Estimating Observables from Bitstrings, T21 (bonus)

Part of the series Intro to Quantum Noise (QGSS 2023).

Also published as a tech note; please cite that.

A short technical note asking how close an observable estimated from M measured bitstrings is to its true value, and how many shots an experiment needs. It sets up computational-basis measurement formally, shows that Pauli-Z expectation values and bitstring probabilities are related by the Walsh-Hadamard transform, and begins the statistics of multinomial counts.

• Measurement setup: probabilities as diagonal entries of the state, observables diagonal in the computational basis
• Pauli-Z strings and computational-basis projectors as informationally equivalent sets of 2^n operators
• Walsh-Hadamard transform linking ideal Pauli-Z expectations to bitstring probabilities
• Counts as a multinomial random vector, with its mean and covariance

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

Cite

@techreport{minev2022t21,
  author = {Zlatko K. Minev},
  title = {{Estimating Observables from Sampled Bit Strings}},
  type = {Technical Note},
  number = {T21},
  institution = {Zlatko's Quantum Notebook},
  year = {2022},
  url = {https://zlatko-minev.github.io/zlatko-minev-quantum-repository/items/t21-estimating-observables-from-sampled-bit-strings/}
}

Copy BibTeX

Reuse