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Acquisition protocols#

The dataset returned by InstrumentCoordinator.retrieve_acquisition() consists of a number of DataArrays containing data for every acquisition channel. This document specifies the format of these data arrays.

Hide imports and auxiliary definitions 
import numpy as np
import xarray as xr
import hvplot.xarray

intermodulation_freq = 1e8  # 100 MHz
voltage_iq = 0.32 + 0.25j
sampling_rate = 1.8e9  # 1.8 GSa/s
readout_duration = 1e-7  # 100 ns
time_grid = xr.DataArray(
    np.arange(0, readout_duration, sampling_rate**-1), dims="trace_index"
)

(Demodulated) Trace Acquisition Protocol#

Readout equipment digitizes a \(V(t)\), where \(V = V_I + i V_Q\) is a complex voltage on inputs of a readout module (up/down conversion of a signal with an IQ mixer is assumed). The signal is demodulated with an intermodulation frequency configured for a readout port.

For example, if we have a readout module (like Qblox QRM or Zurich Instruments UHFQA) that is perfect, and connect its outputs to its inputs directly, raw input on a readout port will look like this:

Hide code cell source 
raw_trace = (
    voltage_iq * np.exp(2j * np.pi * intermodulation_freq * time_grid)
).assign_coords({"trace_time": time_grid})
xr.Dataset({"I": raw_trace.real, "Q": raw_trace.imag}).hvplot(
    x="trace_time", xlabel="t [s]", ylabel="V", group_label="Channel"
)

Demodulated trace will unroll this data with respect to the intermodulation frequency, so the resulting I and Q readouts will look like this:

Hide code cell source 
demodulated_trace = raw_trace * np.exp(-2j * np.pi * intermodulation_freq * time_grid)

xr.Dataset({"I": demodulated_trace.real, "Q": demodulated_trace.imag}).hvplot(
    x="trace_time", xlabel="t [s]", ylabel="V", group_label="Channel"
)

This acquisition protocol is currently supported only in BinMode.AVERAGE binning mode. The resulting dataset must contain data arrays with two dimensions for each acquisition channel: acquisition index (number of an acquisition in a schedule) and trace index (that corresponds to time from the start of the acquisition). All the dimension names should be suffixed with the acquisition channel to avoid conflicts while merging the datasets. It is recommended to annotate the trace index dimension with a coordinate that describes the time since the start of the acquisition. For example, if two acquisition channels read out once, the resulting dataset should have the following structure:

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xr.Dataset(
    {
        0: demodulated_trace.expand_dims("acq_index_0", 0).rename(
            {"trace_index": "trace_index_0", "trace_time": "trace_time_0"}
        ),
        1: demodulated_trace.expand_dims("acq_index_1", 0).rename(
            {"trace_index": "trace_index_1", "trace_time": "trace_time_1"}
        ),
    }
)

<xarray.Dataset> Size: 9kB
Dimensions:       (trace_index_0: 180, acq_index_0: 1, trace_index_1: 180,
                   acq_index_1: 1)
Coordinates:
    trace_time_0  (trace_index_0) float64 1kB 0.0 5.556e-10 ... 9.944e-08
    trace_time_1  (trace_index_1) float64 1kB 0.0 5.556e-10 ... 9.944e-08
Dimensions without coordinates: trace_index_0, acq_index_0, trace_index_1,
                                acq_index_1
Data variables:
    0             (acq_index_0, trace_index_0) complex128 3kB (0.32+0.25j) .....
    1             (acq_index_1, trace_index_1) complex128 3kB (0.32+0.25j) .....

Single-sideband Complex Integration#

In this acquisition protocol acquired voltage trace gets demodulated and averaged. For each acquisition, a single complex voltage value is returned (\(V_I + i V_Q\)).

This acquisition protocol supports BinMode.APPEND binning mode for single-shot readout and BinMode.AVERAGE binning mode for returning data averaged for several executions of a schedule. In the first case data arrays for each acquisition channel will have two dimensions: repetition and acquisition index. All the dimension names except repetition should be suffixed with the acquisition channel to avoid conflicts while merging the datasets, the repetition dimension must be named "repetition". For example, two acquisition channels of which acquisition channel 0 read out three times and acquisition channel two read out two times, the resulting dataset should have the following structure in BinMode.APPEND:

Hide code cell source 
xr.Dataset(
    {
        0: demodulated_trace.reduce(np.average, "trace_index").expand_dims(
            {"repetition": 5, "acq_index_0": 3}
        ),
        2: demodulated_trace.reduce(np.average, "trace_index").expand_dims(
            {"repetition": 5, "acq_index_2": 2}
        ),
    }
)

<xarray.Dataset> Size: 400B
Dimensions:  (repetition: 5, acq_index_0: 3, acq_index_2: 2)
Dimensions without coordinates: repetition, acq_index_0, acq_index_2
Data variables:
    0        (repetition, acq_index_0) complex128 240B (0.32+0.25j) ... (0.32...
    2        (repetition, acq_index_2) complex128 160B (0.32+0.25j) ... (0.32...

In BinMode.AVERAGE repetition dimension gets reduced and only the acquisition index dimension is left for each channel:

Hide code cell source 
xr.Dataset(
    {
        0: demodulated_trace.reduce(np.average, "trace_index").expand_dims(
            {"acq_index_0": 3}
        ),
        2: demodulated_trace.reduce(np.average, "trace_index").expand_dims(
            {"acq_index_2": 2}
        ),
    }
)

<xarray.Dataset> Size: 80B
Dimensions:  (acq_index_0: 3, acq_index_2: 2)
Dimensions without coordinates: acq_index_0, acq_index_2
Data variables:
    0        (acq_index_0) complex128 48B (0.32+0.25j) (0.32+0.25j) (0.32+0.25j)
    2        (acq_index_2) complex128 32B (0.32+0.25j) (0.32+0.25j)

Thresholded Acquisition#

  • Referred to as "ThresholdedAcquisition".

  • Supported by the Qblox backend.

This acquisition protocol is similar to the SSB complex integration, but in this case, the obtained results are compared against a threshold value to obtain 0 or 1. The purpose of this protocol is to discriminate between qubit states.

For example, when acquiring on a single acquisition channel with BinMode.APPEND and repetitions=12, the corresponding dataset could look like:

Hide code cell source 
thresholded_data = np.array([0,0,1,0,1,0,0,1,1,0,0,1])
xr.Dataset(
    {0: xr.DataArray(thresholded_data.reshape(1,12), dims = ['acq_index_0', 'repetitions'])}
)

<xarray.Dataset> Size: 96B
Dimensions:  (acq_index_0: 1, repetitions: 12)
Dimensions without coordinates: acq_index_0, repetitions
Data variables:
    0        (acq_index_0, repetitions) int64 96B 0 0 1 0 1 0 0 1 1 0 0 1

In using BinMode.AVERAGE, the corresponding dataset could like:

Hide code cell source 
xr.Dataset(
    {0: xr.DataArray(np.mean(thresholded_data, keepdims=1), dims = ['acq_index_0'])}

)

<xarray.Dataset> Size: 8B
Dimensions:  (acq_index_0: 1)
Dimensions without coordinates: acq_index_0
Data variables:
    0        (acq_index_0) float64 8B 0.4167

Numerical Separated Weighted Integration#

  • Referred to as "NumericalSeparatedWeightedIntegration".

  • Supported by the Qblox backend.

Equivalent to SSB complex integration, but instead of a simple average of a demodulated signal, the signal is weighted with two waveforms and then integrated. One waveform for the real part of the signal, and one for the imaginary part. The dataset format is also the same.

Integration weights should normally be calibrated in a separate experiment (see, for example, Magesan et al. [MGCorcolesC15]).

Numerical Separated Weighted#

  • Referred to as "NumericalWeightedIntegration".

  • Supported by the Qblox backend.

Equivalent to Numerical Separated Weighted Integration, but the real part of the output is the sum of the real and imaginary part of the output from the Numerical Separated Weighted Integration protocol. The dataset format is also the same. This is equivalent to multiplying the complex signal with complex waveform weights, and only returning the real part of the result. If the integration weights are calibrated as in Magesan et al. [MGCorcolesC15], i.e. the complex weights are the difference between the two signals we wish to distinguish, then the real part of the complex weighted multiplication contains all the relevant information required to distinguish between the states, and the imaginary part contains only noise.

Integration weights should normally be calibrated in a separate experiment (see, for example, Magesan et al. [MGCorcolesC15]).

Trigger Count#

  • Referred to as "TriggerCount".

  • Supported by the Qblox backend.

This acquisition protocol measures how many times a predefined voltage threshold has been passed. The threshold is set via ttl_acq_threshold (see also Sequencer options).

First, let’s see an example when the bin mode is BinMode.APPEND and the schedule repeats once (repetitions=1). The returned data for the acquisition channel is a list, with as many elements as the number of times the trigger was activated. For each element, the value is 1. In the following example, the threshold was passed 5 times for acquisition channel 0, and therefore acq_index_0 goes from 0 to 4, with values 1.

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trigger_data = [1, 1, 1, 1, 1]
xr.Dataset(
    {0: xr.DataArray([trigger_data],
            dims=["repetition", "acq_index_0"],
            coords={"repetition": [0], "acq_index_0": range(len(trigger_data))},
        )
    }
)

<xarray.Dataset> Size: 88B
Dimensions:      (repetition: 1, acq_index_0: 5)
Coordinates:
  * repetition   (repetition) int64 8B 0
  * acq_index_0  (acq_index_0) int64 40B 0 1 2 3 4
Data variables:
    0            (repetition, acq_index_0) int64 40B 1 1 1 1 1

If there are multiple repetitions of the schedule, the acquisition data is still a list for each channel. The list’s first element is a number that counts how many times the threshold was passed at least once. The second element counts how many times the threshold was passed at least twice, and so on for the other elements. Don’t be confused by the repetition dimension: for trigger count, this dimension has one coordinate, namely 0. See an example below.

Hide code cell source 
trigger_data = [8, 6, 3, 3, 1]
xr.Dataset(
    {0: xr.DataArray([trigger_data],
            dims=["repetition", "acq_index_0"],
            coords={"repetition": [0], "acq_index_0": range(len(trigger_data))},
        )
    }
)

<xarray.Dataset> Size: 88B
Dimensions:      (repetition: 1, acq_index_0: 5)
Coordinates:
  * repetition   (repetition) int64 8B 0
  * acq_index_0  (acq_index_0) int64 40B 0 1 2 3 4
Data variables:
    0            (repetition, acq_index_0) int64 40B 8 6 3 3 1

In BinMode.AVERAGE mode, the data is very similar. Each element in the list shows how many times the threshold was passed in each repetition exactly as many times as it’s shown in the "count" dimension. For example, in the example below, the schedule ran 8 times. From these 8 runs,

  • in 1 run, the trigger was counted 5 times,

  • in 2 runs, the trigger was counted 4 times,

  • in 3 runs, the trigger was counted 2 times,

  • in 2 runs, the trigger was counted once.

Note: 0 counts are removed from the returned data, so there will be no entry for “3 times”.

You can think of the append mode values as the cumulative distribution of the average mode values. See an example below.

Hide code cell source 
trigger_data = [1, 2, 3, 2]
counts = [5, 4, 2, 1]
xr.Dataset(
    {0: xr.DataArray([trigger_data],
            dims=["repetition", "counts"],
            coords={"repetition": [0], "counts": counts},
        )
    }
)

<xarray.Dataset> Size: 72B
Dimensions:     (repetition: 1, counts: 4)
Coordinates:
  * repetition  (repetition) int64 8B 0
  * counts      (counts) int64 32B 5 4 2 1
Data variables:
    0           (repetition, counts) int64 32B 1 2 3 2
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