A quantum implementation of high-order power method for estimating geometric entanglement of pure states

Abstract: Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or application under consideration. Each of these measures may be computed or approximated by multiple methods. However, hardly any of these methods can be run on near-term quantum hardware. This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states using rank-1 tensor approximation. This method is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel. This model allows us to post hoc mitigate the effects of noise on the results of the computation.