Primer on Pauli Twirling, Part I

Part of the series Primer on Pauli Twirling (tutorial); cited as one entry below.

Begins operationally by sandwiching a noise channel between random Paulis and showing, with an amplified coherent over-rotation, how twirling scrambles coherent errors. It then sets up notation for easy and hard gate cycles in a noisy circuit and shows how twirls are inserted, conjugated through hard gates and compiled into neighbouring single-qubit gates, ending with a summary of why twirling is used in practice.

• Twirling a CPTP noise channel over the Pauli group
• Coherent over-rotation example and how twirled errors stop adding coherently
• Noisy-circuit cycles of easy and hard gates, and conjugating twirls through Clifford layers
• Practical uses: randomized compiling, PEC, and efficient Clifford simulation of Pauli noise

Summary and key points drafted by a language model from the slides, not yet reviewed by me. The slides are the source.

Cite

@misc{minev2022primerpaulitwirling,
  author = {Zlatko K. Minev},
  title = {{Primer on Pauli Twirling (tutorial)}},
  howpublished = {Lecture series},
  year = {2022},
  url = {https://zlatko-minev.github.io/zlatko-minev-quantum-repository/series/primer-on-pauli-twirling-tutorial/},
  note = {Slides, 4 decks}
}

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