errorcausation - Diraq-Ares: Predicting Error Causation

A package for analysing and quantifying the SPAM + state flip errors in a quantum computer

Summary

Quick start

Installation

1. Clone the repo

git clone  https://github.com/oxquantum-repo/diraq-ares-predicting-error-causation/

2. In your terminal or anaconda prompt, create an environment and activate it, for example using anaconda

conda create --name errorcausation

conda activate errorcausation

3. cd into the cloned repo directory diraq-ares-predicting-error-causation/

4. Install the required packages using pip and the errorcausation pacakage

conda install pip
python3 -m pip install --upgrade build
python3 -m build
pip install -e .

The -e flags means that the package is in "developer/editable" mode, i.e. the changes that you make in the package will be reflected in your working environment

Run Instructions

Below is an example of how one would run the errorcausation package:

import numpy as np
from pathlib import Path
from scipy.io import loadmat
from errorcausation.Categorical.categoricalmodel import CategoricalModel

np.random.seed(0)

file = Path('data/even_init.mat')
data = loadmat(file.resolve())
measured_states = 1 - data['measured_states'].squeeze()

# initialising a qm_model to fit to the data and setting the starting guess of parameters for the Baum-Welch algorithm
# to optimise
model_to_fit = CategoricalModel()
model_to_fit.set_start_prob(0.95)
model_to_fit.set_transition_prob(0.05, 0.05)
model_to_fit.set_emission_prob(0.95, 0.95)

# fitting the qm_model to the data, using the Baum-Welch algorithm. The uncertainty in the parameters is also computed
# using the Cramer-Rao lower bound.
model_to_fit.fit(measured_states, compute_uncertainty=True)

# printing the fitted qm_model, which should be close to the qm_model used to simulate the data
print(model_to_fit)

# using the fitted qm_model to predict the true qubit state from the measured state and plotting the results
predicted_states = model_to_fit.predict(measured_states, plot=True)

This was taken from categorical_example_experimental.py. More examples can be found in the examples folder.

Mission Statement

Problem

• Repeated PSB non-demolition readout (Two states: Even/Odd == (up, up; down, down)/(up, down; down, up)
• We try to initialise into the even state
• In Experiment Number 1 we measured: even, even, even, odd, odd

Questions to answer:

• What caused the change from even to odd in Experiment Number 1 for example?
• Was there a spin flip caused by the non-demolition measurement (back action)?
• Was there a readout error at iterations 4 and 5, i.e. the state was even, be we mistakenly read it as odd twice?
• Could the state have been initialised as odd instead of even, and we read it out incorrectly for the first 3 iterations as even?

Objectives

• Given a sequence of readout data, predict the probability (with uncertainty) of:
  • A readout error
  • Spin flip
  • Initialisation error
• Therefore tell me what happened in this measurement based on these probabilities
• Infer the initialisation state (with uncertainty) based on readout data
• Predict the next state to be read out (with uncertainty) based on previous states

Solution

• Treat the readout sequences as Markovian
• Use a Hidden Markov Model to extract the system probabilities
• Demonstrate success of Hidden Markov Model on simulated data

Example results

Simulated Data

Model Performance

Real Data

Model Performance

P_init: 0.990
P_spin_flip_even_to_odd: 0.016
P_spin_flip_odd_to_even: 0.048
P_readout: 0.935