The largest subuniverse where the Sierpiński cone classifies partial maps is the accessible localisation at interval-parameterised embeddings, strictly contained in Segal types for non-trivial intervals.
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Sampling-based methods for quantum state preparation achieve asymptotically lower T-count than rotation-based methods and maintain an advantage in total gate count after accounting for compilation overhead.
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The Synthetic Sierpi\'nski Cone
The largest subuniverse where the Sierpiński cone classifies partial maps is the accessible localisation at interval-parameterised embeddings, strictly contained in Segal types for non-trivial intervals.
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Logical Resource Estimation for Quantum State Preparation with Compilation
Sampling-based methods for quantum state preparation achieve asymptotically lower T-count than rotation-based methods and maintain an advantage in total gate count after accounting for compilation overhead.
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