{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "a6bdf582", "metadata": { "execution": { "iopub.execute_input": "2025-06-13T13:18:34.734375Z", "iopub.status.busy": "2025-06-13T13:18:34.733941Z", "iopub.status.idle": "2025-06-13T13:18:34.739357Z", "shell.execute_reply": "2025-06-13T13:18:34.738672Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "# Copyright 2025 Keysight Technologies Inc." ] }, { "cell_type": "raw", "id": "16485b3a", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "Dispersive Shift\n", "==================\n", "\n", "In the dispersive regime, the qubit-resonator detuning :math:`\\Delta` =\n", ":math:`\\omega_q` - :math:`\\omega_r` is much larger than the coupling strength `g`.\n", "In this regime the qubit and the resonator do not exchange energy directly, instead\n", "the resonator's frequency changes depending on the qubit state. This is what allows\n", "the measurement of the qubit's state without disturbing it.\n", "In this regime the Hamiltonian can be rewritten in the following form:\n", "\n", ".. math::\n", " H = \\hbar(\\omega_r + \\chi\\sigma_z)a^{\\dagger}a + \\frac{1}{2}\\hbar(\\omega_q\n", " + \\chi)\\sigma_z\n", "\n", "Where we introduced the dispersive shift:\n", "\n", ".. math::\n", " \\chi = \\frac{g^2}{\\Delta}\n", "\n", "\n", "This parameter is what we are characterizing in this guide with the help of the\n", "the :py:class:`~keysight.qcs.experiments.DispersiveShift` class.\n", "To determine the dispersive shift, we are essentially performing two resonator\n", "spectroscopy experiments, with the qubit in either the ground or the excited state.\n", "The procedure is as follows:\n", "\n", " #. Initialize the qudit to the ground state.\n", "\n", " #. Either leave the qubit in the ground state or apply a control pulse to\n", " bring the qubit to the excited state.\n", "\n", " #. Apply a readout pulse at a frequency :math:`\\omega` on the target qudit.\n", "\n", " #. Repeat the above steps for different values of :math:`\\omega`.\n", "\n", "\n", "The result will be two lorentzian peaks separated by :math:`2\\chi` like so:\n", "\n", ".. image:: ../figures/dispersiveshift.png\n", " :align: center\n", " :width: 80%\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "86c6e189", "metadata": { "execution": { "iopub.execute_input": "2025-06-13T13:18:34.743360Z", "iopub.status.busy": "2025-06-13T13:18:34.742728Z", "iopub.status.idle": "2025-06-13T13:18:38.617954Z", "shell.execute_reply": "2025-06-13T13:18:38.617192Z" } }, "outputs": [], "source": [ "# Import the necessary packages\n", "import numpy as np\n", "import keysight.qcs as qcs\n", "from keysight.qcs.experiments import DispersiveShift, make_calibration_set" ] }, { "cell_type": "raw", "id": "eac3f391", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "We start by initializing a qubit and loading a channel mapper, which links up to\n", "the hardware channels. If a channel mapper doesn't exist, we can create a new one and\n", "add the hardware references to it. 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.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "523222f1", "metadata": { "execution": { "iopub.execute_input": "2025-06-13T13:18:38.622489Z", "iopub.status.busy": "2025-06-13T13:18:38.622044Z", "iopub.status.idle": "2025-06-13T13:18:38.790495Z", "shell.execute_reply": "2025-06-13T13:18:38.789600Z" }, "lines_to_next_cell": 0 }, "outputs": [], "source": [ "# set the following to True when connected to hardware\n", "run_on_hw = False\n", "\n", "n_qubits = 1\n", "qubits = qcs.Qudits(range(n_qubits))\n", "\n", "# Set this to True if channel mapper exists\n", "channel_mapper_exists = False\n", "\n", "if channel_mapper_exists:\n", " mapper = qcs.load(\"\")\n", "else:\n", " # generate an empty channel mapper with the correct ip address\n", " mapper = qcs.ChannelMapper(\"127.0.0.1\")\n", "\n", "calibration_set = make_calibration_set(qubits=n_qubits)" ] }, { "cell_type": "raw", "id": "3f885044", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "We can now create a new instance of the\n", ":py:class:`~keysight.qcs.experiments.DispersiveShift` class. We use the\n", ":py:meth:`~keysight.qcs.experiments.Experiment.draw` method to visualize the\n", "experiment program that will be executed on hardware." ] }, { "cell_type": "code", "execution_count": 4, "id": "2c99f04d", "metadata": { "execution": { "iopub.execute_input": "2025-06-13T13:18:38.794543Z", "iopub.status.busy": "2025-06-13T13:18:38.793811Z", "iopub.status.idle": "2025-06-13T13:18:38.935718Z", "shell.execute_reply": "2025-06-13T13:18:38.934804Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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