Variational determination of multi-qubit geometrical entanglement in NISQ computers

Abstract

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 NISQ devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of $3$, $4$, and $5$ 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 states techniques up to $25$ qubits.

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• Detecting entanglement of unknown states by violating the Clauser-Horne-Shimony-Holt inequality
• Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering
• Entanglement Detection with Quantum-inspired Kernels and SVMs
• Optimal Qubit Mapping Search for Encoding Classical Data into Matrix Product State Representation with Minimal Loss
• A variational quantum algorithm for entanglement quantification
• Variational-toolbox-based separability detection of multiqubit states