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Description
We apply the Sample-Based Krylov Quantum Diagonalization (SKQD) algorithm to the SU(2) bosonic two-matrix model, a gauge theory sharing the quartic commutator-squared interaction and bosonic truncation structure of the BFSS and BMN matrix models relevant to holography. Using exact statevector simulation, we demonstrate that SKQD achieves machine-precision ground-state energies (~10^-16) at Fock-space cutoff Λ = 2 (6 qubits) across all tested values of the 't Hooft coupling λ ∈ {0.5, 1.0, 2.0}, outperforming the Variational Quantum Eigensolver (VQE) results of Rinaldi et al. by over ten orders of magnitude. At larger cutoffs Λ = 3 and Λ = 4 (12 qubits), SKQD converges to machine precision with appropriately chosen Krylov dimension and shot count, maintaining clear superiority over VQE at all couplings. We additionally execute SKQD on the IBM Heron r2 superconducting processor ibm_kingston at Λ = 2 with shallow Trotter circuits, demonstrating that the algorithm recovers the exact ground-state energy from hardware-sampled bitstrings even when approximately half of the sampled basis states arise from device noise - a direct empirical demonstration of SKQD's noise resilience. We verify our Hamiltonian construction against published exact diagonalization results to ~10^-9, perform a complete gauge-singlet analysis, and present preliminary measurements of the Fock-mode entanglement entropy between the two matrix subsystems, which vanishes in the free limit and grows monotonically with coupling. This work constitutes the first application of SKQD to matrix quantum mechanics, extending the algorithm's reach beyond condensed matter, lattice gauge theory, and quantum chemistry into the domain of gauge theories with holographic significance.