Quantum implementation of higher-order power method for estimating geometric entanglement of pure states
Phys. Rev. A 113, 062459 – Published 25 June, 2026
DOI: https://doi.org/10.1103/6ym6-yb6m
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 multiqubit pure states using rank-1 tensor approximation. This method is executable on early fault-tolerant (hybrid) quantum hardware and does not depend on quantum memory. We simulate this algorithm and mitigate the effects of noise on the results of the computation using a theoretical model based on a known mitigation approach, which assumes a global depolarizing noise channel.
