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A Complexity Measure for Continuous Time Quantum Algorithms

Dominik Janzing·Thomas Beth
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Abstract

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.

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Dominik Janzing, Thomas Beth. 2000-09-22. A Complexity Measure for Continuous Time Quantum Algorithms. https://doi.org/10.1103/physreva.64.022301

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