Evaluation of properties of clustered quantum circuits / Evaluation von Charakteristiken geclusterter Quantenschaltkreise

This project contains the results of the evaluation of clustered quantum circuits.

The research questions are:

• What is the behavior of the circuits as connectivity increases with respect to the metrics?
  • Is there a smooth transition from separable circuits to dense circuits, or is there a tipping point?
  • Is there a difference between different interaction types?
• What arrangement of circuits is advantageous when using clustered circuits for certain metrics?

The result of our research project is:

• The more qubits are entangled with each other through a loop, the better the expressibility values. However, this does not imply that high entanglement presupposes good expressibility values.
• Expressibility of separable circuits < expressibility of loop circuits < expressibility of all-to-all circuits
• Directly comparing the parametrized rotation operations, the insertion of crx and cry achieves significant improvements in expressibility as entanglement is increased.
• When choosing between crx, cry, and crz: crx and cry behave similarly to each other. On the other hand, crz achieves hardly any improvements in expressibility as entanglement hardly changes.
• Increasing the depth can improve expressibility. However, manipulating the width does not show this effect.

Repository Organization

• results: Contains the txt results of our evaluation.
• implementation: Contains the automatic clustered circuit generation and the expressibility according to [Sim19] & entangling capability according to [Mey02].
• docs: Contains futher explanations for the strategies and decisions.

Learn More

• [Hub20] Hubregtsen, T., Pichlmeier, J., Stecher, P., & Bertels, K.. (2020). Evaluation of Parameterized Quantum Circuits: on the relation between classification accuracy, expressibility and entangling capability. https://doi.org/10.48550/arXiv.2003.09887

• [Mey02] Meyer, David A. & Wallach, Nolan R.. (2002). Global entanglement in multiparticle systems. Journal of Mathematical Physics, 43(9), 4273–4278. https://doi.org/10.1063/1.1497700

• [Sim19] Sim, S., Johnson, Peter D., & Aspuru-Guzik, Alán (2019). Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum-Classical Algorithms. Advanced Quantum Technologies, 2(12), 1900070. https://doi.org/10.1002/qute.201900070

License

The self-produced code is available under the Apache-2.0 License. This project includes parts from third-party libraries. Their use is subject to their license terms. The implementation used the following third-party libraries:

• Kim, Saesun & Scholten, Travis L. (2021). Expressibility of Parametrized Quantum Circuits & Classification Accuracy of Quantum Neural Networks. The library is licensed under the MIT License.