CrossResonanceHamiltonian¶
- class CrossResonanceHamiltonian(qubits, flat_top_widths, backend=None, cr_gate=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 ├┤ H ├┤M├ └────────────────────┘└───┘└╥┘ c: 1/═════════════════════════════════╩═ 0 (Y measurement) ┌───┐┌────────────────────┐ q_0: ┤ P ├┤0 ├─────────────── └───┘│ cr_tone(duration) │┌─────┐┌───┐┌─┐ q_1: ─────┤1 ├┤ Sdg ├┤ H ├┤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 becomeX
gate or just be omitted, respectively. Herecr_tone
is implemented by a single cross resonance tone driving the control qubit at the frequency of the target qubit. The pulse envelope is the flat-topped Gaussian implemented by the parametric pulseGaussianSquare
.This experiment scans the flat-top width of the
GaussianSquare
envelope with the fixed rising and falling edges. The total pulse duration is implicitly computed to meet the timing constraints of the target backend. The edge duration is usually computed as\[\tau_{\rm edges} = 2 r \sigma,\]where the \(r\) is the ratio of the actual edge duration to \(\sigma\) of the Gaussian rising and falling edges. Note that actual edge duration is not identical to the net duration because of the smaller pulse amplitude of the edges.
The net edge duration is an extra fitting parameter with initial guess
\[\tau_{\rm edges}' = \sqrt{2 \pi} \sigma,\]which is derived by assuming a square edges with the full pulse amplitude.
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)
Tutorials
Qiskit Textbook 6.7 (open)
Analysis Class Reference
CrossResonanceHamiltonianAnalysis
Experiment Options
These options can be set by
set_experiment_options()
method.- Parameters:
flat_top_widths (np.ndarray) – The total duration of the square part of cross resonance pulse(s) to scan, in units of dt. This can start from zero and take positive real values representing the durations. Pulse edge effect is considered as an offset to the durations.
amp (complex) – Amplitude of the cross resonance tone.
amp_t (complex) – Amplitude of the cancellation or rotary drive on target qubit.
sigma (float) – Sigma of Gaussian rise and fall edges, in units of dt.
risefall (float) – Ratio of edge durations to sigma.
Transpiler Options
This option can be set by
set_transpile_options()
method.This option is used for circuit optimization. See the documentation of
qiskit.transpile
for available options.Backend Run Options
This option can be set by
set_run_options()
method.This option is used for controlling job execution condition. Note that this option is provider dependent. See provider’s backend runner API for available options. See the documentation of
IBMQBackend.run
for the IBM Quantum Service.Initialization
Create a new experiment.
- Parameters:
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 (
Iterable
[float
]) – 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 parameterssigma
andrisefall
.backend (
Optional
[Backend
]) – Optional, the backend to run the experiment on.cr_gate (
Optional
[Type
[Gate
]]) – Optional, circuit gate instruction of cross resonance pulse.kwargs – Pulse parameters. See
experiment_options()
for details.
- Raises:
QiskitError – When
qubits
length is not 2.
Attributes
Return the analysis instance for the experiment
Return the analysis options for
run()
analysis.Return the backend for the experiment
Return the options for the experiment.
Return experiment type.
Return the number of qubits for the experiment.
Return the device qubits for the experiment.
Return options values for the experiment
run()
method.Return the transpiler options for the
run()
method.Methods
Return a list of experiment circuits.
Return the config dataclass for this experiment
Return a copy of the experiment
Initialize an experiment from experiment config
CrossResonanceHamiltonian.run
([backend, ...])Run an experiment and perform analysis.
Set the experiment options.
Set options values for the experiment
run()
method.Set the transpiler options for
run()
method.