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

Spectroscopy mode and readout mode

Continuous or pulsed resonator spectroscopy

Power spectral density

Weighted integration

Readout up to 16 qubits per channel

2state and multistate discrimination
Description
Control/Tool  Option/Range  Description 

QA Setup 
Configure the Qubit Measurement Unit 
The Quantum Analyzer Setup tab is divided into 2 subtab groups for resonator spectroscopy (see Figure 1) and qubit readout (see Figure 2) application. By selecting Application Mode, Spectroscopy or Readout, the corresponding subtabs provide all configurations of readout pulse generation and acquired data processing (see Table 5). The main differences of the Application Modes are listed in Table 2.
Parameters  Spectroscopy mode  Readout mode 

Waveform generation 
Digital oscillator and envelope 
Sample by Sample 
Waveform output mode 
Continuous or pulsed 
Pulsed 
Waveform length 
Continuous 
Up to 2 μs 
Number of qubits per channel 
1 
Up to 8 or 16 
Integration length 
Up to 16.7 ms 
Up to 2 μs 
Integration weight unit per channel 
Not applicable 
Up to 8 or 16 
Realtime state discrimination 
Not applicable 
Yes 
Multistate discrimination 
Not applicable 
Qubits, qutrits and ququads 
Spectroscopy Mode
Spectroscopy mode is mainly used for resonator spectroscopy and power spectral density measurement. The SHFQA has 1 Digital Oscillator per channel. In Spectroscopy mode, the Digital Oscillator is used for readout waveform generation and integration. The SHFQA Sweeper class (API) is the central controller for the Spectroscopy mode, see tutorial Continuous Resonator Spectroscopy and Pulsed Resonator Spectroscopy.
There are 2 operation modes for readout waveform generation, Continuous and Pulsed. In Continuous mode, signal from the Digital Oscillator is routed to the digital IQ mixing stage (see Functional Overview) for readout waveform generation in the output path, and to multiply the input signal for readout waveform integration in the input path, see Figure 4. In Pulsed mode, signal from the Digital Oscillator modulates the envelope from the Waveform Memory and then is routed to the output and input paths same as in Continuous mode. The pulse envelope can be displayed on the Waveform Viewer subtab of the Readout Pulse Generator tab. The main differences of the 2 operation modes are listed in Table 3.
Parameters  Continuous mode  Pulsed mode 

Readout pulse length 
Continuous wave 
Up to 16 μs or 32 μs 
Envelope delay 
Not applicable 
Up to 131.1 μs 
Readout pules amplitude 
Controlled by output range and gain factor of the Digital Oscillator 
Controlled by output range, gain factor of the Digital Oscillator and the envelope 
Readout Waveform Output In Spectroscopy Mode
The readout waveform on the Instrument output can be expressed as
where \(C_{P\rightarrow A} = 10^{\frac{P_{\mathrm{range,\ output}}10}{20}}\) is the conversion factor converting the power range \(P_{\mathrm{range,\ output}}\) of the output signal in units of dBm to the amplitude in units of V, , \(A(t)\) is the complex readout envelope in Pulsed mode and \(A(t) = 1\) in Continuous mode, \(g_{\mathrm{osc}}\) is the amplitude gain factor of the Digital Oscillator, \(f_0\) is the center frequency set in the Input/Output tab, \(f_{\mathrm{osc}}\) is the offset frequency set by the Digital Oscillator, \(\phi_{\mathrm{output}}\) is the global phase can be reset by resetting the phase of the Digital Oscillator.
The readout waveform envelope \(A(t)\) in Pulsed mode can be displayed on the Waveform Viewer, see Figure 3.
Readout Results In Spectroscopy Mode
The readout input signal after analog frequency downconversion before the ADC is
where \(A_{\mathrm{input}}(t)\) is the amplitude of input signal on the front panel of the instrument, \(f_{\mathrm{before\ ADC}}\) is the frequency of the input signal before ADC, \(\phi_{\mathrm{input}}\) is the global phase of the input signal on the front panel of the instrument. After the ADC, it becomes
where \(C_{\mathrm{scaling}}\) is the conversion factor depending on gain factor, ADC range and bit resolution, \(f_{\mathrm{after\ ADC}}\) is the frequency after the ADC, \(i\) means the \(i\)th sample. The signal \(E_{i,\ \mathrm{after\ ADC}}\) is then downconverted by a digital oscillator at 1 GHz and filtered the high frequency components, as
where \(f_{\mathrm{input,\ LO2}}\) is the frequency of the digital oscillator, \(f_{\mathrm{baseband}} = f_{\mathrm{after\ ADC}}f_{\mathrm{input,\ LO2}} = f_{\mathrm{osc}}\) is the differential frequency, \(f_{\mathrm{sum}} = f_{\mathrm{before\ ADC}}+f_{\mathrm{input,\ LO2}}\) is the sum frequency. The signal at \(f_{\mathrm{sum}}\) is filtered out by the digital filter. By multiplying a factor of \(\sqrt{2}/C_{\mathrm{scaling}}\) the units of the signal is converted to Vrms, and it can be monitored by the SHFQA Scope in a loopback configuration. After the filter the signal is then integrated with the signal from the Digital Oscillator \(e^{i2\pi f_{\mathrm{osc}} t}\) and normalized by the number of integration samples \(N\),
If \(A_{i,\ \mathrm{input}} = A_{\mathrm{input}}\) is constant, then
By multiply the factor of \(\sqrt{2}/C_{\mathrm{scaling}}\), the units of the results is converted to Vrms, and then can be downloaded from the instrument via the Instrument node /DEV…/QACHANNELS/n/SPECTROSCOPY/RESULT/DATA/WAVE, see Device Node Tree. The power of input signal can then be derived as
The power and phase of the input signal can also be calculated and plotted using the Sweeper class.
Power spectral density
Power Spectral Density (PSD) measurements are generally required to characterize an amplification chain. In Spectroscopy mode, a PSD measurement can be performed using the SHFQA Sweeper, see GitHub zhinsttoolkit example or zhinsttoolkit Online Documentation, or using instrument nodes, see Device Node Tree.
Here, the PSD is calculated on the hardware as \(S_{xx}(f) = \lim_{N\to\infty} \frac{(\Delta t)^2}{T}\sum_{n = N}^{n = N} x_ne^{i2\pi f_n\Delta t}^2\) (see Spectral density Wikipedia), where \(\Delta t = 1/f_\mathrm{s}\) is the time step, \(f_\mathrm{s}\) is the sampling rate, \(T = (2N+1)\Delta t\) is the integration length in seconds, \(2N+1\) is the integration length in samples, \(x_ne^{i2\pi f_n\Delta t}\) is the \(n\)th complex data of the input signal. This calculation is done by the Instrument, and it returns the realvalued PSD in units of \(\mathrm{Vrms}^2/\mathrm{Hz}\). The applicable ranges of the PSD measurement are listed in Table 4.
Note that the measurement bandwidth is determined by the inverse of integration time, and the frequency step should be less than or equal to the measurement bandwidth. Typically, the PSD measurement requires many averages to be accurate. Setting the number of averages to a number larger than or equal to 1000 is recommended.
Parameters  Values 

LabOne version 
≥ 23.02 
Number of channels 
2 or 4 for SHFQA; 
Input frequency range 
0.5  8.5 GHz 
Input power 
up to +10 dBm 
Input waveform length 
continuous or pulsed (> 2 ns) 
Measurement bandwidth (1 / integration time) 
60 Hz to 500 MHz (16.7 ms to 2 ns) 
Number of averages 
1 to 131k 
Input voltage noise density 
see Specifications 
Input spurious free dynamic range (excluding harmonics) 
see Specifications 
Readout Mode
Readout mode is mainly used for multi qubit readout. The SHFQA has 8 or 16 readout Waveform Memory slots, and 8 or 16 integration weight units 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, see Figure 5 and tutorial Multiplexed Qubit Readout.
There are 2 state discrimination modes, 2state discrimination (default, see tutorial Multiplexed Qubit Readout and multistate discrimination (see tutorial Multistate discrimination). Both modes are based on the linear Support Vector Machine and one versus one classification. Note that multistate discrimination can only be configured via LabOne APIs.
Readout Waveform Generation In Readout Mode
The readout waveform can be generated parametrically by LabOne GUI and APIs, and then uploaded and saved in the Waveform Memory. All readout waveforms saved in the Waveform Memory can be erased by clicking Clear on LabOne GUI or using LabOne APIs. Each readout waveform can be used for a single qudit readout, and up to 8 or 16 qubits can be readout simultaneously using a sum of the readout waveforms saved in the Waveform Memory. The Readout Waveform Generator controls which and how readout waveforms are played, see the Readout Pulse Generator Tab.
The readout waveform saved in the \(j\)th Waveform Memory slot is complex data, can be expressed as
where \(A_{i,\ j,\ \mathrm{readout}}\ (0\le A_{i,\ j,\ \mathrm{readout}}\le 1)\) is the amplitude factor of the readout waveform at the \(i\)th sample, \(f_{j,\ \mathrm{offset}}\) is the offset frequency, \(\phi_{j,\ \mathrm{readout}}\) is the global phase. The output signal on the front panel is
where the sum depends on number of qudits readout in parallel. Note that the maximum amplitude factor of the sum of all waveforms in use should not exceed 1.
Integration Weights
The integration weights can be parametrically generated or measured with the SHFQA Scope for the best SNR (see tutorial Integration Weights Measurement), and uploaded to the integration weight units. All integration weights saved in the memory can be erased by clicking Clear on LabOne GUI Integration Weights subtab or using LabOne APIs. The length of the integration weight is automatically extended to 4096 Samples once it’s uploaded, and integration length is used to configure how long it integrates. The Readout Waveform Generator controls which and how integration weights are used, see Readout Pulse Generator Tab.
The integration weights saved in the \(k\)th integration weight unit is complex data, can be expressed as
where \(A_{i,\ k,\ \mathrm{weight}}\ (0\le A_{i,\ k,\ \mathrm{weight}}\le 1)\) is the amplitude factor of the integration weight at \(i\)th sample, \(f_{k,\ \mathrm{weight}}\) is the frequency of the integration weight, \(\phi_{k,\ \mathrm{weight}}\) is the global phase of the integration weight.
In 2state discrimination mode, 1 qubit requires 1 integration weight, i.e. the conjugated difference of readout input signal while qubit is prepared in state 0> and 1>, see Figure 6. In multistate discrimination mode, 1 qudit with \(n\) states requires \(n(n1)/2\) integration weighs (one vs one classification), i.e. the conjugated differences of any 2 readout input signal while qudit is prepared in state \(i\)> and \(j\)>, where \(i\ (0\le i\le n2)\) and \(j\ (1\le j\le n1)\) are integer and \(i\neq j\). Only \(n1\) integration weights need to be uploaded, and the integration results from the rest of integration weights are calculated by the Instrument automatically, see Figure 7 and Figure 8.
All integration weights saved in the integration weight units can be displayed on the Waveform Viewer, see Figure 3.
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. 
Thresholding
Thresholding subtab is used to configure thresholds for state discrimination in 2state discrimination mode. In multistate discrimination mode, thresholds and assignment matrix are configured by LabOne APIs.
The readout input signal in Readout mode may include different frequencies for multiplexed readout, as
where \(j\) is the \(j\)th component of the readout input signal. By multiplying a conversion factor \(\sqrt{2}/C_{\mathrm{scaling}}\), the units of the signal is converted to Vrms, then the signal can be downloaded and monitored by the Scope. This signal is then integrated with different integration weights \(A_{j,\ \mathrm{weight}}(t)e^{i2\pi f_{j,\ \mathrm{baseband}}ti\phi_{j,\ \mathrm{weight}}}\) simultaneously. The integration result after 1 weighted integration unit is
where \(A_{i, j,\ \mathrm{weight}}\) is the amplitude of the integration weight, \(\phi_{j,\ \mathrm{weight}}\) is the phase of the integration weight. The result after integration is complex data, and can be downloaded and displayed on the Quantum Analyzer Result Tab after multiplying the conversion factor of \(\sqrt{2}/C_{\mathrm{scaling}}\). For the best SNR, the integration weight is configured such that \(\phi_{j,\ \mathrm{input}}=\phi_{j,\ \mathrm{weight}}\), therefore the imaginary part of the result is 0, as
In 2state discrimination mode, all integration weights can be uploaded via LabOne GUI and APIs, and all integration results saved in the result logger can be displayed on the Quantum Analyzer Result Tab if integration is selected as result source. In multistate discrimination mode, all integration weights can only be uploaded via LabOne APIs, and only \(n1\) integration results are saved in the result logger if integration is selected as result source, the rest are calculated automatically in the pairwise difference units.
Before state discrimination, thresholds for each qudit have to be estimated and uploaded to the Instrument, see tutorial Multistate discrimination). During thresholding, the real part of the result after integration is compared with a threshold, and it returns 0 or 1. Qubit state discrimination can be done in both 2state and multistate discrimination modes. The readout result of qubit after thresholding is
where \(T_j\) is the threshold of the \(j\)th qubit, see Figure 6. The result after thresholding can represent qubit state directly.
For a qutrit, 3 thresholds are used, 2 for the integration results in the weighted integration units and 1 for the integration result in the pairwise difference units, see Figure 7. After thresholding, the 3bit data is assigned to 0, 1 or 2 by the assignment matrix, and the discriminated results can be displayed in the Quantum Analyzer Result Tab. The discriminated result represented by 2bit data can be transferred to control instruments via DIO and ZSync for feedback experiment.
For a ququad, 6 thresholds are used, 3 for the integration results in the weighted integration units and 3 for the integration results in the pairwise difference units, see Figure 8. After thresholding, the 6bit data is assigned to 0, 1, 2 or 3 by the assignment matrix, and the discriminated results can be displayed in the Quantum Analyzer Result Tab. The discriminated result represented by 2bit data can be transferred to control instruments via DIO and ZSync for feedback experiment.
Functional Elements
Control/Tool  Option/Range  Description 

Application Mode 
Spectroscopy 
Using internal digital oscillator for waveform generation and integration. 
Readout 
Using uploaded waveform for output signal generation and customized weights for integration. 

Errors 
Number 
Number of holdoff 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 upconversion. 
Pulse 
The waveform envelope is modulated by the internal digital oscillator before frequency upconversion. 

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. 
File Upload 
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. 
Readout 

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 μs. 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 
Parametric or Upload 
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. 