MLMC-qDRIFT couples multilevel qDRIFT estimators to achieve O(ε^{-2} log²(1/ε)) gate complexity for observable estimation instead of the standard O(ε^{-3}).
Multilevel Monte Carlo methods.Acta numerica, 24:259–328
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Nested MLMC with preintegration achieves a strong convergence rate of -1 for risk estimation, yielding nearly optimal computational complexity compared to standard MLMC's -1/2 rate.
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MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation
MLMC-qDRIFT couples multilevel qDRIFT estimators to achieve O(ε^{-2} log²(1/ε)) gate complexity for observable estimation instead of the standard O(ε^{-3}).
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Nested Multilevel Monte Carlo with Preintegration for Efficient Risk Estimation
Nested MLMC with preintegration achieves a strong convergence rate of -1 for risk estimation, yielding nearly optimal computational complexity compared to standard MLMC's -1/2 rate.