Bayesian techniques for Randomized Benchmarking (cont.)

[ShellyGarion]

Description

Enhance the current Randomized Benchmarking experiments in Qiskit-Experimetns with advanced statistical and Bayesian techniques, based on the following papers:

1. Bayesian Inference for Randomized Benchmarking Protocols

2. Statistical analysis of randomized benchmarking

3. Accelerated randomized benchmarking

Mentor/s

Shelly Garion (@ShellyGarion), Research Staff Member at IBM Research Haifa, Qiskit developer.

Type of participant

Knowledge in statistical and Bayesian methods

Number of participants

1-2

Deliverable

A pull request with these advanced methods merged into Qiskit-Experiments Randomized Benchmarking code

[starktech23]

@pdc-quantum @shesha-raghunathan assigned.

[starktech23]

Ref. qiskit-advocate/qamp-spring-21#20

[HuangJunye]

@pdc-quantum Can you please comment in the issue so that I can assign you?

[pdc-quantum]

Hi @HuangJunye
Nice 😊 to be here
Please assign me

[pdc-quantum]

Here is my 2-slide proposal for Mid-term review (Oct 7, 2021)
# {34} {Bayesian techniques for Randomized Benchmarking (cont.)}.pdf

[pdc-quantum]

Update for Checkpoint 2

What’s new since Checkpoint 1?

Modification of the frequentist model from Qiskit experiments:
When comparing the results of the Bayesian model with those of the frequentist model in Qiskit experiments, a bug was suspected in the latter.
qiskit-community/qiskit-experiments#428
It consists of excessive bounds for the error per gate (EPG), not varying with the number of circuits for each considered length. This is now subject to a PR
qiskit-community/qiskit-experiments#472
The results presented below for the simulator example and the hardware testing were obtained with the corrected code.

Hardware testing of 24 cx gates by 2-qubit interleaved RB in six 5-qubit devices:
We used a pilot experimental protocol adapted to the provider’s limit of 75 circuits in fair share queuing at that time.
Each experiment consisted of 2-qubit interleaved RB with “lengths” set to [1, 30, 60, 100, 150] and “num_samples” set to 7 (thus 70 circuits per job).
Reference values were obtained by cubic spline interpolation from the daily hardware calibrations. For only 7 out of the 24 tested gates, the calibration drift was smooth in the four-day period centered on each experiment (group 1). For the remaining 17 gates there was an oscillation (group 2).
The correlation between the reference values and the RB calculated EPG was studied.
For respectively the frequentist and the Bayesian model, r squared was:

• .849 and .815 in all 24 gates,
• .976 and .981 in group 1
• .730 and .640 in group 2.

In the total sample, the relative error on EPG was lower with the Bayesian model than with the frequentist model (mean ± sd: 7.6% ± 0.02% vs. 10.2% ± 0.19%, p<.001).
Bayesian RB appears to be a reliable method providing slightly narrower error bounds than RB based on least squared fit. A credible interval is also inferred for EPG, with its own useful upper bound.

Check_point_2_^LN {34} {Bayesian techniques for Randomized Benchmarking (cont.)}.pdf

Visual for the project

Visual^LN {34} {Bayesian techniques for Randomized Benchmarking (cont.)}.pptx
Visual^LLN {34} {Bayesian techniques for Randomized Benchmarking (cont.)}.pdf