Variational Determination of Multiqubit Geometrical Entanglement in Noisy Intermediate-Scale Quantum Computers

9 pags., 6 figs.Current noise levels in physical realizations of qubits and quantum operations limit the applicability of conventional methods to characterize entanglement. In this adverse scenario, we follow a quantum variational approach to estimate the geometric measure of entanglement of multiqubit pure states. The algorithm requires only single-qubit gates and measurements, so it is well suited for noisy intermediate-scale quantum devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of three, four, and five qubits. Numerical simulations with random states show the robustness and accuracy of the method. The scalability of the protocol is numerically demonstrated via matrix-product-state techniques up to 25 qubits.This work is supported by ANID—Millennium Science Initiative Program—ICN17−012. A.D. is supported by FONDECYT Grant No. 1180558. L.P. is supported by ANID-PFCHA/DOCTORADO-BECAS-CHILE/2019- 72200275 and by the Spanish Project PGC2018-094792-B-I00 (MCIU/AEI/FEDER, UE). L.Z. is supported by ANID-PFCHA/DOCTORADO-NACIONAL/2018-21181021. J.C.-V. is supported by ANID-PCHA/Doctorado Nacional/2018-21181692