Process tomography

[stavros11]

Allows to reconstruct the channel corresponding to the application of an arbitrary single or two-qubit gate (or gates) on hardware, following https://arxiv.org/abs/quant-ph/9610001.

Some example results:

  - id: Process tomography
    operation: process_tomography
    targets: ["D2"]
    parameters:
      circuit: [["y90"]]
      nshots: 5000

  - id: Process tomography Two-Qubit
    operation: process_tomography
    targets: [["D2", "D1"]]
    parameters:
      circuit: [["cz", "cz"]]
      nshots: 5000

• Single-qubit (Y90 gate): http://login.qrccluster.com:9000/s9QyqzV7RASUWLq-oBqAkg==
• Two-qubit (CZ gate): http://login.qrccluster.com:9000/Vzx-IK8ERZy4LAEnF53TVQ==

The plot corresponds to the chi matrix introduced in Eq. (3. 2) in the operator basis from (4.1)-(4.4). This fully describes the channel. Note that the gate set is currently limited to ["x180", "y180", "x90", "y90", "-x90", "-y90"] for simplification.

Draft mainly becasue it is lacking tests and documentation. Also, ideally this should be written using qibo circuits, similarly to the state tomographies, and potentially also reuse code from there. This would also fix the gate limitations, but I am not doing it because I want to keep it independent from transpiler/compiler until these are debugged.

[codecov]

Codecov Report

Attention: Patch coverage is 30.62201% with 145 lines in your changes missing coverage. Please review.

Project coverage is 95.92%. Comparing base (c8cd2a9) to head (ff65833).

Files with missing lines	Patch %	Lines
src/qibocal/protocols/process_tomography.py	30.28%	145 Missing ⚠️

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@@            Coverage Diff             @@
##             main    #1046      +/-   ##
==========================================
- Coverage   97.35%   95.92%   -1.44%     
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  Lines        9749     9958     +209     
==========================================
+ Hits         9491     9552      +61     
- Misses        258      406     +148     

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Files with missing lines	Coverage Δ
src/qibocal/protocols/__init__.py	100.00% <100.00%> (ø)
src/qibocal/protocols/process_tomography.py	30.28% <30.28%> (ø)

... and 1 file with indirect coverage changes

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[igres26]

Great! Could we add a figure of merit to this? Some distance between the experiment data and the noiseless simulation.

[alecandido]

Great! Could we add a figure of merit to this? Some distance between the experiment data and the noiseless simulation.

This is something that also @stavros11 was looking for.

What I suggested (was the most trivial attempt) was just to use the $\mathbb{L}^2$ norm on the displayed matrix.
However, this might not be meaningful at all as a distance in the space of channels.

Instead, what could have been a meaningful attempt, is to have an $\sup$ norm, maximizing over the space of states' fidelities (i.e. computing the superior of the fidelities of the results of channels applications, simulated and measured, over the possible $\rho$ initial states).
Since with the tomography you have reconstructed the whole channel, no further measure is needed. And since the space is finite-dimensional, the inferior should just be a maximum.
I'm not sure whether this is an actual distance over the space of channels: it is symmetric, and 0 iff the channels are the exact same. Not sure if it's triangular...

In any case, just plotting the difference matrix (instead of the two $\chi_{mn} matrices) it would already help me interpreting the result...