# CrossResonanceHamiltonian¶

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

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

$\tau_{\rm edges}' = \sqrt{2 \pi} \sigma,$

which is usually shorter than the actual edge duration of

$\tau_{\rm edges} = 2 r \sigma,$

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:

• 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.

• backend (Backend | None) – Optional, the backend to run the experiment on.

• cr_gate (Type[Gate] | None) – 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 (Sequence[int] | None) – 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

analysis

Return the analysis instance for the experiment

backend

Return the backend for the experiment

experiment_options

Return the options for the experiment.

experiment_type

Return experiment type.

num_pulses = 1
num_qubits

Return the number of qubits for the experiment.

physical_qubits

Return the device qubits for the experiment.

run_options

Return options values for the experiment run() method.

transpile_options

Return the transpiler options for the run() method.

Methods

circuits()[source]

Return a list of experiment circuits.

Returns:

A list of QuantumCircuit.

Raises:

QiskitError – When the backend is not set and cr gate is CRPulseGate type.

Return type:

List[QuantumCircuit]

config()

Return the config dataclass for this experiment

Return type:

ExperimentConfig

copy()

Return a copy of the experiment

Return type:

BaseExperiment

classmethod from_config(config)

Initialize an experiment from experiment config

Return type:

BaseExperiment

job_info(backend=None)

Get information about job distribution for the experiment on a specific backend.

Parameters:

backend (Backend) – Optional, the backend for which to get job distribution information. If not specified, the experiment must already have a set backend.

Returns:

A dictionary containing information about job distribution.

• ”Total number of circuits in the experiment”: Total number of circuits in the experiment.

• ”Maximum number of circuits per job”: Maximum number of circuits in one job based on backend and experiment settings.

• ”Total number of jobs”: Number of jobs needed to run this experiment on the currently set backend.

Return type:

dict

Raises:

QiskitError – if backend is not specified.

run(backend=None, analysis='default', timeout=None, **run_options)

Run an experiment and perform analysis.

Parameters:
• backend (Backend | None) – Optional, the backend to run the experiment on. This will override any currently set backends for the single execution.

• analysis (BaseAnalysis | None) – Optional, a custom analysis instance to use for performing analysis. If None analysis will not be run. If "default" the experiments analysis() instance will be used if it contains one.

• timeout (float | None) – Time to wait for experiment jobs to finish running before cancelling.

• run_options – backend runtime options used for circuit execution.

Returns:

The experiment data object.

Raises:

QiskitError – If experiment is run with an incompatible existing ExperimentData container.

Return type:

ExperimentData

set_experiment_options(**fields)

Set the experiment options.

Parameters:

fields – The fields to update the options

Raises:

AttributeError – If the field passed in is not a supported options

set_run_options(**fields)

Set options values for the experiment run() method.

Parameters:

fields – The fields to update the options

The Setting options for your experiment guide for code example.

set_transpile_options(**fields)

Set the transpiler options for run() method.

Parameters:

fields – The fields to update the options

Raises:

QiskitError – If initial_layout is one of the fields.