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/tutori...
How to generate random matrices from the classical compact groups: https://arxiv.org/pdf/math-ph/0609050...
The Random Matrix Theory of the Classical Compact Groups: https://case.edu/artsci/math/esmeckes...
Simple factorization of unitary transforms: https://arxiv.org/pdf/1708.00735.pdf
The QR decomposition: https://en.wikipedia.org/wiki/QR_deco...
Discussion forum: https://discuss.pennylane.ai/
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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
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