Fixed upload circuits approximate tunable ones to error ε with depth O_σ[(log(1/ε))^σ] for any σ>1 (improving prior polynomial bounds) and matching Ω(log(1/ε)) lower bounds for mismatch-class targets via auxiliary extensions and Turán-Nazarov analysis.
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The Cost of Removing Tunability in Quantum Data Re-Uploading
Fixed upload circuits approximate tunable ones to error ε with depth O_σ[(log(1/ε))^σ] for any σ>1 (improving prior polynomial bounds) and matching Ω(log(1/ε)) lower bounds for mismatch-class targets via auxiliary extensions and Turán-Nazarov analysis.