docs/source/guide/ipynb/explorer.ipynb

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    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import scqubits as scq"
   ]
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   "source": [
    "# Explorer\n",
    "\n",
    "Sometimes, exploring the properties of coupled quantum systems benefits from visual aides, and the possibility to see how properties change when system parameters are changed. The `Explorer` class in scqubits provides an interactive plot with multiple panels collecting an important set of information. \n",
    "\n",
    "The idea behind the `Explorer` class is simple: the user selects an external parameter that they wish to sweep, e.g., an external magnetic flux. The composite system is user-defined through the `HilbertSpace` and `InteractionTerm` classes, allowing flexibility to include different types and numbers of superconducting qubits and harmonic modes.\n",
    "\n",
    "Once defined, the parameter sweep is computed by means of the `ParameterSweep` class, and spectral data is stored in memory to allow efficient, interactive display of data. \n",
    "\n",
    "## Example 1: fluxonium coupled to resonator\n",
    "As a first example, we consider a system composed of a fluxonium qubit, coupled through its charge operator to the voltage inside a resonator.\n",
    "\n",
    "### HilbertSpace setup\n",
    "The initialization of the composite Hilbert space proceeds as usual; we first define the individual two subsystems that will make up the Hilbert space:"
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    "qbt = scq.Fluxonium(\n",
    "    EJ=2.55,\n",
    "    EC=0.72,\n",
    "    EL=0.12,\n",
    "    flux=0.0,\n",
    "    cutoff=110,\n",
    "    truncated_dim=9\n",
    ")\n",
    "\n",
    "osc = scq.Oscillator(\n",
    "    E_osc=4.0,\n",
    "    truncated_dim=5\n",
    ")"
   ]
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   "source": [
    "Here, the `truncated_dim` parameters are important. For the fluxonium, with `cutoff` set to 110, the internal Hilbert space dimension is 110. Once diagonalized, we will only keep a few eigenstates going forward - in the above example 9. Similarly, we keep 5 levels for the resonators, i.e., photon states n=0,1,...,4 are included in the following.\n",
    "\n",
    "Next, the two subsystems are declared as the two components of a joint Hilbert space:"
   ]
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   "source": [
    "hilbertspace = scq.HilbertSpace([qbt, osc])"
   ]
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   "source": [
    "The interaction between fluxonium and resonator is of the form $H_\\text{int} = g n (a+a^\\dagger)$, where $n$ is the fluxonium's charge operator: `qbt.n_operator()`.  This structure is captured by creating an `InteractionTerm` object via `add_interaction`:"
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    "hilbertspace.add_interaction(\n",
    "    g_strength=0.2,\n",
    "    op1=qbt.n_operator,\n",
    "    op2=osc.creation_operator,\n",
    "    add_hc=True\n",
    ")"
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    "### Parameter sweep setup\n",
    "We consider sweeping the external flux through the fluxonium loop. To create the necessary `ParameterSweep` object, we specify:\n",
    "1. `param_name`: the name of the sweep parameter (below expressed in LaTeX format as the flux in units of the flux quantum)\n",
    "2. `param_vals_by_name`: a dictionary that names our parameter and associates the array of flux values with it\n",
    "3. `subsys_update_info` (optional): a dictionary listing the particular Hilbert space subsystems that change as each parameter (here the flux) is varied\n",
    "4. `update_hilbertspace(param_val)`: a function that shows how a change in the sweep parameter affects the Hilbert space; here only the `.flux` attributed of the fluxonium qubit needs to be changed\n",
    "\n",
    "These ingredients all make it into the initialization of the `ParameterSweep` object. Once initialized, spectral data is generated and stored. Here, we additionally generate data for dispersive shifts and charge matrix elements."
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   "source": [
    "param_name = r'$\\Phi_{ext}/\\Phi_0$'\n",
    "param_vals = np.linspace(-0.5, 0.5, 101)\n",
    "\n",
    "subsys_update_list = [qbt]\n",
    "\n",
    "\n",
    "def update_hilbertspace(param_val):\n",
    "    qbt.flux = param_val\n",
    "\n",
    "\n",
    "sweep = scq.ParameterSweep(\n",
    "    paramvals_by_name={param_name: param_vals},\n",
    "    evals_count=10,\n",
    "    hilbertspace=hilbertspace,\n",
    "    subsys_update_info={param_name: [qbt]},\n",
    "    update_hilbertspace=update_hilbertspace,\n",
    ")"
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   "source": [
    "### Starting the Explorer class\n",
    "At this point, everything is prepared to start the interactive `Explorer` and play with the interactive display!"
   ]
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       "Output()"
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   "source": [
    "explorer = Explorer(\n",
    "    sweep=sweep,\n",
    "    evals_count=10\n",
    ")\n",
    "explorer.interact()"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "![title1](./explorer1.jpg)"
   ]
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   "source": [
    "The `Explorer` plots are currently fixed to:\n",
    "\n",
    "1. Bare spectra of the individual qubits\n",
    "2. Wave functions of the bare qubits\n",
    "3. Dressed spectrum of the composite Hilbert space\n",
    "4. Spectrum for n-photon qubit transitions, starting from a given initial state\n",
    "5. AC Stark shift $\\chi_{01}$ for any of the qubits\n",
    "6. Charge matrix elements for any of the qubits, using the same initial state as in point 4.\n",
    "\n",
    "\n",
    ".. note::  The n-photon qubit transition plot gathers data from the full system spectrum by assessing maximum overlap with bare qubit states. Whenever qubit levels cross and hybridize with, e.g., a resonator, a discontinuity will show up in the spectrum. These discontinuities are correct representations, and not a bug."
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    "## Example 2:  two transmons coupled to a resonator\n",
    "In the following second example, we consider a system composed of two flux-tunable transmons, capacitively coupled to one joint harmonic mode. (The flux is assumed to arise from a global field, and the SQUID-loop areas of the two transmons are different with an area ratio of 1.4) \n",
    "\n",
    "### Hilbert space setup"
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    "qbt1 = scq.Transmon(\n",
    "     EJ=25.0,\n",
    "     EC=0.2,\n",
    "     ng=0,\n",
    "     ncut=30,\n",
    "     truncated_dim=3)\n",
    "\n",
    "qbt2 = scq.Transmon(\n",
    "     EJ=15.0,\n",
    "     EC=0.15,\n",
    "     ng=0,\n",
    "     ncut=30,\n",
    "     truncated_dim=3)\n",
    "\n",
    "\n",
    "resonator = scq.Oscillator(\n",
    "    E_osc=5.5,\n",
    "    truncated_dim=4)\n",
    "\n",
    "hilbertspace = scq.HilbertSpace([qbt1, qbt2, resonator])\n",
    "\n",
    "\n",
    "g1 = 0.1  # coupling resonator-CPB1 (without charge matrix elements)\n",
    "g2 = 0.2  # coupling resonator-CPB2 (without charge matrix elements)\n",
    "\n",
    "hilbertspace.add_interaction(\n",
    "    g_strength = g1,\n",
    "    op1 = qbt1.n_operator,\n",
    "    op2 = resonator.creation_operator,\n",
    "    add_hc = True\n",
    ")\n",
    "\n",
    "hilbertspace.add_interaction(\n",
    "    g_strength = g2,\n",
    "    op1 = qbt2.n_operator,\n",
    "    op2 = resonator.creation_operator,\n",
    "    add_hc = True\n",
    ")"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameter sweep setup"
   ]
  },
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    "param_name = r'$\\Phi_{ext}/\\Phi_0$'\n",
    "param_vals = np.linspace(0.0, 1.0, 151)\n",
    "\n",
    "subsys_update_list = [qbt1, qbt2]\n",
    "\n",
    "\n",
    "def update_hilbertspace(param_val):     # function that shows how Hilbert space components are updated\n",
    "    qbt1.EJ = 30*np.abs(np.cos(np.pi * param_val))\n",
    "    qbt2.EJ = 40*np.abs(np.cos(np.pi * param_val * 2))\n",
    "\n",
    "\n",
    "sweep = scq.ParameterSweep(\n",
    "    paramvals_by_name={param_name: param_vals},\n",
    "    evals_count=15,\n",
    "    hilbertspace=hilbertspace,\n",
    "    subsys_update_info={param_name: [qbt1, qbt2]},\n",
    "    update_hilbertspace=update_hilbertspace,\n",
    ")"
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Start Explorer"
   ]
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       "Output()"
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   "source": [
    "explorer = Explorer(\n",
    "    sweep=sweep,\n",
    "    evals_count=10\n",
    ")\n",
    "explorer.interact()"
   ]
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   "source": [
    "![title2](./explorer2.jpg)"
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