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.
The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach
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abstract
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important, but underappreciated, inequality.
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2025 1verdicts
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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.