Rigorous worst- and average-case error bounds show comparable worst-case scaling for digital and analog quantum simulators under perturbative noise, with distinct average-case error cancellation and concentration bounds for Gaussian and Brownian noise.
Assume that the implemented Hamiltonian: H′ γ=Hγ+δLγ, (C48) whereLγis chosen from an ensemble of Hermitian matrices withE [Lγ] = 0 and∥Lγ∥≤1
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Stability of digital and analog quantum simulations under noise
Rigorous worst- and average-case error bounds show comparable worst-case scaling for digital and analog quantum simulators under perturbative noise, with distinct average-case error cancellation and concentration bounds for Gaussian and Brownian noise.