Understanding and Improving Qubit Measurement
Qubit measurement is a process that consists of generating a measurement pulse, having the pulse interact with the qubit, reading out voltages, integrating the voltages into IQ values, and classifying the IQ values as a particular measurement outcome.
The goal of this project is to understand and characterise this pipeline.
- Qiskit Camp Africa 2019
- Hackathon Team #23
- Presentation: prezi.com
Contents:
What we did
Evaluate measurement performance as a function of measurement pulse frequency
Using the ibmq_armonk system and pulse control, we examined measurement outcomes as a function of measurement pulse frequency.
The IQ plots clearly show how 0 and 1 outcomes become more separable on the IQ plane as the optimal measurement frequency is approached. Separability worsens again as one moves away from the optimal peak.
At the optimal frequency, a small cluster of values can be seen in the lower left of the IQ plane. These might be instances where the qubit decoheres or is excited to the 2 energy level by the measurement pulse. Further investigation of this cluster is needed.
The experiment ran 3 schedules: one with the qubit in the |0> states,
one with a qubit in the |1> state and one with the |0> rotate by
90 degrees about the X axis |0> - i|1> . The third schedule was not
used in the analysis.
512 shots were performed for each of 11 frequency steps.
- Notebook: measurement_freq_experiments.ipynb
- Saved results: ibmq_armonk_measurement_freq_experiment.pickle
Characterise X and K qubit parameters
We used pulse control to determine the X and K values of the ibmq_armonk qubit.
By scanning the measurement frequency across the optimal value, we determined
the shape of the peak of the IQ magnitude for both |0> and |1> states.
X is half the separation between the two peaks and was measured to be
2.1297e-05 GHz.
K is the average full-width at half maximum of the two peaks and was
measured to be 1.8751 GHz.
The notebook includes options to simulate the frequency peaks using either
Gaussian or Lorentzians. Experimental peaks are fitted with Lorentzians
using scipy's curve_fit function.
512 shots were performed for each of 101 frequency steps.
- Notebook: Measure X and K using OpenPulse.ipynb
- Saved results: xk_results
Improved classification of IQ values
The qiskit-ignis package currently includes linear and quadratic discriminators.
We investigated the possibility of using more sophisticated classifiers, and
in particular, sklearn.svm.SVC, an SVM-based classifier provided by sklearn.
We fitted the discriminators to measurements obtained of the |0> and
|1> states on ibmq_armonk.
Various SVC kernels were tried, and the rbf (radial basis function)
kernel was determined give the best separation and to be the most robust.
Various values of the SVC regularization parameter C were compared.
The new SVC discriminator was compared to the existing linear and quadratic discriminators and found to offer a slight deduction in measurement errors.
We have opened a PR for qiskit-ignis to add the new discriminator.
- Notebook (comparison of regularization values): sklearn_discriminators.ipynb
- Notebook (comparison with existing discriminators): sklearn_discriminators_extension.ipynb
- Notebook (for generating results): armonk.ipynb
- Saved results: ibmq_armonk_results.pickle
- qiskit-ignis PR to add SklearnIQDiscriminator: qiskit-community/qiskit-ignis#316
What we learned
- A lot of OpenPulse!
- Measurement pulses
- Integrating voltage readings to generate IQ values using kernels.
- What IQ discriminators are.
Future work
-
Investigate improved kernels: We would have loved to be able to investigate the effect of different kernels on the separability of IQ values, and in particular, in be able to determine which measurements might have given invalid results. Unfortunately no IBM Q systems currently support measurement level 0 (i.e. reading the unintegrated voltage values), so this has to remain future work.
In particular, it would be interesting to see if the shape of the path mapped out on the IQ plane during the reading of the measurement pulse might allow determining which measurements unusual paths.
-
Investigate multi-qubit measurement discriminators: Measuring multiple qubits at once provides the possibility of better discriminating between measurements.
Repository guide:
-
notebooks: Jupyter notebooks and experiment results.
-
papers: PDFs of relevant papers.
-
pkgs: Custom builds of Qiskit packages needed for pulse control.
-
pop_kernels: Python package containing the new IQ discriminators.
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Other:
- measurement-kernels-23.pdf: PDF of the original hackathon issue (used for sharing while the WiFi was spotty).
- theory-notes.rst: Some notes from Nick's lecture on X, K and the IQ plane.