AS-SQD applies an active sampling strategy with Epstein-Nesbet perturbation scores to iteratively expand the basis in sample-based quantum diagonalization, achieving lower energy errors than standard or random methods on spin chains and IBM hardware.
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SQD-AA reduces total query complexity by more than 100x on model distributions and achieves the lowest T-gate counts with 3-4 orders shallower circuits than iQPE for molecular examples.
SQD needs an exponentially increasing number of computational-basis configurations to approximate ground-state energies of Heisenberg and Hubbard models within fixed accuracy, even when configurations are chosen optimally by probability.
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Sample-Based Quantum Diagonalization with Amplitude Amplification
SQD-AA reduces total query complexity by more than 100x on model distributions and achieves the lowest T-gate counts with 3-4 orders shallower circuits than iQPE for molecular examples.