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A Complexity Measure for Continuous Time Quantum Algorithms
We consider unitary dynamical evolutions on n qubits caused by time dependent
pair-interaction Hamiltonians and show that the running time of a parallelized
two-qubit gate network simulating the evolution is given by the time integral
over the chromatic index of the interaction graph. This defines a complexity
measure of continuous and discrete quantum algorithms which are in exact
one-to-one correspondence. Furthermore we prove a lower bound on the growth of
large-scale entanglement depending on the chromatic index.Comment: 6 pages, Revte