Source code for qiskit_experiments.library.characterization.zz_ramsey

# This code is part of Qiskit.
#
# (C) Copyright IBM 2022.
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# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
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"""
ZZ Ramsey experiment
"""

from typing import List, Tuple, Union

import numpy as np

from qiskit import QuantumCircuit
from qiskit.providers.backend import Backend
from qiskit.circuit import Parameter, ParameterExpression

from qiskit_experiments.framework import BackendTiming, BaseExperiment, Options
from .analysis.zz_ramsey_analysis import ZZRamseyAnalysis


[docs] class ZZRamsey(BaseExperiment): r"""An experiment to characterize the static :math:`ZZ` interaction for a qubit pair. # section: overview This experiment assumes a two qubit Hamiltonian of the form .. math:: H = h \left(\frac{f_0}{2} ZI + \frac{f_1}{2} IZ + \frac{f_{ZZ}}{4} ZZ\right) and measures the strength :math:`f_{ZZ}` of the :math:`ZZ` term. :math:`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 :math:`f_{ZZ}` is symmetric in qubit index, it can also be expressed with the roles of 0 and 1 reversed. Experimentally, we measure :math:`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 :math:`X` axis of Bloch sphere, waiting for some time, and then measuring the qubit project along :math:`X`. By measuring the :math:`X` projection versus time the qubit frequency can be inferred. See :class:`~qiskit_experiments.library.characterization.T2Ramsey` and :class:`~qiskit_experiments.library.characterization.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 :class:`~qiskit_experiments.library.characterization.T2Hahn`), but we add a simultaneous X gate to qubit 1 as well. Flipping qubit 1 inverts the sign of the :math:`f_{ZZ}` term. The net result is that qubit 0 continues to accumulate phase proportional to :math:`f_{ZZ}` while the phase due to any ZI term is canceled out. This technique allows :math:`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 :math:`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 :math:`f` in the circuits shown below) is removed, leaving only the :math:`f_{ZZ}` value. The value of :math:`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. .. parsed-literal:: 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 # section: analysis_ref :class:`ZZRamseyAnalysis` # section: example .. jupyter-execute:: :hide-code: # backend from qiskit_ibm_runtime.fake_provider import FakePerth from qiskit_aer import AerSimulator from qiskit_aer.noise import NoiseModel noise_model = NoiseModel.from_backend(FakePerth(), thermal_relaxation=True, gate_error=False, readout_error=False, ) backend = AerSimulator.from_backend(FakePerth(), noise_model=noise_model) .. jupyter-execute:: from qiskit_experiments.library.characterization import ZZRamsey exp = ZZRamsey(physical_qubits=(0,1), backend=backend) exp_data = exp.run().block_for_results() display(exp_data.figure(0)) exp_data.analysis_results(dataframe=True) """ def __init__( self, physical_qubits: Tuple[int, int], backend: Union[Backend, None] = None, **experiment_options, ): """Create new experiment. Args: physical_qubits: The qubits on which to run the Ramsey XY experiment. backend: Optional, the backend to run the experiment on. experiment_options: experiment options to set """ super().__init__(physical_qubits, analysis=ZZRamseyAnalysis(), backend=backend) # Override the default of get_processor() which is "1" * num_qubits. We # only fit the probability of the target qubit. self.analysis.set_options(outcome="1") self.set_experiment_options(**experiment_options) @classmethod def _default_experiment_options(cls) -> Options: """Default values for the :math:`ZZ` Ramsey experiment. Experiment Options: delays (list[float]): 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): Maximum delay time to use. min_delay (float): Minimum delay time to use. num_delays (int): Number of circuits to use per control state preparation. num_rotations (float): The extra rotation added to qubit 0 uses a frequency that gives this many rotations in the case where :math:`f_{ZZ}` is 0. """ options = super()._default_experiment_options() options.delays = None options.min_delay = 0e-6 options.max_delay = 10e-6 options.num_delays = 50 options.num_rotations = 5 return options
[docs] def delays(self) -> List[float]: """Delay values to use in circuits Returns: The list of delays to use for the different circuits based on the experiment options. """ # This method allows delays to be set by the user as an explicit # sequence or as a minimum, maximum and number of values for a linearly # spaced sequence. options = self.experiment_options if options.delays is not None: return options.delays return np.linspace(options.min_delay, options.max_delay, options.num_delays).tolist()
[docs] def frequency(self) -> float: """Frequency of qubit rotation when ZZ is 0 This method calculates the simulated frequency applied to both sets of circuits. The value is chosen to induce `num_rotations` number of rotation within the time window that the delay is swept through. Returns: The frequency at which the target qubit will rotate when ZZ is zero based on the current experiment options. """ delays = self.delays() freq = self.experiment_options.num_rotations / (max(delays) - min(delays)) return freq
def _template_circuits( self, frequency: Union[None, float, ParameterExpression] = None, ) -> Tuple[QuantumCircuit, QuantumCircuit]: """Template circuits for series 0 and 1 parameterized by delay The generated circuits have the length of the delay instructions as the only parameter. Args: dt_value: the value of the backend ``dt`` value. Used to convert delay values into units of seconds. delay_unit: the unit of circuit delay instructions. Returns: Circuits for series 0 and 1 """ delay = Parameter("delay") timing = BackendTiming(self.backend) frequency = frequency if frequency is not None else self.frequency() # frequency is always in units of Hz. delay_freq has inverse units to # the units of `delay`. # # If the backend does not have a `dt`, the delays will be treated as in # units of seconds. Otherwise they will be in units of samples. For the # samples case, we multiply by `dt` so that `delay_freq` is in inverse # samples per cycle. if timing.delay_unit != "s": delay_freq = timing.dt * frequency else: delay_freq = frequency # Template circuit for series 0 # Control qubit starting in |0> state, flipping to |1> in middle circ0 = QuantumCircuit(2, 1) circ0.metadata["series"] = "0" circ0.sx(0) circ0.barrier() circ0.delay(delay, 0, timing.delay_unit) circ0.barrier() circ0.x(0) circ0.x(1) circ0.barrier() circ0.delay(delay, 0, timing.delay_unit) circ0.barrier() circ0.rz(2 * np.pi * delay_freq * (2 * delay), 0) circ0.sx(0) # Flip control back to 0, so control qubit is in 0 for all circuits # when qubit 1 is measured. circ0.x(1) circ0.barrier() circ0.measure(0, 0) # Template circuit for series 1 # Control qubit starting in |1> state, flipping to |0> in middle circ1 = QuantumCircuit(2, 1) circ1.metadata["series"] = "1" circ1.x(1) circ1.sx(0) circ1.barrier() circ1.delay(delay, 0, timing.delay_unit) circ1.barrier() circ1.x(0) circ1.x(1) circ1.barrier() circ1.delay(delay, 0, timing.delay_unit) circ1.barrier() circ1.rz(2 * np.pi * delay_freq * (2 * delay), 0) circ1.sx(0) circ1.barrier() circ1.measure(0, 0) return circ0, circ1
[docs] def parametrized_circuits(self) -> Tuple[QuantumCircuit, QuantumCircuit]: r"""Create circuits with parameters for numerical quantities This method is primarily intended for generating template circuits that visualize well. It inserts :class:`qiskit.circuit.Parameter`\ s for :math:`π` and `dt` as well the target qubit rotation frequency `f`. Return: Parameterized circuits for the case of the control qubit being in 0 and in 1. """ f_param = Parameter("f") dt = Parameter("dt") pi = Parameter("pi") freq = dt * pi * f_param / np.pi timing = BackendTiming(self.backend) if timing.dt is not None: freq = freq / timing.dt circs = self._template_circuits(frequency=freq) return circs
[docs] def circuits(self) -> List[QuantumCircuit]: """Create circuits Returns: A list of circuits with a variable delay. """ timing = BackendTiming(self.backend) circ0, circ1 = self._template_circuits() circs = [] for delay in self.delays(): for circ in (circ0, circ1): assigned = circ.assign_parameters( {circ.parameters[0]: timing.round_delay(time=delay / 2)}, inplace=False ) assigned.metadata["xval"] = 2 * timing.delay_time(time=delay / 2) circs.append(assigned) return circs