Experiment: :math:T_\varphi characterization ============================================== :math:\Gamma_\varphi is defined as the rate of pure dephasing or depolarization in the :math:x - y plane. We compute :math:\Gamma_\varphi by computing :math:\Gamma_2*, the transverse relaxation rate, and subtracting :math:\Gamma_1, the longitudinal relaxation rate. The pure dephasing time is defined by :math:T_\varphi = 1/\Gamma_\varphi. Or more precisely, :math:1/T_\varphi = 1/T_{2*} - 1/2T_1 We therefore create a composite experiment consisting of a :math:T_1 experiment and a :math:T_2* experiment. From the results of these two, we compute the results for :math:T_\varphi. .. jupyter-execute:: import numpy as np import qiskit from qiskit_experiments.library.characterization import Tphi, TphiAnalysis, T1Analysis, T2RamseyAnalysis .. jupyter-execute:: # An Aer simulator from qiskit.test.mock import FakeVigo from qiskit.providers.aer import AerSimulator from qiskit.providers.aer.noise import NoiseModel # Create a pure relaxation noise model for AerSimulator noise_model = NoiseModel.from_backend( FakeVigo(), thermal_relaxation=True, gate_error=False, readout_error=False ) # Create a fake backend simulator backend = AerSimulator.from_backend(FakeVigo(), noise_model=noise_model) # Time intervals to wait before measurement for t1 and t2 delays_t1 = np.arange(1e-6, 300e-6, 10e-6) delays_t2 = np.arange(1e-6, 50e-6, 2e-6) .. jupyter-execute:: # Create an experiment for qubit 0 with the specified time intervals exp = Tphi(qubit=0, delays_t1=delays_t1, delays_t2=delays_t2, osc_freq=1e5) tphi_analysis = TphiAnalysis([T1Analysis(), T2RamseyAnalysis()]) expdata = exp.run(backend=backend, analysis=tphi_analysis, seed_simulator=101).block_for_results() result = expdata.analysis_results("T_phi") .. jupyter-execute:: # Print the result for T_phi print(result) .. jupyter-execute:: # It is possible to see the results of the sub-experiments: print(expdata) .. jupyter-execute:: print(expdata.analysis_results("T1")) .. jupyter-execute:: display(expdata.figure(0)) .. jupyter-execute:: print(expdata.analysis_results("T2star")) .. jupyter-execute:: display(expdata.figure(1)) .. jupyter-execute:: import qiskit.tools.jupyter %qiskit_copyright