StarkRamseyXYAmpScan¶

class StarkRamseyXYAmpScan(physical_qubits, backend=None, **experiment_options)[source]¶

A fast characterization of Stark frequency shift by varying Stark tone amplitude.

Overview

This experiment scans Stark tone amplitude at a fixed tone duration. The experimental circuits are identical to the StarkRamseyXY experiment except that the Stark pulse amplitude is the scanned parameter rather than the pulse width.

(Ramsey X)  The pulse before measurement rotates by pi-half around the X axis

         ┌────┐┌───────────────────┐┌───┐┌───────────────────┐┌────────┐┌────┐┌─┐
      q: ┤ √X ├┤ StarkV(stark_amp) ├┤ X ├┤ StarkU(stark_amp) ├┤ Rz(-π) ├┤ √X ├┤M├
         └────┘└───────────────────┘└───┘└───────────────────┘└────────┘└────┘└╥┘
    c: 1/══════════════════════════════════════════════════════════════════════╩═
                                                                               0

(Ramsey Y) The pulse before measurement rotates by pi-half around the Y axis

         ┌────┐┌───────────────────┐┌───┐┌───────────────────┐┌───────────┐┌────┐┌─┐
      q: ┤ √X ├┤ StarkV(stark_amp) ├┤ X ├┤ StarkU(stark_amp) ├┤ Rz(-3π/2) ├┤ √X ├┤M├
         └────┘└───────────────────┘└───┘└───────────────────┘└───────────┘└────┘└╥┘
    c: 1/═════════════════════════════════════════════════════════════════════════╩═
                                                                                  0

The AC Stark effect can be used to shift the frequency of a qubit with a microwave drive. To calibrate a specific frequency shift, the StarkRamseyXY experiment can be run to scan the Stark pulse duration at every amplitude, but such a two dimensional scan of the tone duration and amplitude may require many circuit executions. To avoid this overhead, the StarkRamseyXYAmpScan experiment fixes the tone duration and scans only amplitude.

Recall that an observed Ramsey oscillation in each quadrature may be represented by

\[\begin{split}{\cal E}_X(\Omega, t_S) = A e^{-t_S/\tau} \cos \left( 2\pi f_S(\Omega) t_S \right), \\ {\cal E}_Y(\Omega, t_S) = A e^{-t_S/\tau} \sin \left( 2\pi f_S(\Omega) t_S \right),\end{split}\]

where \(f_S(\Omega)\) denotes the amount of Stark shift at a constant tone amplitude \(\Omega\), and \(t_S\) is the duration of the applied tone. For a fixed tone duration, one can still observe the Ramsey oscillation by scanning the tone amplitude. However, since \(f_S\) is usually a higher order polynomial of \(\Omega\), one must manage to fit the y-data for trigonometric functions with phase which non-linearly changes with the x-data. The StarkRamseyXYAmpScan experiment thus drastically reduces the number of circuits to run in return for greater complexity in the fitting model.

User manual

AC Stark Effect

Analysis class reference

qiskit_experiments.library.driven_freq_tuning.StarkRamseyXYAmpScanAnalysis

Experiment options

These options can be set by the set_experiment_options() method.

Options

Defined in the class StarkRamseyXYAmpScan:
- stark_channel (PulseChannel)
  
  Default value: None
  
  Pulse channel on which to apply Stark tones. If not provided, the same channel with the qubit drive is used. See Stark tone channel for details.
- stark_freq_offset (float)
  
  Default value: 80000000.0
  
  Offset of Stark tone frequency from the qubit frequency. This offset should be sufficiently large so that the Stark pulse does not Rabi drive the qubit. See Stark tone frequency for details.
- stark_sigma (float)
  
  Default value: 1.5e-08
  
  Gaussian sigma of the rising and falling edges of the Stark tone, in seconds.
- stark_risefall (float)
  
  Default value: 2
  
  Ratio of sigma to the duration of the rising and falling edges of the Stark tone.
- stark_length (float)
  
  Default value: 5e-08
  
  Time to accumulate Stark shifted phase in seconds.
- min_stark_amp (float)
  
  Default value: -1.0
  
  Minimum Stark tone amplitude.
- max_stark_amp (float)
  
  Default value: 1.0
  
  Maximum Stark tone amplitude.
- num_stark_amps (int)
  
  Default value: 101
  
  Number of Stark tone amplitudes to scan.
- stark_amps (list[float])
  
  Default value: None
  
  The list of amplitude that will be scanned in the experiment. If not set, then num_stark_amps evenly spaced amplitudes between min_stark_amp and max_stark_amp are used. If stark_amps is set, these parameters are ignored.
Defined in the class BaseExperiment:
- max_circuits (Optional[int])
  
  Default value: None
  
  The maximum number of circuits per job when running an experiment on a backend.