Quantum Algorithmic Complexity of Three-Qubit Pure States

Abstract

For pure three-qubit states the classification of entanglement is both non-trivial and well understood. In this work, we study the quantum algorithmic complexity introduced in [1] of three-qubit pure states belonging to the most general class of entanglement. Contrary to expectations we find out that the degree of entanglement of states in this class quantified by the measure of 3-tangle, does not correlate with the quantum algorithmic complexity, defined as the length of the shortest circuit needed to prepare the state. For a given entangled state the evaluation of its quantum complexity is done via a pseudo random evolutionary algorithm. This algorithm allows us not only to determine the complexity of a quantum circuit in terms of the number of required quantum gates, but also to estimate another type of complexity related to the time required to obtain the correct answer.