The trainability boundary for variational quantum objectives is the affine regime; non-affine amplification-capable losses can mitigate barren plateaus when using coarse-grained statistics at polynomial widths.
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A non-unitary extension of Grover's algorithm achieves O(sqrt(N)) query complexity matching the optimal bound by using a single large rotation via block encoding and Chebyshev approximation, at the cost of one additional qubit.
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Trainability Beyond Linearity in Variational Quantum Objectives
The trainability boundary for variational quantum objectives is the affine regime; non-affine amplification-capable losses can mitigate barren plateaus when using coarse-grained statistics at polynomial widths.
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Non-unitary extension of Grover's search algorithm
A non-unitary extension of Grover's algorithm achieves O(sqrt(N)) query complexity matching the optimal bound by using a single large rotation via block encoding and Chebyshev approximation, at the cost of one additional qubit.