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2

Is the correct analogy that in a computer, the implementation of a function is some sequence of gates. Yes, that's almost always what an oracle will be. The oracle could be some physical object that you are trying to analyze. For example, the computation could look like "pass these carefully polarized photons through the rock sample and check what ...


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I wonder if there are explicit examples where the T-count scales stronger with n. [...] maybe superlinear or even exponential. Here's an existence proof of an $n$ qubit magic state with a T count of $\Theta(2^{n/4})$, based on caching QROM reads. It takes $\Theta(2^{n/4})$ T gates to prepare the cached-QROM state, and also you can consume the cached-QROM ...


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Liu and Winter (http://arxiv.org/abs/2010.13817) have shown that any "reasonable" magic monotone is asymptotically bounded by $n$. Moreover, Haar-random pure states cluster around that value (deviation is exponentially suppressed in $n$). By a standard argument (as in Beverland et al.), $\Omega(n)$ magic implies that we need $\Omega(n)$ copies of ...


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For 2x2 unitary, it is just a U3-gate. For 4x4 unitary, TwoQubitBasisDecomposer is used. TwoQubitBasisDecomposer implements KAK decomposition method described in arXiv:0806.4015 by Drury and Love. This method uses optimal number of CNOT gates. For larger unitaries, Isometry class is used. This class implements the method introduced by Iten et al. in arXiv:...


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