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@mttmantovani
Last active October 10, 2019 16:50
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# QuTiP example notebook\n",
"\n",
"A few useful links:\n",
"\n",
"* [Python official tutorial](https://docs.python.org/3/tutorial/); \n",
"* [QuTiP official website](http://qutip.org);\n",
"* [QuTiP users manual](http://qutip.org/docs/latest/guide/guide.html);\n",
"* [QuTiP tutorials](http://qutip.org/tutorials.html);\n",
"\n",
"* To install `python3` on the MacBook, follow [this guide](https://docs.python-guide.org/starting/install3/osx/);\n",
"* `python` uses a package manager, `pip`. To install it, launch this command on the terminal:\n",
"\n",
" ```\n",
" sudo pip install --upgrade pip\n",
" ```\n",
"* Install QuTiP with the command: \n",
" ```\n",
" pip install qutip\n",
" ```\n",
" it should also install other useful packages like `numpy`, `scipy` and `matplotlib`.\n",
"\n",
" \n",
" \n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Two coupled qubits (time evolution without dissipation)\n",
"\n",
"Here, we will consider the problem of two qubits coupled with a simple interaction and will compute the time evolution. \n",
"The model Hamiltonian is the following:\n",
"\n",
"$$\n",
"H = \\frac{\\omega_1}{2} \\sigma_z^{(1)} + \\frac{\\omega_2}{2}\\sigma_z^{(2)} + J_x \\sigma_x^{(1)} \\sigma_x^{(2)},\n",
"$$\n",
"\n",
"with $\\omega_i$ the qubit frequencies and $J_x$ the coupling strength ($i = 1, 2$).\n",
"\n",
"For the moment, we will not consider any dissipation in the system. The evolution is thus given by the Schrödinger equation, $i \\frac{d\\psi}{dt} = H \\psi$, or Liouville equation for the density matrix, $\\dot{\\rho} = -i [H, \\rho]$ ($\\hbar=1$). We will plot the evolution of the two qubit populations over time."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [],
"source": [
"# This imports the module (QuTiP) so that we can access its functions\n",
"import qutip as qt\n",
"\n",
"# This import numpy which is useful for array operations\n",
"import numpy as np\n",
"\n",
"\n",
"\n",
"# Define the value of the parameters\n",
"w1 = 1.\n",
"w2 = 0.5\n",
"Jx = 0.2\n",
"\n",
"# Now, we need to define the operators for the system in order to build the hamiltonian.\n",
"# The Hilbert space of the system is 4-dimensional. \n",
"# We can define the sigma_z and sigma_x operator acting on qubit 1 (or 2) with the tensor product\n",
"\n",
"sz1 = qt.tensor(qt.sigmaz(), qt.identity(2)) # Note that for qubit 2 we use the identity\n",
"sz2 = qt.tensor(qt.identity(2), qt.sigmaz())\n",
"sx1 = qt.tensor(qt.sigmax(), qt.identity(2)) \n",
"sx2 = qt.tensor(qt.identity(2), qt.sigmax())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To view, e.g., the matrix form of the $\\sigma_z^{(1)}$ and $\\sigma_x^{(2)}$ operators we can use `print`:"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sz1:\n",
"Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
"Qobj data =\n",
"[[ 1. 0. 0. 0.]\n",
" [ 0. 1. 0. 0.]\n",
" [ 0. 0. -1. 0.]\n",
" [ 0. 0. 0. -1.]]\n",
"sz2:\n",
"Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
"Qobj data =\n",
"[[0. 1. 0. 0.]\n",
" [1. 0. 0. 0.]\n",
" [0. 0. 0. 1.]\n",
" [0. 0. 1. 0.]]\n"
]
}
],
"source": [
"print('sz1:')\n",
"print(sz1)\n",
"\n",
"print('sx2:')\n",
"print(sx2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can construct the Hamiltonian by simply multiplying the operators:"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
"Qobj data =\n",
"[[ 0.75 0. 0. 0.2 ]\n",
" [ 0. 0.25 0.2 0. ]\n",
" [ 0. 0.2 -0.25 0. ]\n",
" [ 0.2 0. 0. -0.75]]\n"
]
}
],
"source": [
"H = 0.5*w1*sz1 + 0.5*w2*sz2 + Jx*sx1*sx2\n",
"\n",
"print(H)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The next step is the solution of the Schrödinger equation. We use the QuTip function `mesolve` (which will also solve the Lindblad equation with dissipation). We will need \n",
"\n",
"1) an initial state for our system; \n",
"2) a list of times at which to compute the evolution; \n",
"3) a list of operators of which we want the expectation value at all times. \n",
"\n",
"As initial state we will consider the qubit 1 in the ground state and the qubit 2 in the excited state. The single-qubit states can be accessed through `qt.basis(2, 0)` (excited state) and `qt.basis(2, 1)` (ground state). They both return a vector of two components:"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
"Qobj data =\n",
"[[1.]\n",
" [0.]]\n",
"Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [1.]]\n"
]
}
],
"source": [
"print(qt.basis(2,0))\n",
"\n",
"print(qt.basis(2,1))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To build the two-qubit initial state $\\psi_0$, we again tensorize them:"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [0.]\n",
" [1.]\n",
" [0.]]\n"
]
}
],
"source": [
"psi0 = qt.tensor(qt.basis(2,1), qt.basis(2,0))\n",
"\n",
"print(psi0)"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# List of times. Recall that the time is in units of the unit of energy set with the hamiltonian (hbar=1)\n",
"tlist = np.linspace(0, 100, 1001)\n",
"\n",
"# List of operators of which we want expectation values to be computed (just sigma_z for now)\n",
"e_ops = [sz1, sz2]\n",
"\n",
"# This is an empty list of 'collapse' operators. They are used when there is dissipation\n",
"c_ops = []\n",
"\n",
"# Solve the equation and save all data in an object `result`.\n",
"result = qt.mesolve(H, psi0, tlist, c_ops, e_ops) \n",
"\n",
"# We can access the two arrays of expectation values and reference them with two different names\n",
"e_sz1 = result.expect[0]\n",
"e_sz2 = result.expect[1]\n",
"\n",
"# We now use `matplotlib` to plot the results (expectation values of $\\sigma_z$ for both qubits)\n",
"\n",
"# Import the plotting package\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(12,6))\n",
"ax.plot(tlist, np.real(e_sz1)) # We convert the arrays to real because maybe there are small imaginary parts\n",
"ax.plot(tlist, np.real(e_sz2)) \n",
"\n",
"ax.legend((r\"$\\langle\\sigma_z^{(1)}\\rangle$\", r\"$\\langle\\sigma_z^{(2)})\\rangle$\")) # Set up a legend\n",
"ax.set_xlabel(r\"$\\omega_1 t$\") # Set the x-axis label (time is in units of \\omega_1)\n",
"\n",
"plt.show() # Show the plot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Two coupled qubits with dissipation (Lindblad Master Equation)\n",
"\n",
"We will now add a simple relaxation rate $\\Gamma$ to both qubits, and include it in a Lindblad equation.\n",
"The evolution of the system density matrix $\\rho$ takes the form:\n",
"\n",
"$$ \n",
"\\dot{\\rho} = -i [H, \\rho] + \\Gamma \\mathcal{D}[\\sigma_z^{(1)}]\\rho + \\Gamma \\mathcal{D}[\\sigma_z^{(2)}] \\rho,\n",
"$$\n",
"\n",
"with the dissipator $\\mathcal{D}[x]\\rho = x \\rho x^\\dagger - \\frac{1}{2}\\{x^\\dagger x, \\rho\\}$.\n",
"\n",
"To include this in QuTiP, we will still use the master equation solver `mesolve`, but we will add two \"collapse operators\" given by $c_1 = \\sqrt{\\Gamma} \\sigma_z^{(1)}$ and $c_2 = \\sqrt{\\Gamma} \\sigma_z^{(2)}$ (see [here](http://qutip.org/docs/latest/guide/guide-dynamics.html) for more details on how this is implemented). The initial state and the list of times are the same as before."
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"G = 0.015 # Gamma\n",
"\n",
"c_ops = [np.sqrt(G)*sz1, np.sqrt(G)*sz2]\n",
"\n",
"result_dissipation = qt.mesolve(H, psi0, tlist, c_ops, e_ops) \n",
"e_sz1_diss = result_dissipation.expect[0]\n",
"e_sz2_diss = result_dissipation.expect[1]\n",
"\n",
"\n",
"fig, ax = plt.subplots(figsize=(12,6))\n",
"ax.plot(tlist, np.real(e_sz1_diss)) # We convert the arrays to real because maybe there are small imaginary parts\n",
"ax.plot(tlist, np.real(e_sz2_diss)) \n",
"\n",
"ax.legend((r\"$\\langle\\sigma_z^{(1)}\\rangle$\", r\"$\\langle\\sigma_z^{(2)})\\rangle$\")) # Set up a legend\n",
"ax.set_xlabel(r\"$\\omega_1 t$\") # Set the x-axis label (time is in units of \\omega_1)\n",
"\n",
"plt.show()\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As one can see the two qubits tend to the equilibrium state."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Two coupled qubits with dissipation (Quantum Trajectories)\n",
"\n",
"We will repeat here part 2, but using the quantum trajectories method (see [here](http://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html) for details). The advantage of the quantum trajectories method is that it doesn't require the full density matrix of the system, but repeats the evolution many times for a given initial state and a for a set of quantum jumps which are performed stochastically (they are given again by the collapse operators). When the number of trajectories is large, the same result from the Lindblad equation should be recovered. Here we can change the number of trajectories in the `mcsolve` function to compare it to the Lindblad evolution. The advantage of the quantum trajectories method is more apparent when one deals with large Hilbert spaces, such as systems including cavities with many states available."
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10.0%. Run time: 0.77s. Est. time left: 00:00:00:06\n",
"20.0%. Run time: 1.46s. Est. time left: 00:00:00:05\n",
"30.0%. Run time: 2.09s. Est. time left: 00:00:00:04\n",
"40.0%. Run time: 2.73s. Est. time left: 00:00:00:04\n",
"50.0%. Run time: 3.34s. Est. time left: 00:00:00:03\n",
"60.0%. Run time: 3.91s. Est. time left: 00:00:00:02\n",
"70.0%. Run time: 4.55s. Est. time left: 00:00:00:01\n",
"80.0%. Run time: 5.22s. Est. time left: 00:00:00:01\n",
"90.0%. Run time: 5.89s. Est. time left: 00:00:00:00\n",
"100.0%. Run time: 6.53s. Est. time left: 00:00:00:00\n",
"Total run time: 6.56s\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
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"source": [
"result_montecarlo = qt.mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=600) \n",
"e_sz1_MC = result_montecarlo.expect[0]\n",
"e_sz2_MC = result_montecarlo.expect[1]\n",
"\n",
"\n",
"fig, ax = plt.subplots(figsize=(12,6))\n",
"ax.plot(tlist, np.real(e_sz1_diss), lw=2) \n",
"ax.plot(tlist, np.real(e_sz2_diss), lw=2) \n",
"ax.plot(tlist, np.real(e_sz1_MC), ls='--')\n",
"ax.plot(tlist, np.real(e_sz2_MC), ls='--') \n",
"\n",
"ax.legend((r\"$\\langle\\sigma_z^{(1)}\\rangle$ (Lindblad)\", r\"$\\langle\\sigma_z^{(2)})\\rangle$ (Lindblad)\",\n",
" r\"$\\langle\\sigma_z^{(1)}\\rangle$ (Monte Carlo)\", r\"$\\langle\\sigma_z^{(2)})\\rangle$ (Monte Carlo)\"))\n",
"ax.set_xlabel(r\"$\\omega_1 t$\") \n",
"\n",
"plt.show()"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Two qubits + cavity, steady state solver\n",
"\n",
"Here, we will add a cavity to the system (coupled to both qubits) and find the steady state $\\rho_\\mathrm{st}$ of the system, i.e., the solution to the equation $\\dot{\\rho} = 0$.\n",
"\n",
"The new Hamiltonian reads:\n",
"\n",
"$$\n",
"H = \\frac{\\omega_1}{2} \\sigma_z^{(1)} + \\frac{\\omega_2}{2}\\sigma_z^{(2)} + J_x \\sigma_x^{(1)} \\sigma_x^{(2)} + \\omega_c b^\\dagger b + g (b + b^\\dagger)(\\sigma_z^{(1)} + \\sigma_z^{(2)}).\n",
"$$\n",
"\n",
"The cavity has frequency $\\omega_c$ and is coupled with strength $g$ to the qubits. To include the decay of the cavity in the Lindblad equation, we modify it as following:\n",
"\n",
"\n",
"$$ \n",
"\\dot{\\rho} = -i [H, \\rho] + \\Gamma \\mathcal{D}[\\sigma_z^{(1)}]\\rho + \\Gamma \\mathcal{D}[\\sigma_z^{(2)}] \\rho + \\kappa ( 1 + n_\\mathrm{th}) \\mathcal{D}[b]\\rho + \\kappa n_\\mathrm{th} \\mathcal{D}[b^\\dagger] \\rho \\equiv \\mathcal{L} \\rho\n",
"$$\n",
"\n",
"with the thermal equilibrium occupation at temperature $T$, $n_\\mathrm{th} = [e^{\\omega_c / T} - 1]^{-1}$ ($k_B = 1$).\n",
"The Liouvillian operator $\\mathcal{L}$ will be build by QuTiP and we will find its steady-state, i.e., its null eigenvector.\n",
"\n",
"In order to include the cavity, we must choose a maximum number of Fock states to be included, since the actual number of Fock states available is infinite and cannot be fully included numerically. Furthermore, we must rebuild all the operators for the qubits with the `tensor` function, since now the system has become tripartite.\n",
"\n",
"The annihilation operator for a bosonic mode is implemented in `qutip` through the function `destroy`. The creation operator is given by the function `create`, but we can also access it by taking the hermitian conjugate of `destroy` with the `.dag()` method (which stands for \"dagger\"). After building the new Hamiltonian, we choose a temperature and build the new collapse operators. Then, we can build the Liouvillian and find the steady state with the builtin `qutip` functions, `liovillian` and `steadystate`. At the end, we will compute a few expectation values on the steady state, with the `expect` function. An useful value to compute is the expectation value of the commutator of the bosonic mode, $\\langle[b, b^\\dagger]\\rangle$. If it is too different from 1, it means that the number of states chosen is too small."
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<sz1> = -0.3666177559891698\n",
"<sz2> = -0.36661775598916957\n",
"<nph> = 0.6433339176497366\n",
"<[b, b*]> = 0.9999998025755675\n"
]
}
],
"source": [
"Nmax = 20 # Number of states \n",
"wc = 1. # Cavity frequency\n",
"g = 0.1 # Cavity-qubit coupling\n",
"T = 1 # Temperature\n",
"k = 0.05 # Cavity decay rate\n",
"\n",
"b = qt.tensor(qt.identity(2), qt.identity(2), qt.destroy(Nmax)) # Annihilation operator\n",
"sz1 = qt.tensor(qt.sigmaz(), qt.identity(2), qt.identity(Nmax)) # Rebuild qutip operators\n",
"sz2 = qt.tensor(qt.identity(2), qt.sigmaz(), qt.identity(Nmax)) \n",
"sx1 = qt.tensor(qt.sigmax(), qt.identity(2), qt.identity(Nmax)) \n",
"sx2 = qt.tensor(qt.identity(2), qt.sigmax(), qt.identity(Nmax)) \n",
"\n",
"H = 0.5*w1*sz1 + 0.5*w2*sz2 + Jx*sx1*sx2 + wc*b.dag()*b + g*(b.dag() + b)*(sz1 + sz2)\n",
"\n",
"\n",
"# Here we define the Bose function\n",
"def nb(e, T):\n",
" if T==0 or e==0:\n",
" return 0.\n",
" else:\n",
" return 1./(np.exp(e/T) - 1.)\n",
"\n",
"# New collapse operators\n",
"c_ops = [np.sqrt(G)*sz1, np.sqrt(G)*sz1, np.sqrt(k*(nb(wc, T)+1))*b, np.sqrt(k*nb(wc, T))*b.dag()]\n",
"\n",
"\n",
"# Build the system liouvillian\n",
"L = qt.liouvillian(H, c_ops)\n",
" \n",
"# Find steady state\n",
"rhost = qt.steadystate(L)\n",
"\n",
"# Compute some expectation values on the steady state\n",
"nph = b.dag()*b # Cavity number\n",
"comm = qt.commutator(b, b.dag())\n",
"\n",
"print(f\"<sz1> = {qt.expect(sz1, rhost)}\")\n",
"print(f\"<sz2> = {qt.expect(sz2, rhost)}\")\n",
"print(f\"<nph> = {qt.expect(nph, rhost)}\")\n",
"print(f\"<[b, b*]> = {qt.expect(comm, rhost)}\")\n"
]
},
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