The Haar Measure | PennyLane Tutorial

Isaac DeVlugt introduces you to the Haar measure using PennyLane (www.pennylane.ai) and explains the importance of it in variational quantum algorithms. - PennyLane demo of the Haar measure: https://pennylane.ai/qml/demos/tutorial_haar_measure - How to generate random matrices from the classical compact groups: https://arxiv.org/pdf/math-ph/0609050.pdf - The Random Matrix Theory of the Classical Compact Groups: https://case.edu/artsci/math/esmeckes/Haar_book.pdf - Simple factorization of unitary transforms: https://arxiv.org/pdf/1708.00735.pdf - The QR decomposition: https://en.wikipedia.org/wiki/QR_decomposition Discussion forum: https://discuss.pennylane.ai/ ------------------------------------------------------------------------------------------------------- PennyLane Cloud Notebooks are out of commission as of September 12, 2023, at 1:00 PM EDT (17:00:00 UTC). We recommend that you start using PennyLane locally or on Google Colab. Install PennyLane locally: https://pennylane.ai/install/ ------------------------------------------------------------------------------------------------------- Timestamps: 0:00 Intro 0:16 When and why would we need the Haar measure? 0:34 What is a measure? 1:19 What is the Haar measure? 1:56 How to generate Haar-random unitaries 3:11 Code to generate Haar-random unitaries 5:10 Use Haar-random unitaries in quantum circuits 8:10 Pros and cons of Haar-random circuits ------------------------------------------------------------------------------------------------------- PennyLane is an open-source Python library for differentiable programming of quantum computers. We're focused on the community, making content that suits anybody wanting to learn quantum computing, quantum machine learning, and quantum chemistry. ------------------------------------------------------------------------------------------------------- Install PennyLane: https://pennylane.ai/install/ Check out our amazing demos: https://pennylane.ai/qml/demonstrations Follow us on: - Twitter: https://twitter.com/PennyLaneAI - LinkedIn: https://www.linkedin.com/company/pennylaneai/ - GitHub: https://github.com/PennyLaneAI/pennylane ------------------------------------------------------------------------------------------------------- Built with ❤️ by Xanadu (https://xanadu.ai)