Simple Noise Models and Gate Fidelity

Works through the single- and n-qubit depolarizing channel in several equivalent representations (Kraus-like, Pauli transfer matrix, Lindblad generator, product of single-Pauli channels) and links them to the sparse Pauli-Lindblad model used in PEC and T-REX. It derives average gate and entanglement fidelity, conversions between fidelity and error probability, CPTP bounds on the depolarizing parameter, and a worked fidelity calculation between a CNOT and a random Pauli process.

• Depolarizing channel in χ, PTM, generator and product-channel forms, with parameter conversions
• CPTP condition from the Choi matrix and the PEC sampling overhead
• Average gate fidelity and entanglement fidelity, including converting two-qubit gate fidelity to a depolarizing rate
• Example: fidelity of a CNOT against a random (Z,X) Pauli process, with PTM and χ matrices

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

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@techreport{minev2023t27,
  author = {Zlatko K. Minev},
  title = {{Simple Noise Models and Gate Fidelity}},
  type = {Technical Note},
  number = {T27},
  institution = {Zlatko's Quantum Notebook},
  year = {2023},
  url = {https://zlatko-minev.github.io/zlatko-minev-quantum-repository/items/t27-simple-noise-models-and-gate-fidelity/}
}

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