantum Diagonalization

Sample-based Quantum Diagonalization (SQD) is a hybrid quantum-classical algorithm designed to estimate molecular ground-state energies without the instability of variational optimization. While SQD is theoretically robust, practitioners often lack empirical guidance on how to configure its deployment—specifically regarding classical initialization, hardware-level execution, and sampling budgets. This study evaluates the robustness of SQD on IBM's Heron-r2 processor across these three dimensions.

The authors conducted a systematic case study on three molecules (BeH2, H2O, and N2) using the following probes:

• Classical-Input Perturbations: They introduced structured noise into the CCSD amplitudes used to initialize the Local Unitary Cluster Jastrow (LUCJ) circuit, including sign flips, HOMO scaling, and complete zeroing.
• Hardware Execution: They compared different qubit-to-physical-qubit mappings (naive, randomized, and zigzag) and tested the impact of noise-mitigation techniques like dynamical decoupling and Pauli twirling.
• Shot-Budget Scaling: They swept the number of QPU shots from 100 to 100,000 to determine if increased sampling improves the final recovered energy.

The recovery loop in SQD acts as a powerful filter that absorbs many deployment-related errors:

• Initialization Robustness: Even when CCSD amplitudes were completely zeroed, the algorithm converged to energies only slightly worse than the clean baseline, suggesting the recovery loop successfully reconstructs the necessary subspace from the Hamiltonian.
• Layout and Mitigation: While initial iterations showed massive performance gaps between different qubit layouts, these differences narrowed significantly after a few iterations of the recovery loop. Noise mitigation provided marginal benefits but did not fundamentally alter the convergence behavior.
• Saturation of Accuracy: Increasing the shot budget does not lead to linear improvements. In fact, moderate budgets (1,000–10,000 shots) often outperformed very large budgets (100,000 shots), likely because the algorithm selects a fixed-size working set, making additional samples redundant or potentially noisy.