Why flips are pairs of flips ?

[jevillegasd]

In the flip sequence, for every item in the range of flips used we apply two 180 gates, which is a bit counterintuitive since this would double the number of flips. Yesterday with @lballerio we discussed about this. Would it not make better sense if the number of flips matches the number of rx180 gates. To make sure that you always measure in positive then the final RX90 gate can just have a conditional phase of 180 degrees depending on whether the number of gates is even or odd. The final sequence would look like:

    sequence = PulseSequence()
    natives = platform.natives.single_qubit[qubit]
    sequence |= natives.R(theta=np.pi / 2)
    for _ in range(flips):
        if rx90:
            qd_channel, qd_pulse = natives.RX90()[0]
        else:
            qd_channel, qd_pulse = natives.RX()[0]

        qd_detuned = update.replace(
            qd_pulse, amplitude=qd_pulse.amplitude + delta_amplitude
        )
        sequence.append((qd_channel, qd_detuned))
        # sequence.append((qd_channel, qd_detuned))

        if rx90:
            sequence.append((qd_channel, qd_detuned))
            sequence.append((qd_channel, qd_detuned))
    sequence |= natives.R(theta=np.pi / 2, phi = 0.0 if flips%2 == 0 else np.pi)
    sequence |= natives.MZ()

    return sequence

This is how 2D flip experiment (PR #1504 ) looks with the current schedule: http://login.qrccluster.com:9000/fIeddKqHT26EMLdwDhKYXA==

And this is with the updated one: http://login.qrccluster.com:9000/oW8UKGzARoCNOUKtiTI7gw==/

[jevillegasd]

In the paper from S. Sheldon (https://arxiv.org/pdf/1504.06597) she indeed uses pairs of gates, but they apply it $R_{x,\pi/2}$ rotations, not $R_{x, \pi}$ (which we currently apply 4 RX90 if the users passes rx90 = true to the routine)

[alecandido]

Hi @jevillegasd, sorry for the late reply.

It is certainly fine to adapt the Qibocal implementation to the literature, whatever the reason for both.

Instead, if we want to discuss about the optimality of the experiment, I see some differences, which most likely make the one in the literature advantageous. But I'm not completely sure.

Mainly, the difference is coming from the rapid oscillations about 0.5. Taking double steps, we would avoid that effect. If the classification is reliable, that could also be avoided just by fitting the distance from equator (i.e. abs(x - equator), with equator = 0.5 for perfect classification), and you can add it back in the predictions as an alternating minus sign.
However, this is just for the sake of the explanation, not a practical proposal. Since you could obtain the same just fitting the alternating function with least squares.

So, we should lose nothing by taking 10 alternating points as opposed to 10 only positive points. While the latter strategy has the disadvantage of a longer average sequence, which increases the duration of the experiment (worse performance) and walks deeper into decoherence.

Moreover, flipping has a naturally limited resolution, because of its discrete nature. In this way, we are halving it, cutting the regions of errors that can be detected with this experiment.
Arguably, a large error is more properly corrected by Rabi, and we do not need flipping for it. Still, if it can work even in that regime, it is only more pleasant. Even if, because of experimentalist error or parameters fluctuations, the error turns out to be larger, a higher resolution flipping may still succeed in properly detecting it. Which is strictly better than failing (or, almost equivalently, quoting a very large uncertainty on extracted parameters).

In any case, the short answer is: yes, I agree we can use single $\pi$ steps (or double $\pi/2$ - but possibly even single $\pi/2$, if we had time to waste in adapting the fit).

[jevillegasd]

@alecandido the alternating points are "fixed" with the conditional $\pi$ in the last pulse in

sequence |= natives.R(theta=np.pi / 2, phi = 0.0 if flips%2 == 0 else np.pi)

[alecandido]

As mentioned offline, better the strategy suggested by @jevillegasd, conditionally applying a phase in the instruction, since this is taking effect upstream to classification, so it saves the trouble to first identify the effective baseline (the equator) wrt which correcting the oscillating sign.