Performance and Stability of Quantum Krylov Diagonalization for the Hubbard Model

This study investigates the performance, convergence, and stability of Quantum Krylov Diagonalization (QKD) for the one-dimensional Hubbard model. QKD is a hybrid quantum-classical algorithm that constructs a Krylov subspace using real-time quantum evolution, allowing for the estimation of ground-state properties without the iterative optimization loops required by the Variational Quantum Eigensolver (VQE). The authors systematically analyze how algorithmic parameters—specifically Krylov dimension, Hamiltonian evolution time, Trotter number, and singular-value truncation (SVT) thresholds—impact the accuracy of ground-state energy (GSE) calculations on both ideal simulators and IBM quantum hardware.

The researchers demonstrate that QKD's performance is governed by a delicate interplay between the Hamiltonian's low-energy spectral structure and numerical stability. Systems with near-closing energy gaps require longer evolution times to resolve nearby eigenstates effectively. However, increasing evolution time can introduce numerical instabilities and accumulated time-discretization errors. The study establishes that these errors can be managed by balancing the Krylov dimension with the Trotter number and applying SVT to remove nearly linearly dependent basis states. Experimental validation on IBM quantum hardware confirms that these findings hold under realistic conditions, with the algorithm reproducing convergence trends observed in ideal simulations using only lightweight readout-error mitigation.

QKD offers a promising path for studying strongly correlated fermionic systems on current Noisy Intermediate-Scale Quantum (NISQ) devices. By avoiding the complex optimization landscapes and potential barren plateaus associated with traditional variational approaches, QKD provides a more stable and predictable framework for ground-state estimation. The practical guidelines provided in this paper for selecting algorithmic parameters are essential for researchers aiming to implement QKD on near-term hardware.