Computational complexity of random multi-qudit states and unitaries scales exponentially with qudit number, while physical complexity scales more slowly.
Indeed, it might seem surprising that implement- ing a unitary operator on a quantum computer requires an exponentially large number of gates
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Computational and physical complexity of synthesizing random multi-qudit quantum states and unitary operators
Computational complexity of random multi-qudit states and unitaries scales exponentially with qudit number, while physical complexity scales more slowly.