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.

ZZRamsey

class ZZRamsey(physical_qubits, backend=None, **experiment_options)

An experiment to characterize the static $ZZ$ interaction for a qubit pair.

Overview

This experiment assumes a two qubit Hamiltonian of the form

$$H=h(\frac{f_0}{2}ZI+\frac{f_1}{2}IZ+\frac{f_{ZZ}}{4}ZZ)$$

and measures the strength $f_{ZZ}$ of the $ZZ$ term. $f_{ZZ}$ can be described as the difference between the frequency of qubit 0 when qubit 1 is excited and the frequency of qubit 0 when qubit 1 is in the ground state. Because $f_{ZZ}$ is symmetric in qubit index, it can also be expressed with the roles of 0 and 1 reversed. Experimentally, we measure $f_{ZZ}$ by performing Ramsey sequences on qubit 0 with qubit 1 in the ground state and again with qubit 1 in the excited state. The standard Ramsey experiment consists of putting a qubit along the $X$ axis of Bloch sphere, waiting for some time, and then measuring the qubit project along $X$. By measuring the $X$ projection versus time the qubit frequency can be inferred. See T2Ramsey and RamseyXY.

Because we are interested in the difference in qubit 0 frequency between the two qubit 1 preparations rather than the absolute frequencies of qubit 0 for those preparations, we modify the Ramsey sequences (the circuits for the modified sequences are shown below). First, we add an X gate on qubit 0 to the middle of the Ramsey delay. This would have the effect of echoing out the phase accumulation of qubit 0 (like a Hahn echo sequence as used in T2Hahn), but we add a simultaneous X gate to qubit 1 as well. Flipping qubit 1 inverts the sign of the $f_{ZZ}$ term. The net result is that qubit 0 continues to accumulate phase proportional to $f_{ZZ}$ while the phase due to any ZI term is canceled out. This technique allows $f_{ZZ}$ to be measured using longer delay times than might otherwise be possible with a qubit with a slow frequency drift (i.e. the measurement is not sensitive to qubit frequency drift from shot to shot, only to drift within a single shot).

The resulting excited state population of qubit 0 versus delay time exhibits slow sinusoidal oscillations (assuming $f_{ZZ}$ is relatively small). To help with distinguishing between qubit decay and a slow oscillation, an extra Z rotation is applied before the final pulse on qubit 0. The angle of this Z rotation is set proportional to the delay time of the sequence. This angle proportional to time behaves similarly to measuring at a fixed angle with the qubit rotating at a constant frequency. This virtual frequency is common to the two qubit 1 preparations. By looking at the difference in frequency fitted for the two cases, this virtual frequency (called $f$ in the circuits shown below) is removed, leaving only the $f_{ZZ}$ value. The value of $f$ in terms of the experiment options is num_rotations / (max(delays) - min(delays)).

This experiment consists of the following two circuits repeated with different delay values.

Modified Ramsey sequence with qubit 1 initially in the ground state

     ┌────┐ ░ ┌─────────────────┐ ░ ┌───┐ ░ ┌─────────────────┐ ░ »
q_0: ┤ √X ├─░─┤ Delay(delay[s]) ├─░─┤ X ├─░─┤ Delay(delay[s]) ├─░─»
     └────┘ ░ └─────────────────┘ ░ ├───┤ ░ └─────────────────┘ ░ »
q_1: ───────░─────────────────────░─┤ X ├─░─────────────────────░─»
            ░                     ░ └───┘ ░                     ░ »
c: 1/═════════════════════════════════════════════════════════════»
                                                                  »
«     ┌─────────────────────┐┌────┐ ░ ┌─┐
«q_0: ┤ Rz(4*delay*dt*f*pi) ├┤ √X ├─░─┤M├
«     └────────┬───┬────────┘└────┘ ░ └╥┘
«q_1: ─────────┤ X ├────────────────░──╫─
«              └───┘                ░  ║
«c: 1/═════════════════════════════════╩═
«                                      0

Modified Ramsey sequence with qubit 1 initially in the excited state

     ┌────┐ ░ ┌─────────────────┐ ░ ┌───┐ ░ ┌─────────────────┐ ░ »
q_0: ┤ √X ├─░─┤ Delay(delay[s]) ├─░─┤ X ├─░─┤ Delay(delay[s]) ├─░─»
     ├───┬┘ ░ └─────────────────┘ ░ ├───┤ ░ └─────────────────┘ ░ »
q_1: ┤ X ├──░─────────────────────░─┤ X ├─░─────────────────────░─»
     └───┘  ░                     ░ └───┘ ░                     ░ »
c: 1/═════════════════════════════════════════════════════════════»
                                                                  »
«     ┌─────────────────────┐┌────┐ ░ ┌─┐
«q_0: ┤ Rz(4*delay*dt*f*pi) ├┤ √X ├─░─┤M├
«     └─────────────────────┘└────┘ ░ └╥┘
«q_1: ──────────────────────────────░──╫─
«                                   ░  ║
«c: 1/═════════════════════════════════╩═
«                                      0

Analysis class reference

ZZRamseyAnalysis

Experiment options

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

Options

• Defined in the class ZZRamsey:

  • delays (list[float])

    Default value: None

    The list of delays that will be scanned in the experiment, in seconds. If not set, then num_delays evenly spaced delays between min_delay and max_delay are used. If delays is set, max_delay, min_delay, and num_delays are ignored.

  • max_delay (float)

    Default value: 1e-05

    Maximum delay time to use.

  • min_delay (float)

    Default value: 0.0

    Minimum delay time to use.

  • num_delays (int)

    Default value: 50

    Number of circuits to use per control state preparation.

  • num_rotations (float)

    Default value: 5

    The extra rotation added to qubit 0 uses a frequency that gives this many rotations in the case where $f_{ZZ}$ is 0.

• 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 new experiment.

Parameters:

• physical_qubits (Tuple[int, int]) – The qubits on which to run the Ramsey XY experiment.

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

• experiment_options – experiment options to set

Attributes

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

Methods

ZZRamsey.circuits()	Create circuits
ZZRamsey.config()	Return the config dataclass for this experiment
ZZRamsey.copy()	Return a copy of the experiment
ZZRamsey.delays()	Delay values to use in circuits
ZZRamsey.frequency()	Frequency of qubit rotation when ZZ is 0
ZZRamsey.from_config(config)	Initialize an experiment from experiment config
ZZRamsey.parametrized_circuits()	Create circuits with parameters for numerical quantities
ZZRamsey.run([backend, analysis, timeout])	Run an experiment and perform analysis.
ZZRamsey.set_experiment_options(**fields)	Set the experiment options.
ZZRamsey.set_run_options(**fields)	Set options values for the experiment run() method.
ZZRamsey.set_transpile_options(**fields)	Set the transpiler options for run() method.