{
"cells": [
{
"cell_type": "markdown",
"id": "e8596ea3",
"metadata": {},
"source": [
"# 4.05 New LOM and Two Coupled Transmon Example with sequence"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "9a97f615-d5a9-4167-a19a-99d1cfda80ae",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The autoreload extension is already loaded. To reload it, use:\n",
" %reload_ext autoreload\n"
]
}
],
"source": [
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"import numpy as np\n",
"\n",
"from qiskit_metal.analyses.quantization.lumped_capacitive import (\n",
" load_q3d_capacitance_matrix,\n",
")\n",
"from qiskit_metal.analyses.quantization.lom_core_analysis import (\n",
" CompositeSystem,\n",
" Cell,\n",
" Subsystem,\n",
")\n",
"\n",
"from scipy.constants import speed_of_light as c_light\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "a2a49da4",
"metadata": {},
"source": [
"> 💡 **Using this tutorial without the Qt GUI**\n",
"> \n",
"> This tutorial uses the desktop `MetalGUI`. To follow along on Colab, Binder, JupyterHub, or any environment where Qt isn't available, **replace any `gui.rebuild()` / `gui.screenshot()` call with `qm.view(design)`** — it renders the design to a matplotlib `Figure` you can display inline or save with `fig.savefig(...)`.\n",
"> \n",
"> See [1.4 Headless quick view](../1-Overview/1.4-Headless-quick-view-%28no-Qt-GUI%29.ipynb) for a complete runnable walkthrough and [`docs/headless-usage.rst`](../../../docs/headless-usage.rst) for the full reference."
]
},
{
"cell_type": "markdown",
"id": "32717ec8-f907-4902-bc2c-f5a17a7516bc",
"metadata": {},
"source": [
"## Example: two transmons coupled by a direct coupler\n",
"this part is identical to tutorial 4.05; please reference it for more detailed comments"
]
},
{
"cell_type": "markdown",
"id": "772a4f4a-0881-499f-a370-3e69494a817a",
"metadata": {},
"source": [
"### load transmon cell Q3d simulation results"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "b4b1be2d-19f7-410d-a0ca-ed273907a630",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Imported capacitance matrix with UNITS: [fF] now converted to USER UNITS:[fF] from file:\n",
"\t./Q1_TwoTransmon_CapMatrix.txt\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
" \n",
" \n",
" | | \n",
" coupler_connector_pad_Q1 | \n",
" ground_main_plane | \n",
" pad_bot_Q1 | \n",
" pad_top_Q1 | \n",
" readout_connector_pad_Q1 | \n",
"
\n",
" \n",
" \n",
" \n",
" | coupler_connector_pad_Q1 | \n",
" 59.20 | \n",
" -37.28 | \n",
" -2.01 | \n",
" -19.11 | \n",
" -0.23 | \n",
"
\n",
" \n",
" | ground_main_plane | \n",
" -37.28 | \n",
" 246.33 | \n",
" -39.79 | \n",
" -39.86 | \n",
" -37.30 | \n",
"
\n",
" \n",
" | pad_bot_Q1 | \n",
" -2.01 | \n",
" -39.79 | \n",
" 93.05 | \n",
" -30.61 | \n",
" -19.22 | \n",
"
\n",
" \n",
" | pad_top_Q1 | \n",
" -19.11 | \n",
" -39.86 | \n",
" -30.61 | \n",
" 92.99 | \n",
" -2.01 | \n",
"
\n",
" \n",
" | readout_connector_pad_Q1 | \n",
" -0.23 | \n",
" -37.30 | \n",
" -19.22 | \n",
" -2.01 | \n",
" 59.33 | \n",
"
\n",
" \n",
"
\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"path1 = \"./Q1_TwoTransmon_CapMatrix.txt\"\n",
"ta_mat, _, _, _ = load_q3d_capacitance_matrix(path1)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "4256eb88-ef19-4bbb-a5d3-b9cb8c0e968e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Imported capacitance matrix with UNITS: [fF] now converted to USER UNITS:[fF] from file:\n",
"\t./Q2_TwoTransmon_CapMatrix.txt\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
" \n",
" \n",
" | | \n",
" coupler_connector_pad_Q2 | \n",
" ground_main_plane | \n",
" pad_bot_Q2 | \n",
" pad_top_Q2 | \n",
" readout_connector_pad_Q2 | \n",
"
\n",
" \n",
" \n",
" \n",
" | coupler_connector_pad_Q2 | \n",
" 64.52 | \n",
" -38.63 | \n",
" -2.18 | \n",
" -22.93 | \n",
" -0.22 | \n",
"
\n",
" \n",
" | ground_main_plane | \n",
" -38.63 | \n",
" 267.40 | \n",
" -49.28 | \n",
" -49.30 | \n",
" -38.67 | \n",
"
\n",
" \n",
" | pad_bot_Q2 | \n",
" -2.18 | \n",
" -49.28 | \n",
" 121.38 | \n",
" -45.24 | \n",
" -23.06 | \n",
"
\n",
" \n",
" | pad_top_Q2 | \n",
" -22.93 | \n",
" -49.30 | \n",
" -45.24 | \n",
" 121.24 | \n",
" -2.18 | \n",
"
\n",
" \n",
" | readout_connector_pad_Q2 | \n",
" -0.22 | \n",
" -38.67 | \n",
" -23.06 | \n",
" -2.18 | \n",
" 64.70 | \n",
"
\n",
" \n",
"
\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"path2 = \"./Q2_TwoTransmon_CapMatrix.txt\"\n",
"tb_mat, _, _, _ = load_q3d_capacitance_matrix(path2)"
]
},
{
"cell_type": "markdown",
"id": "4ed9aaaf-2b6d-4371-a853-0a2f22e2b421",
"metadata": {},
"source": [
"### Create LOM cells from capacitance matrices"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c1fd4755-9160-4895-b722-23ba6eaa8eb3",
"metadata": {},
"outputs": [],
"source": [
"# cell 1: transmon Alice cell\n",
"\n",
"opt1 = dict(\n",
" node_rename={\n",
" \"coupler_connector_pad_Q1\": \"coupling\",\n",
" \"readout_connector_pad_Q1\": \"readout_alice\",\n",
" },\n",
" cap_mat=ta_mat,\n",
" ind_dict={(\"pad_top_Q1\", \"pad_bot_Q1\"): 10}, # junction inductance in nH\n",
" jj_dict={(\"pad_top_Q1\", \"pad_bot_Q1\"): \"j1\"},\n",
" cj_dict={(\"pad_top_Q1\", \"pad_bot_Q1\"): 2}, # junction capacitance in fF\n",
")\n",
"cell_1 = Cell(opt1)\n",
"\n",
"\n",
"# cell 2: transmon Bob cell\n",
"opt2 = dict(\n",
" node_rename={\n",
" \"coupler_connector_pad_Q2\": \"coupling\",\n",
" \"readout_connector_pad_Q2\": \"readout_bob\",\n",
" },\n",
" cap_mat=tb_mat,\n",
" ind_dict={(\"pad_top_Q2\", \"pad_bot_Q2\"): 12}, # junction inductance in nH\n",
" jj_dict={(\"pad_top_Q2\", \"pad_bot_Q2\"): \"j2\"},\n",
" cj_dict={(\"pad_top_Q2\", \"pad_bot_Q2\"): 2}, # junction capacitance in fF\n",
")\n",
"cell_2 = Cell(opt2)"
]
},
{
"cell_type": "markdown",
"id": "4ceffcfc-6cc1-444e-9a92-2fe022b2385a",
"metadata": {},
"source": [
"### Make subsystems"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b2ec34e2-3a7e-4946-88c2-e497fc8d5836",
"metadata": {},
"outputs": [],
"source": [
"# subsystem 1: transmon Alice\n",
"transmon_alice = Subsystem(name=\"transmon_alice\", sys_type=\"TRANSMON\", nodes=[\"j1\"])\n",
"\n",
"\n",
"# subsystem 2: transmon Bob\n",
"transmon_bob = Subsystem(name=\"transmon_bob\", sys_type=\"TRANSMON\", nodes=[\"j2\"])\n",
"\n",
"\n",
"# subsystem 3: Alice readout resonator\n",
"q_opts = dict(\n",
" f_res=8, # resonator dressed frequency in GHz\n",
" Z0=50, # characteristic impedance in Ohm\n",
" vp=0.404314 * c_light, # phase velocity\n",
")\n",
"res_alice = Subsystem(\n",
" name=\"readout_alice\",\n",
" sys_type=\"TL_RESONATOR\",\n",
" nodes=[\"readout_alice\"],\n",
" q_opts=q_opts,\n",
")\n",
"\n",
"\n",
"# subsystem 4: Bob readout resonator\n",
"q_opts = dict(\n",
" f_res=7.6, # resonator dressed frequency in GHz\n",
" Z0=50, # characteristic impedance in Ohm\n",
" vp=0.404314 * c_light, # phase velocity\n",
")\n",
"res_bob = Subsystem(\n",
" name=\"readout_bob\", sys_type=\"TL_RESONATOR\", nodes=[\"readout_bob\"], q_opts=q_opts\n",
")"
]
},
{
"cell_type": "markdown",
"id": "fee92273-fbdb-46cf-9b5b-950cb4516146",
"metadata": {},
"source": [
"### Creat the composite system from the cells and the subsystems"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0666953a-c1e4-49b2-8c8e-998edf97a070",
"metadata": {},
"outputs": [],
"source": [
"composite_sys = CompositeSystem(\n",
" subsystems=[transmon_alice, transmon_bob, res_alice, res_bob],\n",
" cells=[cell_1, cell_2],\n",
" grd_node=\"ground_main_plane\",\n",
" nodes_force_keep=[\"readout_alice\", \"readout_bob\"],\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7021dfb3-62e0-484f-8c67-b1d81f07a5ec",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"node_jj_basis:\n",
"-------------\n",
"\n",
"['j1', 'pad_bot_Q1', 'j2', 'pad_bot_Q2', 'readout_alice', 'readout_bob', 'coupling']\n",
"\n",
"nodes_keep:\n",
"-------------\n",
"\n",
"['j1', 'j2', 'readout_alice', 'readout_bob']\n",
"\n",
"\n",
"L_inv_k (reduced inverse inductance matrix):\n",
"-------------\n",
"\n",
" j1 j2 readout_alice readout_bob\n",
"j1 0.1 0.000000 0.0 0.0\n",
"j2 0.0 0.083333 0.0 0.0\n",
"readout_alice 0.0 0.000000 0.0 0.0\n",
"readout_bob 0.0 0.000000 0.0 0.0\n",
"\n",
"C_k (reduced capacitance matrix):\n",
"-------------\n",
"\n",
" j1 j2 readout_alice readout_bob\n",
"j1 63.185549 -0.766012 8.318893 -0.323188\n",
"j2 -0.766012 84.343548 -0.342145 10.039921\n",
"readout_alice 8.318893 -0.342145 55.591197 -0.144354\n",
"readout_bob -0.323188 10.039921 -0.144354 60.347427\n",
"\n",
"\n"
]
}
],
"source": [
"cg = composite_sys.circuitGraph()\n",
"print(cg)"
]
},
{
"cell_type": "markdown",
"id": "26229dbe-9842-425a-b2fd-946e17b5f29b",
"metadata": {},
"source": [
"### Generate the hilberspace from the composite system, leveraging the scqubits package"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "ef9ca844-eb2b-47ef-b7d8-9b9e4670738c",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[10, 10, 3, 3], [10, 10, 3, 3]], shape = (900, 900), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}-2.438\\times10^{+04} & 0.108j & 0.0 & 0.127j & -0.436 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-0.108j & -1.678\\times10^{+04} & 0.153j & 0.436 & 0.127j & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -0.153j & -9.184\\times10^{+03} & 0.0 & 0.617 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-0.127j & 0.436 & 0.0 & -1.638\\times10^{+04} & 0.108j & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-0.436 & -0.127j & 0.617 & -0.108j & -8.784\\times10^{+03} & \\cdots & -1.839\\times10^{-08} & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & -1.839\\times10^{-08} & \\cdots & 7.287\\times10^{+04} & 706.553j & 0.617 & 862.863j & -0.872\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & -706.553j & 8.047\\times10^{+04} & 0.0 & 0.872 & 862.863j\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.617 & 0.0 & 7.327\\times10^{+04} & 499.608j & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & -862.863j & 0.872 & -499.608j & 8.087\\times10^{+04} & 706.553j\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & -0.872 & -862.863j & 0.0 & -706.553j & 8.847\\times10^{+04}\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[10, 10, 3, 3], [10, 10, 3, 3]], shape = (900, 900), type = oper, isherm = True\n",
"Qobj data =\n",
"[[-24384.00898603+0.00000000e+00j 0. +1.08232559e-01j\n",
" 0. +0.00000000e+00j ... 0. +0.00000000e+00j\n",
" 0. +0.00000000e+00j 0. +0.00000000e+00j]\n",
" [ 0. -1.08232559e-01j -16784.00898603+0.00000000e+00j\n",
" 0. +1.53063953e-01j ... 0. +0.00000000e+00j\n",
" 0. +0.00000000e+00j 0. +0.00000000e+00j]\n",
" [ 0. +0.00000000e+00j 0. -1.53063953e-01j\n",
" -9184.00898603+0.00000000e+00j ... 0. +0.00000000e+00j\n",
" 0. +0.00000000e+00j 0. +0.00000000e+00j]\n",
" ...\n",
" [ 0. +0.00000000e+00j 0. +0.00000000e+00j\n",
" 0. +0.00000000e+00j ... 73269.11342615+0.00000000e+00j\n",
" 0. +4.99608155e+02j 0. +0.00000000e+00j]\n",
" [ 0. +0.00000000e+00j 0. +0.00000000e+00j\n",
" 0. +0.00000000e+00j ... 0. -4.99608155e+02j\n",
" 80869.11342615+0.00000000e+00j 0. +7.06552629e+02j]\n",
" [ 0. +0.00000000e+00j 0. +0.00000000e+00j\n",
" 0. +0.00000000e+00j ... 0. +0.00000000e+00j\n",
" 0. -7.06552629e+02j 88469.11342615+0.00000000e+00j]]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hilbertspace = composite_sys.create_hilbertspace()\n",
"hilbertspace = composite_sys.add_interaction()\n",
"hilbertspace.hamiltonian()"
]
},
{
"cell_type": "markdown",
"id": "d5e863ce-26e3-41da-a503-7691f55585c3",
"metadata": {},
"source": [
"### Print the results"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "7b826d90-0b97-4caf-9f33-19212b763cbc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished eigensystem. \n",
"\n",
"system frequencies in GHz:\n",
"--------------------------\n",
"{'transmon_alice': 6.053360688806868, 'transmon_bob': 4.7989883222888094, 'readout_alice': 8.009054820710865, 'readout_bob': 7.604412010766995}\n",
"\n",
"Chi matrices in MHz\n",
"--------------------------\n",
" transmon_alice transmon_bob readout_alice readout_bob\n",
"transmon_alice -353.239816 -0.542895 -4.132854 -0.003120\n",
"transmon_bob -0.542895 -263.940098 -0.001154 -1.460416\n",
"readout_alice -4.132854 -0.001154 4.283111 -0.000017\n",
"readout_bob -0.003120 -1.460416 -0.000017 3.829744\n"
]
}
],
"source": [
"hamiltonian_results = composite_sys.hamiltonian_results(hilbertspace, evals_count=30)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5138689d-3384-4763-aeef-ad9a7d481ae8",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" transmon_alice | \n",
" transmon_bob | \n",
" readout_alice | \n",
" readout_bob | \n",
"
\n",
" \n",
" \n",
" \n",
" | transmon_alice | \n",
" -353.239816 | \n",
" -0.542895 | \n",
" -4.132854 | \n",
" -0.003120 | \n",
"
\n",
" \n",
" | transmon_bob | \n",
" -0.542895 | \n",
" -263.940098 | \n",
" -0.001154 | \n",
" -1.460416 | \n",
"
\n",
" \n",
" | readout_alice | \n",
" -4.132854 | \n",
" -0.001154 | \n",
" 4.283111 | \n",
" -0.000017 | \n",
"
\n",
" \n",
" | readout_bob | \n",
" -0.003120 | \n",
" -1.460416 | \n",
" -0.000017 | \n",
" 3.829744 | \n",
"
\n",
" \n",
"
\n",
"