EchoedCrossResonanceHamiltonian¶

class EchoedCrossResonanceHamiltonian(physical_qubits, backend=None, cr_gate=None, durations=None, **kwargs)[source]¶

Echoed cross resonance Hamiltonian tomography experiment.

Overview

This is a variant of CrossResonanceHamiltonian for which the experiment framework is identical but the cross resonance operation is realized as an echoed sequence to remove unwanted single qubit rotations. The cross resonance circuit looks like:

     ┌────────────────────┐  ┌───┐  ┌────────────────────┐
q_0: ┤0                   ├──┤ X ├──┤0                   ├──────────
     │  cr_tone(duration) │┌─┴───┴─┐│  cr_tone(duration) │┌────────┐
q_1: ┤1                   ├┤ Rz(π) ├┤1                   ├┤ Rz(-π) ├
     └────────────────────┘└───────┘└────────────────────┘└────────┘

Here two cr_tone are applied, where the latter one is with the control qubit state flipped and with a phase flip of the target qubit frame. This operation is equivalent to applying the cr_tone with a negative amplitude. The Hamiltonian for this decomposition has no IX and ZI interactions, and also a reduced IY interaction to some extent (not completely eliminated) [1]. Note that the CR Hamiltonian tomography experiment cannot detect the ZI term. However, it is sensitive to the IX and IY terms.

References

[1] Neereja Sundaresan, Isaac Lauer, Emily Pritchett, Easwar Magesan, Petar Jurcevic, Jay M. Gambetta, Reducing unitary and spectator errors in cross resonance with optimized rotary echoes, PRX Quantum 1, 020318 (2020), doi: 10.1103/PRXQuantum.1.020318 (open)

Analysis class reference

CrossResonanceHamiltonianAnalysis

Experiment options

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

Options

Defined in the class CrossResonanceHamiltonian:
- durations (np.ndarray)
  
  Default value: None
  
  The total duration of the cross resonance pulse(s) to scan, in units of sec. Values should be longer than pulse ramps.
- min_durations (int)
  
  Default value: 6e-08
  
  The minimum default pulse duration in samples.
- max_durations (int)
  
  Default value: 1.2e-06
  
  The maximum default pulse duration in samples.
- num_durations (int)
  
  Default value: 48
  
  The number of measured durations. The experiment automatically creates durations of linear increment along with min_durations and max_durations when user doesn’t explicitly provide durations.
- amp (complex)
  
  Default value: 0.5
  
  Amplitude of the cross resonance tone.
- amp_t (complex)
  
  Default value: 0.0
  
  Amplitude of the cancellation or rotary drive on target qubit.
- sigma (float)
  
  Default value: 64
  
  Sigma of Gaussian rise and fall edges, in units of dt.
- risefall (float)
  
  Default value: 2
  
  Ratio of edge durations to sigma.
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.