Note

This is the documentation for the current state of the development branch of Qiskit Experiments. The documentation or APIs here can change prior to being released.

CrossResonanceHamiltonian

class CrossResonanceHamiltonian(physical_qubits, flat_top_widths=None, backend=None, cr_gate=None, durations=None, **kwargs)

Cross resonance Hamiltonian tomography experiment.

Overview

This experiment assumes the two qubit Hamiltonian in the form

$$H=\frac{I\otimes A}{2}+\frac{Z\otimes B}{2}$$

where $A$ and $B$ are linear combinations of the Pauli operators $\in X,Y,Z$. The coefficient of each Pauli term in the Hamiltonian can be estimated with this experiment.

This experiment is performed by stretching the pulse duration of a cross resonance pulse and measuring the target qubit by projecting onto the x, y, and z bases. The control qubit state dependent (controlled-) Rabi oscillation on the target qubit is observed by repeating the experiment with the control qubit both in the ground and excited states. The fit for the oscillations in the three bases with the two control qubit preparations tomographically reconstructs the Hamiltonian in the form shown above. See Ref. [1] for more details.

More specifically, the following circuits are executed in this experiment.

(X measurement)

     ┌───┐┌────────────────────┐
q_0: ┤ P ├┤0                   ├────────────────────
     └───┘│  cr_tone(duration) │┌─────────┐┌────┐┌─┐
q_1: ─────┤1                   ├┤ Rz(π/2) ├┤ √X ├┤M├
          └────────────────────┘└─────────┘└────┘└╥┘
c: 1/═════════════════════════════════════════════╩═
                                                  0

(Y measurement)

     ┌───┐┌────────────────────┐
q_0: ┤ P ├┤0                   ├─────────
     └───┘│  cr_tone(duration) │┌────┐┌─┐
q_1: ─────┤1                   ├┤ √X ├┤M├
          └────────────────────┘└────┘└╥┘
c: 1/══════════════════════════════════╩═
                                       0

(Z measurement)

     ┌───┐┌────────────────────┐
q_0: ┤ P ├┤0                   ├───
     └───┘│  cr_tone(duration) │┌─┐
q_1: ─────┤1                   ├┤M├
          └────────────────────┘└╥┘
c: 1/════════════════════════════╩═
                                 0

The P gate on the control qubit (q_0) indicates the state preparation. Since this experiment requires two sets of sub experiments with the control qubit in the excited and ground state, P will become X gate or just be omitted, respectively. Here cr_tone is implemented by a single cross resonance tone driving the control qubit at the frequency of the target qubit. The pulse envelope might be a flat-topped Gaussian implemented by the parametric pulse GaussianSquare.

This experiment scans the total duration of the cross resonance pulse including the pulse ramps at both edges. The pulse shape is defined by the GaussianSquare, and an effective length of these Gaussian ramps with $\sigma$ can be computed by

$${\tau }_{\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}\mathrm{s}}^{\prime }=\sqrt{2\pi }\sigma ,$$

which is usually shorter than the actual edge duration of

$${\tau }_{\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}\mathrm{s}}=2r\sigma ,$$

where the $r$ is the ratio of the actual edge duration to $\sigma$. This effect must be considered in the following curve analysis to estimate interaction rates.

References

[1] Sarah Sheldon, Easwar Magesan, Jerry M. Chow, Jay M. Gambetta, Procedure for systematically tuning up crosstalk in the cross resonance gate, Phys. Rev. A 93, 060302 (2016), doi: 10.1103/PhysRevA.93.060302 (open)

User manual

Qiskit Textbook 6.7 (open)

Analysis class reference

CrossResonanceHamiltonianAnalysis

Experiment options

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

Options

• Defined in the class CrossResonanceHamiltonian:

  • flat_top_widths (np.ndarray)

    Default value: None

    Deprecated. Length of Gaussian flat top to scan.

  • 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.

Initialization

Create a new experiment.

Parameters:

• physical_qubits (Tuple[int, int]) – Two-value tuple of qubit indices on which to run tomography. The first index stands for the control qubit.

• flat_top_widths (Optional[Iterable[float]]) – Deprecated. The total duration of the square part of cross resonance pulse(s) to scan, in units of dt. The total pulse duration including Gaussian rising and falling edges is implicitly computed with experiment parameters sigma and risefall.

• backend (Optional[Backend]) – Optional, the backend to run the experiment on.

• cr_gate (Optional[Type[Gate]]) – Optional, circuit gate class representing the cross resonance pulse. Providing this object allows us to run this experiment with circuit simulator, and this object might be used for testing, development of analysis protocol, and educational purpose without needing to wait for hardware queueing. Note that this instance must provide matrix representation, such as unitary gate or Hamiltonian gate, and the class is expected to be instantiated with a single parameter width in units of sec.

• durations (Optional[Sequence[int]]) – Optional. The total duration of cross resonance pulse(s) including rising and falling edges. The minimum number should be larger than the total lengths of these ramps. If not provided, then num_durations evenly spaced durations between min_durations and max_durations are automatically generated from these experiment options. The default numbers are chosen to have a good sensitivity for the Hamiltonian coefficient of interest at the rate around 1 MHz. This argument should be provided in units of sec.

• kwargs – Pulse parameters. See experiment_options() for details.

Raises:

QiskitError – When qubits length is not 2.

Attributes

CrossResonanceHamiltonian.analysis	Return the analysis instance for the experiment
CrossResonanceHamiltonian.backend	Return the backend for the experiment
CrossResonanceHamiltonian.experiment_options	Return the options for the experiment.
CrossResonanceHamiltonian.experiment_type	Return experiment type.
CrossResonanceHamiltonian.num_pulses
CrossResonanceHamiltonian.num_qubits	Return the number of qubits for the experiment.
CrossResonanceHamiltonian.physical_qubits	Return the device qubits for the experiment.
CrossResonanceHamiltonian.run_options	Return options values for the experiment run() method.
CrossResonanceHamiltonian.transpile_options	Return the transpiler options for the run() method.

Methods

CrossResonanceHamiltonian.circuits()	Return a list of experiment circuits.
CrossResonanceHamiltonian.config()	Return the config dataclass for this experiment
CrossResonanceHamiltonian.copy()	Return a copy of the experiment
CrossResonanceHamiltonian.from_config(config)	Initialize an experiment from experiment config
CrossResonanceHamiltonian.run([backend, ...])	Run an experiment and perform analysis.
CrossResonanceHamiltonian.set_experiment_options(...)	Set the experiment options.
CrossResonanceHamiltonian.set_run_options(...)	Set options values for the experiment run() method.
CrossResonanceHamiltonian.set_transpile_options(...)	Set the transpiler options for run() method.