For every Boolean f, bounded-error quantum and classical deterministic communication complexity of f ∘ AND₂ are polynomially related up to polylog n, both characterized by log of De Morgan sparsity of f.
Almost optimal lower bounds for small depth circuits
3 Pith papers cite this work. Polarity classification is still indexing.
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Any n-qubit unitary can be implemented approximately with Õ(2^{n/2}) oracle queries or exactly with Õ(2^{n/2}) circuit depth via Grover search reductions, with matching lower bounds for certain implementations.
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Query and Depth Upper Bounds for Quantum Unitaries via Grover Search
Any n-qubit unitary can be implemented approximately with Õ(2^{n/2}) oracle queries or exactly with Õ(2^{n/2}) circuit depth via Grover search reductions, with matching lower bounds for certain implementations.