For pure three-qubit states the classification ofentanglement is both non-trivial and well understood. In thiswork, we study the quantum algorithmic complexity introducedin [1] of three-qubit pure states belonging to the most generalclass of entanglement. Contrary to expectations we find out thatthe degree of entanglement of states in this class quantified bythe measure of 3-tangle, does not correlate with the quantumalgorithmic complexity, defined as the length of the shortestcircuit needed to prepare the state. For a given entangled statethe evaluation of its quantum complexity is done via a pseudorandomevolutionary algorithm. This algorithm allows us notonly to determine the complexity of a quantum circuit in termsof the number of required quantum gates, but also to estimateanother type of complexity related to the time required to obtainthe correct answer.
['Martin Lukac', 'Aikaterini Mandilara']
Quantum Algorithmic Complexity of Three-Qubit Pure States