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Quantum Simulation
Approximate pushforward designs and image bounds on approximations
arXiv
Authors: Jakub Czartowski, Adam Sawicki, Karol Życzkowski
Year
2025
Paper ID
16371
Status
Preprint
Abstract Read
~2 min
Abstract Words
81
Citations
N/A
Abstract
We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten p-norms and Lipschitz continuity arguments, we derive bounds on the approximation parameters of pushforward designs obtained from complex projective spaces, including simplices, mixed states, and quantum channels. In the mixed-state case, we refine the bounds by exploiting the symmetric subspace structure, leading to asymptotically tighter estimates. Numerical simulations support our theoretical results, showing near-optimality in low-dimensional scenarios.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision.
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