All-to-all Hamiltonians can simulate any two-qubit gate in about 1/N time and any depth-D circuit in about D/√N time, with polynomially small error.
Universal quantum circuit for two-qubit transformations with three controlled-not gates,
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Fast quantum computation with all-to-all Hamiltonians
All-to-all Hamiltonians can simulate any two-qubit gate in about 1/N time and any depth-D circuit in about D/√N time, with polynomially small error.