Measuring detuning of qubit frequency using fast flux-pulses

The following experiments are similar to the Flux tunable qubits but instead of modifying the static bias and measuring the qubit frequency with a spectroscopic measurement the qubit frequency is measured through a Ramsey-like experiment.

After bringing the qubit to a superposition state with a \(R_Y(\pi/2)\), we apply a flux pulse for a fixed time \(\tau\) and we measure \(\langle X \rangle\) and \(\langle Y \rangle\) by rotating the qubit accordingly before the measurement. By repeating the sequence for different flux pulse amplitude values we should observe a detuning described by Eq. (1), the detuning is defined as

\[\Delta f_q(\Phi) = f_q(\Phi=0) - f_q(\Phi)\]

where \(f_q(\Phi=0)\) corresponds to the qubit frequency when no magnetic flux generated by fast-flux pulses is present. In the case where the qubit is biased at the sweetspot \(f_q(\Phi=0) = f_q^{\text{max}}\).

Parameters

class qibocal.protocols.flux_amplitude_frequency.FluxAmplitudeFrequencyParameters(amplitude_min: int, amplitude_max: int, amplitude_step: int, duration: float, crosstalk_qubit: Optional[Union[int, str]] = None, flux_pulse_amplitude: float = 0)

FluxAmplitudeFrequency runcard inputs.

amplitude_min: int

Minimum flux pulse amplitude.

amplitude_max: int

Maximum flux amplitude.

amplitude_step: int

Flux pulse amplitude step.

duration: float

Flux pulse duration.

crosstalk_qubit: Optional[Union[int, str]] = None

If provided a flux pulse will be applied on this qubit.

Enable to compute the crosstalk matrix.

flux_pulse_amplitude: float = 0

Flux pulse amplitude on target qubits to bias from sweetstpot.

It should be provided only if crosstalk is not None.

hardware_average: bool = False

By default hardware average will be performed.

nshots: int

Number of executions on hardware.

relaxation_time: float

Wait time for the qubit to decohere back to the gnd state.

Here is a possible runcard to run the experiment:

- id: flux_amplitude_frequency
  operation: flux_amplitude_frequency
  parameters:
      amplitude_max: 0.3
      amplitude_min: 0
      amplitude_step: 0.005
      duration: 60

After running the protocol the results should be the following

On the left we can see the detuning on the qubit frequency as a function of the flux pulse amplitude (blue) with the corresponding fit (green). Although the correct formula is given by Eq. (1) in this protocol we approximate the dependence using a quadratic form.

On the right we derive the how the magnetic flux changing by applying a flux pulse by inverting Eq. Eq. (1) to compute the flux experienced by the qubit. We are using an approximation where we neglect both the anharmonicity and asymmetry of the junction. We expect a linear dependence which is fitted accordingly.

Flux-crosstalk measurements

Using the same protocol we can select to sweep the amplitude of a flux pulse applied to a neighboring qubit with the option crosstalk_qubit. In this case to measure effectively the crosstalk coefficient it might be necessary to move the target qubit on a flux-sensitive point. This can be done with the parameter flux_pulse_amplitude which will apply a flux pulse on the target qubit with the specified amplitude while sweeping the amplitude of the flux pulse applied to crosstalk_qubit.

Here is a possible runcard.

- id: flux_amplitude_frequency
  operation: flux_amplitude_frequency
  parameters:
      amplitude_max: 0.3
      amplitude_min: 0
      amplitude_step: 0.005
      crosstalk_qubit: B1
      duration: 60
      flux_pulse_amplitude: 0.2

with the corresponding outcome.

Requirements

• Single Shot Experiments