Tech Notes
Estimating Observables from Sampled Bit Strings
Sets up computational-basis measurement of an n-qubit state and diagonal observables, and shows that bitstring probabilities and Pauli-Z expectations are related by the Walsh-Hadamard transform. It then models the counts from M shots as multinomial, giving their mean and covariance, as a starting point for how many shots a given confidence needs; the note is marked work in progress.
- Measurement operators and outcome probabilities for an n-qubit register
- Diagonal observables and Pauli-Z strings indexed by bitstrings
- Walsh-Hadamard transform between projector and Pauli-Z expectations
- Multinomial statistics of shot counts: 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/}
}Reuse
Unless a deck says otherwise, the slides and notes here are © Zlatko K. Minev and shared under CC BY-NC-ND 4.0: you're welcome to read, download and share them, unchanged and non-commercially, with credit and a link back. Commercial use or a reworked slide or figure in your own talk, course or paper needs permission; please ask, the answer is usually yes. If you use something in teaching or a publication, I'd love a short note telling me where.
Some slides include figures, photos, logos or excerpts from other people and institutions, credited where they appear. Those aren't mine to license, so please ask the original source. Spotted a missing credit? Tell me and I'll fix it.
