AWG Precompensation for high-fidelity CZ gates in transmon qubits

High quantum gate fidelity is essential for all quantum hardware platforms. Temporal sensitivity to flux noise and flux pulse distortion can pose major limitations to achieving high fidelity with repeatable two-qubit gates in transmon qubits. In recent publication, Rol et al. demonstrated

  • a fast (40 ns),
  • low-leakage (0.1%),
  • high-fidelity (99.1%), and
  • repeatable

conditional phase (CZ) gate (Phys. Rev. Lett. 123, 120502, arXiv:1903.02492). They implemented a bipolar flux pulsing method called Net-Zero (NZ) pulse that helped to suppress the leakage from the computational subspace substantially while reducing the susceptibility to electronic noise on the flux line relative to the unipolar pulse. Arbitrary Waveform Generators (AWG) driving flux pulses with a low noise spectral density from 1 kHz up to 100 MHz are needed for high-fidelity gate operation.

Fig. 1 shows the 1/f noise of the Zurich Instruments HDAWG from 100 Hz to 100 kHz. It has a significantly better performance compared to competing instruments such as Tektronix’s AWG5200. Moreover, the HDAWG has a very low noise floor (≤ -145 dBm/Hz @ >1 MHz), as discussed in more detail here.

Figure 1. HDAWG noise amplitude spectral density at 5 V range (Amp path) and 0.8 V range (Dir path). Please note that this measurement was performed with the MFLI (1 mV Range) and into a 50 Ohm Input.

 

Compensating distortion

High-fidelity gate operations and minimal leakage are guaranteed only if accurate signals are delivered to the physical qubit . Short-timescale distortions of flux pulses are a dominating leakage factor, as pointed out by Rol et al. In almost all experimental scenarios, the transfer function between the AWG output and the qubit deviates significantly from a perfect transmission line. Luckily, there exist methods to measure and characterize the transfer function. By conjugating this transfer function, it is then possible to correct the distortion on the desired waveform patterns before they are uploaded to the AWG.

 

Why is it important to be able to compensate setup imperfections in real time?

When the exact pulse trains are determined only after operation has started, for instance, because the waveforms must be adapted based on feedback-uploading compensated waveform patterns would require anticipating all possible options. That will quickly lead to a huge overhead, imposing severe limitations due to memory constraints. The implementation of an right at the AWG output that compensate for setup imperfections in real time avoids pre-adjustments on every waveform and allows for a more economic use of the finite memory.

 

How well does real-time precompensation work?

In the CZ gate measurement, Rol et al. showed significant reduction of phase s using unipolar pulses with real-time precompensation. They also achieved distortion compensation with an accuracy of ±0.1 %, which improves leakage by a factor of 4 relative to operation without compensation.

 

What are the available filters and what effects can they compensate?

The Zurich Instrument HDAWG-PC Real-Time Precompensation option, displayed on the user interface shown in Fig. 2, offers a range of filter tuning capabilities summarised in Table 1.

 

Figure 2. LabOne user interface: Precompensation tab.

 

Table 1 Filters chain specification of HDAWG-PC Real-Time Precompensation option.

 

Conclusion

The Zurich Instruments HDAWG, with its Real-Time Precompensation option and its excellent noise performance, is the right choice to drive fast and high-fidelity NZ gates in transmon qubits.