N-qubit-nonlinear-protocol

This project provides code and scripts that reproduce the key findings presented in the paper 'Rozgonyi, Á., Széchenyi, G., Kálmán, O. and Kiss, T., 2025. Practical scheme for efficient distillation of GHZ states'. arXiv preprint arXiv:2501.12268.

Overview

We develop an efficient local operation and classical communication (LOCC) scheme for the distillation of Greenberger-Horne-Zeilinger (GHZ) states from tripartite systems subjected to both coherent and incoherent errors. The proposed method employs an iterative process that employs a postselection based non-linear transformation to increase the entanglement of 3-qubit states. In contrast to traditional distillation protocols that require an exponential number of initial states as a resource, our method achieves subexponential convergence towards a pure GHZ state. The proposed scheme practical in the sense that it employs a small set of relatively simple unitary operations and projective measurements in the computational basis. We systematically develop a double-iteration protocol by providing a mathematical framework for the transformation processes involved, emphasizing the role of unitary operations in correcting arbitrary small errors in the initial states. Through analytical derivations and numerical simulations, we demonstrate the protocol's ability to progressively eliminate noise and improve fidelity over subsequent iterations. Significantly, our protocol not only corrects for small arbitrary distortions in the GHZ states, but also maintains operational simplicity, making it feasible for practical quantum computing applications. Finally, our hardware-efficient design is implementable on recent quantum computers, as evidenced by the low number of qubits required and the few 1- and 2-qubit gates needed. We employ the IBM Qiskit quantum simulator to test the protocol's performance on actual quantum hardware.

References:

[1] Áron Rozgonyi, Gábor Széchenyi, Orsolya Kálmán, Tamás Kiss. “Training iterated protocols for distillation of GHZ states with variational quantum algorithms.” Physics Letters A

Repository Structure

• notebooks/: Source code for implementing the quantum protocols.
• authors/: Lists people who are significant authors of the project.
• docs/: Documentation and references for understanding the theory and implementation details.
• citation/: Full citation details are available, if you use this code or mention its results, please cite it.

Code availability:

• 3qubit_analitics.nb Wolfram Mathematica notebook contains the analytical investigation of the 3-qubit GHZ distillation scheme and prepares the unitary operators.
• Nqubit_numerics.ipynb Jupyter notebook contains the numerical analysis of the N-qubit algorithm.

Requirements

• Wolfram Mathematica
• Python