Qblox Compensation Matrix

Explanation of changes

Adds crosstalk and crosstalk_compensation_enable fields to the hardware configuration. If crosstalk compensation is enabled, an extra compilation step is added, which introduces compensation pulses and also modifies the amplitude of the original pulse.

Motivation of changes

When driving qubits, crosstalk between channels presents a problem, causing unwanted interactions between qubits and control signals. Fortunately, if the coupling strength is known, crosstalk can be mitigated by multiplying the pulse with the compensation matrix, which is the inverse of the crosstalk matrix.

As a small example, consider the following crosstalk matrix for 2 qubits with a coupling strength (C) = 0.5 both ways:

$$C = \begin{pmatrix} 1 & 0.5 \\ 0.5 & 1 \end{pmatrix}$$

We then have the accompanying compensation matrix:

$$C^{-1} = \begin{pmatrix} \frac{4}{3} & -\frac{2}{3} \\ -\frac{2}{3} & \frac{4}{3} \end{pmatrix}$$

If we then have a control signal with amplitude 0.8 on qubit 1, while nothing is driving qubit 2, we get the final result:

$$\begin{pmatrix} \frac{4}{3} & -\frac{2}{3} \\ -\frac{2}{3} & \frac{4}{3} \end{pmatrix} \begin{pmatrix} 0.8 \\ 0 \end{pmatrix} = \begin{pmatrix} \frac{16}{15} \\ -\frac{8}{15} \end{pmatrix}$$

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Merge checklist

See also merge request guidelines

• Merge request has been reviewed (in-depth by a knowledgeable contributor), and is approved by a project maintainer.
• New code is covered by unit tests (or N/A).
• New code is documented and docstrings use numpydoc format (or N/A).
• New functionality: considered making private instead of extending public API (or N/A).
• Public API changed: added @deprecated and entry in deprecated code suggestions (or N/A).
• Newly added/adjusted documentation and docstrings render properly (or N/A).
• Pipeline fix or dependency update: post in #software-for-developers channel to merge main back in or update local packages (or N/A).
• Tested on hardware (or N/A).
• CHANGELOG.md for breaking changes and AUTHORS.md have been updated (or N/A).
• Update Hardware backends documentation if backend interface change or N/A
• Check whether performance is significantly affected by looking at the Performance metrics results.
• Windows tests in CI pipeline pass (manually triggered by maintainers before merging).
  • Maintainers do not hit Auto-merge, we need to actively check as manual tests do not block pipeline

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For reference, the issues workflow is described in the contribution guidelines.

assigned to @dvos2

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This MR is in favor of the other one? Shall we close that one?

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Only a few comments. crosstalk_compensation.py is pretty clean, easy to read!

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