# Quantum Analyzer Setup Tab

The Quantum Analyzer Setup is the main control panel for the qubit measurement unit on the Instrument (see Functional Overview for an overview block diagram). It is available on all SHFQA Instruments.

## Features

• 2 Application modes

• Readout up to 16 qubits

• Up to 16 customized integration weights

• Qubit state discrimination

• Graphic representation of data processing

## Description

Table 1. App icon and short description
Control/Tool Option/Range Description

QA Setup

Configure the Qubit Measurement Unit

The Quantum Analyzer Setup tab is divided into 2 sub-tab groups for resonator spectroscopy (see Figure 1) and qubit readout (see Figure 2) application. By selecting Application Mode, Spectroscopy or Readout, the corresponding sub-tabs provide all configuration of readout pulse generation and acquired data processing (see Table 2).

Figure 1. LabOne GUI: QA Setup Tab - Spectroscopy Mode
Figure 2. LabOne GUI: QA Setup Tab - Readout Mode
Figure 3. LabOne GUI: Readout Pulse Generator Tab - Waveform Viewer

### Spectroscopy Mode

The SHFQA has 1 Digital Oscillator per channel. In Spectroscopy mode, the Digital Oscillator is used for readout waveform generation and integration. There are 2 operation modes for readout waveform generation, Continuous and Pulse.

In Continuous mode, the output signal on the front panel is a continuous wave. The frequency of the output signal is configured by the center frequency of the frequency up-conversion chain and the offset frequency of the Digital Oscillator. The amplitude of the output signal is configured by the output range of the frequency up-conversion chain and the amplitude gain of the Digital Oscillator. The SHFQA Sweeper class (API) is the central controller in the Spectroscopy mode. The simplified measurement flow in Continuous mode is shown in Figure 4 (see tutorial Continuous Resonator Spectroscopy).

• Configure parameters for frequency sweep and integration

• Sweeper sets the start frequency to the Digital oscillator

• Sweeper waits for a trigger signal from a Hardware Trigger Engine to start integration

• after the integration is finished the Sweeper set a new frequency and continue the measurement

The complex signal generated by the Digital Oscillator is

\tag{1} \begin{aligned} E_{\mathrm{IF},\ n} & = g_{\mathrm{osc}}e^{i2\pi f_{\mathrm{IF}}t_n},\\ \end{aligned}

where $$g_{\mathrm{osc}}\ (0\le g_{\mathrm{osc}}\le1)$$ is the amplitude gain of the Digital Oscillator, $$f_{\mathrm{IF}}$$ is the frequency of the oscillator. The signal is then filtered and up-converted by a 2 GHz digital oscillator on the signal output path, and reaches the Digital To Analog Converter (DAC) as $$g_{\mathrm{osc}}e^{i 2\pi (f_{\mathrm{IF}}+f_{\mathrm{2\ GHz}})t_n}$$. After the ADC and analog frequency up-conversion, the output signal on the front panel is

\tag{2} \begin{aligned} E_{\mathrm{out}} & = g_{\mathrm{osc}}C\cos(2\pi f_{\mathrm{RF}}t + \phi),\\ \end{aligned}

where $$C = 10^{\frac{P_{\mathrm{range,\ out}}-10}{20}}$$ is a factor converting the power range of the output signal in units of dBm to the amplitude in units of V, $$f_{\mathrm{RF}} = f_0 + f_{\mathrm{IF}}$$, $$f_0$$ is the center frequency. The output power calculation is detailed in Inputs/Outputs Tab.

The frequency down-conversion and integration data processing of the input signal in both Spectroscopy and Readout mode is detailed in Quantum Analyzer Result Tab.

Figure 4. Instrument connectivity in Spectroscopy mode

In Pulse mode, the output signal on the front panel is pulsed. The readout pulse is generated by an uploaded waveform envelope modulated by the Digital Modulator. In this mode the readout amplitude is also controlled by the amplitude of the waveform envelope. The simplified measurement flow in Pulse mode is the following (see Figure 4 and tutorial Pulsed Resonator Spectroscopy).

• Configure Sweeper parameters for frequency sweep and integration

• Sweeper sets the start frequency to the Digital oscillator

• Sweeper waits for a trigger signal from the Hardware Trigger Engine to playback a readout pulse and start integration

• After the integration is finished the Sweeper set a new frequency and continue the measurement.

Please note that there is a delay between the starting time of pulse generation and integration due to the Instrument’s internal delay and the physical system’s external delay. The delay can be measured and compensated by setting the integration delay.

The results after integration in both Continuous and Pulse mode are saved in the result logger, and the power and phase can be calculated and plotted with the Sweeper.

#### Output Signal

The complex signal generated by the Digital Oscillator and the Envelope is

\tag{3} \begin{aligned} E_{\mathrm{IF},\ n} & = g_{\mathrm{osc}}A_ne^{i2\pi f_{\mathrm{IF}}t_n},\\ \end{aligned}

where $$A_n$$ is the complex envelope and $$|A_n|\le 1$$. The output signal on the front panel is

\tag{4} \begin{aligned} E_{\mathrm{RF}} & = g_{\mathrm{osc}}C(A_{\ \mathrm{real}}(t)\cos(2\pi f_{\mathrm{RF}}t) - A_{\ \mathrm{imag}}(t)\sin(2\pi f_{\mathrm{RF}}t)),\\ \end{aligned}

where $$A_{\ \mathrm{real}}(t)$$ ($$A_{\ \mathrm{imag}}(t)$$) is the real (imaginary) part of the envelope.

The SHFQA has 8 or 16 readout waveform memory slots, and 8 or 16 integration weights memory slots per channel. In readout mode, these memory slots are used for readout pulse generation and weighted integration. The SHFQA Readout Pulse Generator is the central controller in Readout mode. The simplified measurement flow is shown in Figure 5 (see tutorial Multiplexed Qubit Readout).

• Configure integration parameters

• Upload and compile a measurement sequence in a sequencer of the SHFQA Readout Pulse Generator

• Configure a digital trigger if a trigger is desired to run the sequence

• Run the measurement sequence

The last 3 steps are configured in the SHFQA Readout Pulse Generator Tab. Please note that overflow of output (OVO) could happen if the amplitude setting or the overshoot of the readout waveform exceeds 1. The readout pulse playback and weighted integration are both started with startQA command, and the measurement results are saved in the SHFQA result logger and displayed in the Quantum Analyzer Result Tab. If Integration is selected as the result source, the returned data is complex data with I as real part and Q as imaginary part. If Thresholding is selected, the real part of the complex data will be compared with a threshold on the Thresholding sub-tab, and the result will be either 0 or 1.

#### Output Signal

The complex data uploaded from a CSV file or APIs, or parametrically generated by using LabOne UI saved in a single waveform memory slot is

\tag{5} \begin{aligned} E_{\mathrm{IF},\ n} & = A_ne^{i(2\pi f_{\mathrm{IF}}t_n + \phi)}\\ & = (A_n\cos{(\phi)} + i A_n\sin{(\phi)})e^{i2\pi f_{\mathrm{IF}}t_n}\\ & = (A_{n,\ \mathrm{real}} + i A_{n,\ \mathrm{imag}})e^{i2\pi f_{\mathrm{IF}}t_n},\\ \end{aligned}

where $$A_n \le 1$$ ($$n$$ means the n-th sample) is the amplitude, $$f_{\mathrm{IF}}$$ is the offset frequency, $$\phi$$ is the phase. In case of parametric waveform generation, $$A_n$$ is constant. Please note that the maximum amplitude of sum of all waveforms in use should not exceed 1. The output signal on the front panel is

\tag{6} \begin{aligned} E_{\mathrm{RF}} & = C(A_{\ \mathrm{real}}(t)\cos(2\pi f_{\mathrm{RF}}t) - A_{\ \mathrm{imag}}(t)\sin(2\pi f_{\mathrm{RF}}t)),\\ \end{aligned}

where $$C$$ is a conversion factor depending on selected output power range. For multi-qubit readout in the same readout line, the output signal is

\tag{7} \begin{aligned} E_{\mathrm{RF}} & = C\sum_{i}(A_{i,\ \mathrm{real}}(t)\cos(2\pi f_{i,\ \mathrm{RF}}t) - A_{i,\ \mathrm{imag}}(t)\sin(2\pi f_{i,\mathrm{\ RF}}t)),\\ \end{aligned}

where $$i$$ indicates i-th waveform memory slot.

#### Integration weights

The complex integration weight can be uploaded from a CSV file or APIs, or parametrically generated by using LabOne GUI and saved into a single integration weight memory slot as

\tag{8} \begin{aligned} E_{\mathrm{weight},\ n} & = A_{\mathrm{weight},\ n}e^{i(2\pi f_{\mathrm{weight}}t_n + \phi_{\mathrm{weight}})}\\ & = (A_{\mathrm{weight},\ n}\cos{(\phi_{\mathrm{weight}})} + i A_{\mathrm{weight},\ n}\sin{(\phi_{\mathrm{weight}})})e^{i2\pi f_{\mathrm{weight}}t_n}\\ & = (A_{\mathrm{weight,\ real},\ n} + i A_{\mathrm{weight,\ imag},\ n})e^{i2\pi f_{\mathrm{weight}}t_n},\\ \end{aligned}

where $$A_{\mathrm{weight},\ n} \le 1$$ is the amplitude of the integration weight, $$f_{\mathrm{weight}}$$ is the frequency of the integration weight, $$\phi_{\mathrm{weight}}$$ is the phase of the integration weight. The integration result is then calculated by multiplying the frequency down-converted complex input signal by the conjugate of the integration weight.

 In order to achieve the highest possible resolution in the signal after integration, it’s advised to scale the dimensionless readout integration weights with a factor so that their maximum absolute value is equal to 1.
Figure 5. Instrument connectivity in Qubit Readout mode

## Functional Elements

Table 2. QA setup settings
Control/Tool Option/Range Description

Application Mode

Spectroscopy

Using internal digital oscillator for waveform generation and integration.

Using uploaded waveform for output signal generation and customized weights for integration.

Errors

Number

Number of hold-off errors detected since last reset.

Spectroscopy

Trigger Signal

Selects the source of the trigger for the integration and envelope in Spectroscopy mode.

Integration Length

$$2^2$$ to $$2^{25}$$

Sets the integration length in Spectroscopy mode in number of samples. Up to 33.5 MSa (2^25 samples, with granularity of 4 Samples ) can be recorded, which corresponds to 16.7 ms.

Integration Delay

-4 ns to 131.1 μs

Sets the delay of the integration in Spectroscopy mode with respect to the trigger signal. The resolution is 2 ns.

Operation Mode

Continuous

The output of the internal digital oscillator is used directly for frequency up-conversion.

Pulse

The waveform envelope is modulated by the internal digital oscillator before frequency up-conversion.

Length

4 to 32 k (SHFQA 2 without 16W option) or 64 k

Indicate the length of uploaded envelope waveform in units of Samples. The granularity is 4 Samples.

Delay

0 ns to 131.1 μs

Set a delay between readout pulse playback trigger and the first sample of the readout pulse (in Pulsed mode). The resolution is 2 ns.

CSV file

Drop CSV file to upload the envelope waveform.

Center Frequency

1 - 8 GHz

Display center frequency in Spectroscopy mode.

Offset Frequency

- 1 to +1 GHz

Set offset frequency to the internal digital oscillator in Spectroscopy mode.

Output Frequency

0.5 to 8.5 GHz

Display frequency of the output signal in Spectroscopy mode.

Amplitude

0 to 1

Set gain of the internal digital oscillator in Spectroscopy mode. The recommended range is from 0.01 to 1 in pulsed mode.

Integration Length

4 to 4096

Sets the length of all Integration Weights in number of samples. A maximum of 4096 samples can be integrated, which corresponds to 2.05 us. The granularity is 4 Samples.

Integration Delay

0 ns to 131.1 μs

Sets a common delay for the start of the readout integration for all Integration Weights with respect to the time when the trigger is received. The resolution is 2 ns.

Sequencer Run/Stop

Run or Stop

Enables the Sequencer.

Waveforms Clear

Empty all readout Waveform Memory slots or Integration weight Units.

Waveform Generation

Select the way to generate waveform.

Parametric Amplitude

0 to 1

Set amplitude factor for parametric readout pulse and integration weight generation.

Parametric Frequency

-1 to +1 GHz

Set offset frequency for parametric readout pulse or integration weight generation.

Parametric Phase

-180 to 180 degree

Set phase for parametric readout pulse and integration weight generation.

Parametric Window Type

Rectangular

Display window function to be applied in complex exponential function for parametric readout pulse and integration weight generation.

Parametric Window Length

4 to 4096

Length of the selected window in samples for parametric readout pulse and integration weight generation.

Parametric Set To Device

Yes or No

Set parametrically generated readout pulse and integration weight to waveform memory slot and integration memory slot, respectively.

Thresholding

-14.51 kV to 14.51 kV

Set threshold for quantum state discrimination. Note that the data before thresholding is not normalized by the integration length.