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"# Copyright 2025 Keysight Technologies Inc."
]
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"Ramsey Experiment\n",
"=================\n",
"\n",
"\n",
"This section shows how to perform a Ramsey experiment to learn the dephasing time of a\n",
"qubit. This experiment can be easily generated with\n",
":py:class:`~keysight.qcs.experiments.RamseyExperiment`\\.\n",
"\n",
"Following the :doc:`qubit_spec` and :doc:`qubit_rabi`, we have determined the qubit's\n",
"resonance frequency and :math:`\\pi`-pulse amplitude which were stored in the\n",
"calibration set. Given these, we are now able to implement the :math:`\\frac{\\pi}{2}`\n",
"gate to create an equal superposition between the ground and excited state. We begin\n",
"characterizing the intrinsic noise of the system by\n",
"learning the decay rate of the coherence between the ground and excited states of\n",
"the qubit. The time scale associated with this decoherence is commonly referred to\n",
"as the :math:`T_2^*` time. The Ramsey experiment can also be used to measure the\n",
"error in the measured resonance frequency of the qubit (the detuning frequency), and\n",
"further tune up the calibration parameters.\n",
"\n",
"A :math:`\\frac{\\pi}{2}` gate applied to a qubit in the ground state creates an equal\n",
"superposition state, shown below as a point on the :math:`XY` plane of the Bloch\n",
"sphere. The phase of the state evolves in time, corresponding to a natural precession\n",
"around the :math:`Z` axis. At the same time, dephasing occurs as the state shrinks on\n",
"the Bloch sphere towards the center (the completely mixed state). After some time has\n",
"elapsed, a second :math:`\\frac{\\pi}{2}` gate can be applied to drive the qubit to\n",
"either the ground or excited state. The magnitude of the dephasing can then be\n",
"measured as the population in the excited state. The rotation shows up in the\n",
"measurement as an oscillation between the ground and excited states, while the\n",
"dephasing appears as an exponentially decaying envelope. By varying the delay time, we\n",
"can learn the characteristic time scale of the decay.\n",
"\n",
"If the control frequency and the qubit frequency match, i.e. there is no detuning,\n",
"then we would not observe any oscillations between the ground and excited state.\n",
"In the case of detuning, we observe an oscillation and this can be used to\n",
"recalibrate the qubit's resonance frequency.\n",
"\n",
".. image:: ../figures/ramsey_exp.png\n",
" :align: center\n",
" :width: 120%\n",
"\n",
"To learn the :math:`T_2^*` time and detuning frequency, we perform a Ramsey experiment\n",
"as follows:\n",
"\n",
"#. Initialize the qubit to an equal superposition state between the ground and\n",
" excited state (in the :math:`XY` plane of the Bloch sphere) by applying a\n",
" :math:`\\frac{\\pi}{2}` gate.\n",
"\n",
"#. Apply a delay.\n",
"\n",
"#. Apply a second :math:`\\frac{\\pi}{2}` gate to drive the qubit toward either the\n",
" ground or excited state.\n",
"\n",
"#. Measure the population of the qubit in the excited state.\n",
"\n",
"#. Repeat the above steps with varying delay time.\n",
"\n",
".. note::\n",
" :class: admonition-blue\n",
"\n",
" When selecting a value for the detuning frequency, users must ensure that the\n",
" control frequency does not deviate from the LO frequency by more then 1 GHz,\n",
" otherwise an error message will show up during execution.\n",
" Also, to prevent the control frequency from being set to a value unsupported\n",
" by the hardware, the library restricts the detune_frequency parameter to a\n",
" range between -30 MHz and 30 MHz.\n"
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"We start by initializing a qubit and loading a channel mapper to\n",
"create a new instance of the :py:class:`~keysight.qcs.experiments.RamseyExperiment`\n",
"class. Next, we generate a calibration set for the qubit\n",
"using :py:func:`~keysight.qcs.experiments.make_calibration_set`. This file includes\n",
"the quantum operations and variables we will need to run the experiment."
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