PEC Derivation: Single Qubit, Simple (C65B)

Part of the series Quantum Error Mitigation (Boulder Summer School 2023); cited as one entry below.

Short notebook pages working through PEC for one qubit. The noisy gate is decomposed as a superoperator channel and as an unraveling into trajectories, and the inverse is chosen so that error-free trajectories add up and erroneous ones cancel; an equivalent algebraic condition is also noted.

• Decomposing a noisy single-qubit gate into channel and trajectory representations
• An ansatz for the inverse (quasi-probability) correction
• Interfering trajectories so error terms cancel and the ideal term sums to one
• The equivalent algebraic condition for the correction coefficient

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

Cite

@misc{minev2023quantumerrormitigation,
  author = {Zlatko K. Minev},
  title = {{Quantum Error Mitigation (Boulder Summer School 2023)}},
  howpublished = {Lecture series, Boulder Summer School},
  year = {2023},
  url = {https://zlatko-minev.github.io/zlatko-minev-quantum-repository/series/quantum-error-mitigation-boulder-summer-school-2023/},
  note = {Slides, 7 decks}
}

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