02_unitary_dynamics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unitary Quantum Dynamics with Neural networks\n",
    "Filippo Vicentini\n",
    "\n",
    "7 December 2021\n",
    "\n",
    "\n",
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/PhilipVinc/NetKet-lectures/blob/master/02_unitary_dynamics.ipynb)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to solve the Schroedinger's equation of motion given an initial state $\\psi(t_0)$\n",
    "\n",
    "$$\n",
    "\\frac{d\\vert\\psi(t)\\rangle}{dt} = -i\\hat{H}\\vert\\psi(t)\\rangle\n",
    "$$\n",
    "\n",
    "To avoid the lengthy derivation of the Time-Dependent Variational-Principle (TDVP) we\n",
    "recall that the variational reformulation of imaginary time evolution, given by the ODE:\n",
    "\n",
    "$$\n",
    "\\frac{d\\vert\\psi(t)\\rangle}{d\\tau} = \\hat{H}\\vert\\psi(t)\\rangle\n",
    "$$\n",
    "where the real time has been replaced by $\\tau=it$, is given by the Stochastic-Reconfiguration\n",
    "method, where the update of the variational parameters is given by the solution to the\n",
    "linear system\n",
    "$$\n",
    "\\Delta W = -d\\tau S^{-1} \\vec{F}\n",
    "$$\n",
    "\n",
    "where $\\Delta W$ are the updates during a timestep of the parameters $W$, and where the gradient is:\n",
    "$$\n",
    "\\vec{F^j} = \\langle O^j E^\\text{loc}\\rangle = \\frac{1}{N}\\sum_\\sigma^N \\left(O^{\\star i}(\\sigma)O^j(\\sigma) - \\langle O^j\\rangle\\right) \\left(E^\\text{loc}(\\sigma) - \\langle E^\\text{loc} \\rangle \\right)\n",
    "$$\n",
    "And the S matrix is:\n",
    "$$\n",
    "\\langle S_i^j \\rangle = \\frac{1}{N}\\sum_\\sigma^N \\left(O^i(\\sigma) - \\langle O^i \\rangle\\right)^\\star\\left(O^j(\\sigma) - \\langle O^i \\rangle\\right)\n",
    "$$\n",
    "\n",
    "Therefore, it is possible to show that the TDVP requires the solution of the equation\n",
    "\n",
    "$$\n",
    "\\Delta W = -iS\\vec{F}\n",
    "$$\n",
    "\n",
    "Netket, unfortunately, does not support this out of the box, but we can't write it\n",
    "ourselves quite easily\n",
    "\n",
    "## Setting up the initial state\n",
    "The ansatz we want to work with is the Neural Quantum State, or Restricted Boltzmann\n",
    "Machine ansatz that we have first seen yesterday.\n",
    "$$\n",
    "\\log\\psi(\\sigma^1, \\sigma^2, \\dots, \\sigma^L) = \\sum_i\\log\\cosh\\left(\\sum_jW^{(i)}_j\\sigma^j  + b^j\\right)\n",
    "$$\n",
    "Notice that if the parameters $\\{W,b\\}$ are real-valued, then $\\log\\psi$will be real valued, and if they\n",
    "are complex-valued, the wavefunction will be complex-valued.\n",
    "\n",
    "Yesterday we were working with real parameters, that is, $W^i_j\\in\\mathbb{R}$ and $b^j\\in mathbb{R}.\n",
    "That was legit because the Hamiltonian of the Transverse-Ising model is real, so\n",
    "we knew that we groundstate wavefunction would have been real.\n",
    "\n",
    "However, today we want to time-evolve the system. So we must give the ansatz the\n",
    "freedom to represent any possible state. Therefore we need to use complex-valued\n",
    "parameters.\n",
    "\n",
    "We now need to define the initial state.\n",
    "If you just initialise a Neural-Quantum-State with random parameters, you will have\n",
    "a very random state.\n",
    "\n",
    "Therefore, in order to have a physically-interesting state, we will use the variational optimisation\n",
    "described yesterday in order to find the ground state of a certain hamiltonian.\n",
    "When this state has been found, we will move forward to time-integrating the Schroedinger's equation.\n",
    "\n",
    "Notice that we will be optimising the state at $g=0.5$ this time, which\n",
    "we expect to be much easier to optimise.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Installing Netket \n",
    "\n",
    "Installing NetKet is relatively straightforward. For this Tutorial, if you are running it locally on your machine, we recommend that you create a clean virtual environment and install NetKet within: \n",
    "\n",
    "```bash\n",
    "python3 -m venv netket\n",
    "source netket/bin/activate\n",
    "pip install --upgrade \"netket>=3.2\"\n",
    "```\n",
    "\n",
    "**If you are on Google Colab**, uncomment the following cell and run it to install the required packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install --upgrade netket"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Alternatively, if you want to experiment with the current master version of netket, you can run\n",
    "#! pip install 'git+https://github.com/netket/netket.git'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also want to sure that this notebook is running on the cpu. \n",
    "You can edit the field by changing \"cpu\" to \"gpu\" to make it runa on the GPU if you want. \n",
    "But you'll need to use much larger systems to see a benefit in the runtime.\n",
    "For systems with less than 40 spins GPUs slow you down remarkably."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First, let's make sure to run on CPU\n",
    "import os\n",
    "os.environ[\"JAX_PLATFORM_NAME\"] = \"cpu\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can check that the installation was succesfull doing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import netket as nk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should also check that your version of netket is at least 3.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NetKet version: 3.3.dev8+gd1eb9e981f.d20211202\n"
     ]
    }
   ],
   "source": [
    "print(f\"NetKet version: {nk.__version__}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Dynamics\n",
    "\n",
    "First, we want to setup our system and the variational state on it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import netket as nk\n",
    "\n",
    "# Define the lattice: Chains of 12 sites with PBC\n",
    "graph = nk.graph.Hypercube(12, n_dim=1, pbc=True)\n",
    "\n",
    "# Define the hilbert space of wavefunction son this lattice\n",
    "hilb = nk.hilbert.Spin(1/2, N=graph.n_nodes)\n",
    "\n",
    "# define the Neural Network ånsatz\n",
    "machine = nk.models.RBM(alpha=1, dtype=complex)\n",
    "\n",
    "# define the MC sampler\n",
    "sampler = nk.sampler.MetropolisLocal(hilb, n_chains=16, n_sweeps=graph.n_nodes)\n",
    "\n",
    "# Construct the variational Monte Carlo state by combining the sampler and the neural\n",
    "# network ansatz. We also specify a few options for the sampler.\n",
    "vs = nk.vqs.MCState(sampler, machine, n_samples=3008, n_discard_per_chain=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The state we initialised has random parameters (so it's a random wavefunction, most likely pretty flat).\n",
    "Since the hilbert space is small enough, we can plot it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa6806ff3d0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.plot(vs.to_array().real, label=\"$\\Re[\\psi(\\sigma)]$\")\n",
    "plt.plot(vs.to_array().imag, label=\"$\\Im[\\psi(\\sigma)]$\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we want to start from a specific state.\n",
    "As we don't know which parameters correspond to the state that we want, but we do know that a specific hamiltonian has the state we want as ground state, we can run a ground-state optimisation to find the good parameters.\n",
    "\n",
    "For the Ground-state optimisation we take the TFIM model with $h=0.5$, and we use Natural Gradient descent (or Stochastic Reconfiguration, as it's known in VMC literature)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": false,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "source='code/2_gs.py', evaluate=False",
     "results": "verbatim",
     "source": "code/2_gs.py",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 300/300 [00:54<00:00,  5.50it/s, Energy=-12.76261-0.00007j ± 0.00059 [σ²=0.00105, R̂=0.9993]]\n"
     ]
    }
   ],
   "source": [
    "from netket.operator.spin import sigmax\n",
    "\n",
    "# Define the Hamiltonian\n",
    "H = nk.operator.Ising(hilb, graph=graph, h=0.5, J=1.0)\n",
    "\n",
    "# Define an observable\n",
    "Mx = (1/graph.n_nodes) * sum([sigmax(hilb, i) for i in graph.nodes()])\n",
    "\n",
    "# The optimiser\n",
    "op = nk.optimizer.Sgd(learning_rate=0.05)\n",
    "\n",
    "# preconditioner for the optimiser (induces imaginary time evolution)\n",
    "sr = nk.optimizer.SR(diag_shift=0.001)\n",
    "\n",
    "# Create the optimization driver\n",
    "gs = nk.VMC(H, op, preconditioner=sr, variational_state=vs)\n",
    "\n",
    "logger = nk.logging.JsonLog(\"data/rbm1_sr_05\")\n",
    "                            \n",
    "# Run 300 steps of SR optimisation, computing Mx observable\n",
    "gs.run(300, out=logger, obs={'Mx': Mx}, show_progress=True)\n",
    "\n",
    "# We store the parameters at the end of the optimisation\n",
    "W_gs = vs.parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We first check that the optimisation was succesfull\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": true,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "include=True",
     "results": "verbatim",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Energy $\\\\langle E \\\\rangle$')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Store the output into a variable\n",
    "res_MF = logger.data\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(res_MF['Energy']['iters'], res_MF['Energy']['Mean'].real, label=r'$RBM(\\alpha=1)$')\n",
    "plt.legend()\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel(r'Energy $\\langle E \\rangle$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the magnetisation along the x direction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": false,
     "evaluate": true,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "include=True, echo=False",
     "results": "verbatim",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnetization $\\\\langle S_x \\\\rangle$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(res_MF['Mx'].iters, res_MF['Mx'].Mean.real, label=r'$RBM(\\alpha=1)$')\n",
    "plt.legend()\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel(r'Magnetization $\\langle S_x \\rangle$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time evolution\n",
    "\n",
    "First, we generate some 'exact' data using QuTiP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We build the new quenched hamiltonian, with g=1.0, under which the system evolves dynamically\n",
    "Ham_quench = nk.operator.Ising(hilb, graph=graph, h=1.0, J=1.0)\n",
    "\n",
    "# We get the initial state and Hamiltonian in qutip-format\n",
    "psi_gs_qutip = vs.to_qobj()\n",
    "Ham_quench_qutip = Ham_quench.to_qobj()\n",
    "Mx_qutip = Mx.to_qobj()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnetization')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we import qutip and use it to do the time-evolution\n",
    "import qutip as qt\n",
    "import numpy as np\n",
    "\n",
    "# I define all time-points I will be passing through\n",
    "tvals_exact = np.arange(0.0, 2.0, 0.001)\n",
    "\n",
    "# I use the Schroedinger's equation solver to integrate the Schroedinger's equation\n",
    "# with initial state psi_gs, computing Mx along the time evolution\n",
    "sol = qt.sesolve(Ham_quench_qutip, psi_gs_qutip, tvals_exact, e_ops=[Mx_qutip])\n",
    "\n",
    "# I plot Mx\n",
    "plt.plot(sol.times, sol.expect[0])\n",
    "plt.xlabel('time t')\n",
    "plt.ylabel('Magnetization')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now want to perform the full fledged time evolution with VMC\n",
    "\n",
    "First, we need to define the code to compute the timestep.\n",
    "The things to do are the following:\n",
    "\n",
    " - Estimate the energy, and it's gradient F\n",
    "   - We need to sample the wavefunction first, but that's done automatically by NetKet\n",
    " - Compute the S matrix\n",
    "   - Also done automatically by netket. We call it QGT, or Quantum Geometric Tensor, and you can easily access it.\n",
    " - solve the syste $\\Delta W = -i S \\vec{F}$\n",
    "\n",
    "So we define a function named `timestep` which takes as inputs:\n",
    " - The variational state\n",
    " - The hamiltonian generating the time-evolution\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": true,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "include=True, source='code/3_timestep.py'",
     "results": "verbatim",
     "source": "code/3_timestep.py",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [],
   "source": [
    "from jax import tree_map\n",
    "\n",
    "def timestep(vstate, hamiltonian, *, diag_shift=1e-4):\n",
    "    # Then we compute ⟨E⟩ and F=∇⟨E⟩\n",
    "    E, F = vstate.expect_and_grad(hamiltonian)\n",
    "\n",
    "    # We multiply every element of the gradient by -1.0j\n",
    "    mF = tree_map(lambda x: -1.0j * x, F)\n",
    "    \n",
    "    # We compute the QGT (or S matrix) of our state\n",
    "    S = vstate.quantum_geometric_tensor()\n",
    "    \n",
    "    # We add a diagonal shift to the QGT\n",
    "    # this is added only to the diagonal.\n",
    "    S = S + diag_shift\n",
    "    \n",
    "    # We solve the linear system\n",
    "    dW, _ = S.solve(jax.scipy.sparse.linalg.cg, mF)\n",
    "    \n",
    "    return dW"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we use this function to perform the actual time evolution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": false,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "source='code/4_tevo.py', evaluate=False",
     "results": "verbatim",
     "source": "code/4_tevo.py",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 400/400 [02:47<00:00,  2.39it/s]\n"
     ]
    }
   ],
   "source": [
    "import jax\n",
    "from tqdm import tqdm\n",
    "\n",
    "# We first build the new hamiltonian, with g=1.0\n",
    "Ham_quench = nk.operator.Ising(hilb, graph=graph, h=1.0, J=1.0)\n",
    "\n",
    "# the timestep\n",
    "dt = 0.005\n",
    "\n",
    "# I define some observables to keep track of along the time-evolution\n",
    "res = {'Sx':[]}\n",
    "\n",
    "# I define all time-points I will be passing through\n",
    "tvals = np.arange(0.0, 2.0, dt)\n",
    "\n",
    "# Set the initial cofniguration\n",
    "vs.parameters = W_gs\n",
    "\n",
    "# at every timestep\n",
    "for t in tqdm(tvals):\n",
    "    # (Before evolving): compute the observables\n",
    "    res['Sx'].append(vs.expect(Mx).mean.real)\n",
    "\n",
    "    # We compute the update of the parameters\n",
    "    dw = timestep(vs, Ham_quench, diag_shift=1e-4)\n",
    "    \n",
    "    # We update the parameters\n",
    "    vs.parameters = jax.tree_multimap(lambda w, dw: w+dt*dw, vs.parameters, dw)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Having performed the time-evoltion, we plot the data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnetization')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol.times, sol.expect[0], label='Exact (QuTiP)')\n",
    "plt.plot(tvals, res['Sx'], label=r\"RBM($\\alpha=1$)\")\n",
    "plt.legend()\n",
    "plt.xlabel('time t')\n",
    "plt.ylabel('Magnetization')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice that it does not look too great.\n",
    "\n",
    "## 3. Increasing the Representation Power\n",
    "\n",
    "We need to increase the representation power of our neural network to better approximate our state during the time-evolution. \n",
    "\n",
    "To do so, we want to change the hidden layer density from 1 to 2, which will approximately double the number of variational parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RBM(α=1) variational state has 168 parameters\n",
      "The RBM(α=2) variational state has 324 parameters\n"
     ]
    }
   ],
   "source": [
    "# define the Neural Network ånsatz\n",
    "machine2 = nk.models.RBM(alpha=2, dtype=complex)\n",
    "\n",
    "# Construct a new variational state with the new machine\n",
    "vs2 = nk.vqs.MCState(sampler, machine2, n_samples=3008, n_discard_per_chain=50)\n",
    "\n",
    "# Compare the number of parameters\n",
    "print(f\"The RBM(α=1) variational state has {vs.n_parameters} parameters\")\n",
    "print(f\"The RBM(α=2) variational state has {vs2.n_parameters} parameters\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to also optimise the initial state of the new model\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 300/300 [01:26<00:00,  3.46it/s, Energy=-12.7616+0.0003j ± 0.0011 [σ²=0.0036, R̂=0.9993]]    \n"
     ]
    }
   ],
   "source": [
    "# Create the optimization driver\n",
    "gs = nk.VMC(H, op, preconditioner=sr, variational_state=vs2)\n",
    "                            \n",
    "# Run 300 steps of SR optimisation, computing Mx observable\n",
    "log2 = nk.logging.RuntimeLog()\n",
    "gs.run(300, out=log2, obs={'Mx': Mx}, show_progress=True)\n",
    "\n",
    "W_gs2 = vs2.parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now that we have the initial parameters of the new ansatz with $\\alpha=2$, we need to perform the new time-evolution.\n",
    "\n",
    "Hopefully, you've already learnt how to write down the TDVP equations above, so we will now showcase the Dynamics driver of NetKet, which essentially integrates the same equatino as the code above does, but is more flexible and comes with a few nice additions.\n",
    "\n",
    "*NOTE*: This is a new feature of NetKet 3.3 (to be released on december 14). Make sure you have an up to date version with `pip install --upgrade netket` and by checking `netket.__version__`). If you want to run this before december 14, then `pip install 'git+https://github.com/netket/netket.git'`. Otherwise, you can just rerun the same code as above!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████▉| 1.9949999999999999/1.995 [01:37<00:00, 48.88s/it, Generator=-14.229-0.011j ± 0.040 [σ²=4.089, R̂=1.0015]]  /home/filippovicentini/Documents/pythonenvs/netket_env/lib64/python3.8/site-packages/tqdm/std.py:533: TqdmWarning: clamping frac to range [0, 1]\n",
      "  full_bar = Bar(frac,\n",
      "100%|██████████| 1.9999999999999998/1.995 [01:37<00:00, 49.00s/it, Generator=-14.229-0.011j ± 0.040 [σ²=4.089, R̂=1.0015]]\n"
     ]
    }
   ],
   "source": [
    "from netket import experimental as nkx\n",
    "\n",
    "# You can pick from many different integrators, with and without adaptive timestepping.\n",
    "# In this example we chose Euler\n",
    "integrator = nkx.dynamics.Euler(dt=dt)\n",
    "\n",
    "# We now construct the TDVP (Time-Dependent-Variational-Principle) driver\n",
    "# Note: The qgt argument takes an argument that specifies how the Quantum Geometric Tensor (or S matrix) should\n",
    "# be computed. This is a purely technical detail, but properly chosing the right implementation will give you\n",
    "# a remarkable speedup! Read more at https://www.netket.org/docs/sr.html\n",
    "te = nkx.TDVP(\n",
    "    Ham_quench, # can also be time-dependent\n",
    "    variational_state=vs2,\n",
    "    integrator=integrator, # RK-style integrator.\n",
    "    t0=0.0,     # initial integration time\n",
    "    qgt=nk.optimizer.qgt.QGTJacobianDense(holomorphic=True, diag_shift=1e-4), # QGT implementation. \n",
    ")\n",
    "\n",
    "# integrate the dynamics\n",
    "tevo2 = nk.logging.RuntimeLog()\n",
    "te.run(\n",
    "    T=tvals[-1], # end time\n",
    "    out=tevo2,   # logger\n",
    "    show_progress=True,\n",
    "    obs={\"Sx\": Mx},\n",
    "    tstops=tvals, # at what timesteps should observables be computed\n",
    ")\n",
    "\n",
    "res2 = tevo2.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": true,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "",
     "results": "verbatim",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/filippovicentini/Documents/pythonenvs/netket_env/lib64/python3.8/site-packages/numpy/core/_asarray.py:102: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnetization')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol.times, sol.expect[0], label='Exact (QuTiP)')\n",
    "plt.plot(tvals, res['Sx'], label=r\"RBM($\\alpha=1$)\")\n",
    "plt.plot(tvals, res2['Sx'], label=r\"RBM($\\alpha=2$)\")\n",
    "plt.legend()\n",
    "plt.xlabel('time t')\n",
    "plt.ylabel('Magnetization')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": false,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "evaluate=False",
     "results": "verbatim",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [],
   "source": [
    "sampler_obs = nk.sampler.MetropolisLocal(machine=machine.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Putting everything together\n",
    "If we collate all the things you have seen above, and run the optimisation, we get:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": false,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "source='code/5_open.py', evaluate=False, echo=True",
     "results": "verbatim",
     "source": "code/5_open.py",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [],
   "source": [
    "import netket as nk\n",
    "import jax\n",
    "\n",
    "L = 6\n",
    "H = build_hamiltonian(L=L, g=-0.49/2, J=0.25)\n",
    "Sx = build_Sx(L=L)\n",
    "Sy = build_Sy(L=L)\n",
    "Sz = build_Sz(L=L)\n",
    "\n",
    "# Generate the list of collapse/jump operators:\n",
    "jump_ops = []\n",
    "for i in range(L):\n",
    "    op = nk.operator.spin.sigmam(H.hilbert, i)\n",
    "    jump_ops.append(op)\n",
    "\n",
    "# Construct the Lindblad Super-Operator\n",
    "lindblad = nk.operator.LocalLiouvillian(H, jump_ops)\n",
    "\n",
    "# Construct the machine and initialise it's parameters\n",
    "machine = nk.machine.density_matrix.NdmSpin(hilbert=H.hilbert, alpha=1, beta=2)\n",
    "machine.init_random_parameters(sigma=0.01, seed=123)\n",
    "\n",
    "# Sampler for the machine\n",
    "sampler = nk.sampler.MetropolisLocal(machine, n_chains=16, sweep_size=2*L)\n",
    "# Sampler of the diagonal of the density matrix, for the observables\n",
    "sampler_obs = nk.sampler.MetropolisLocal(machine=machine.diagonal())\n",
    "\n",
    "optimizer = nk.optimizer.Sgd(machine, 0.01)\n",
    "sr = nk.optimizer.SR(machine, diag_shift=0.001, use_iterative=True)\n",
    "\n",
    "# Construct the object looking for the steady state\n",
    "ss = nk.SteadyState(lindblad, sampler, optimizer, n_samples=1000,\n",
    "                    sampler_obs=sampler_obs, n_samples_obs=500)\n",
    "\n",
    "# Run the optimisation\n",
    "ss.run(n_iter=300, out=\"data/open_ndm12_3\", obs={'Sx':Sx, 'Sy': Sy, 'Sz':Sz})\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "And if we plot the results:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": "auto",
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "options": {
     "caption": false,
     "complete": true,
     "display_data": true,
     "display_stream": true,
     "dpi": 200,
     "echo": true,
     "evaluate": true,
     "f_env": null,
     "f_pos": "htpb",
     "f_size": [
      6,
      4
     ],
     "f_spines": true,
     "fig": true,
     "include": true,
     "name": null,
     "option_string": "",
     "results": "verbatim",
     "term": false,
     "wrap": "output"
    }
   },
   "outputs": [],
   "source": [
    "ss = read_open('data/open_ndm11')\n",
    "\n",
    "fig, ax = plt.subplots(4)\n",
    "\n",
    "ax[0].plot(ss['iter'], ss['LdagL'])\n",
    "ax[0].get_xaxis().set_visible(False)\n",
    "ax[0].set(ylabel='LdagL')\n",
    "ax[1].plot(ss['iter'], ss['Sx'])\n",
    "ax[1].get_xaxis().set_visible(False)\n",
    "ax[1].set(ylabel='Sx')\n",
    "ax[2].plot(ss['iter'], ss['Sy'])\n",
    "ax[2].get_xaxis().set_visible(False)\n",
    "ax[2].set(ylabel='Sy')\n",
    "ax[3].plot(ss['iter'], ss['Sz'])\n",
    "ax[3].set(ylabel='Sz')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('Iteration step')\n",
    "plt.ylabel('Magnetization')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "python3"
  },
  "kernelspec": {
   "display_name": "Python (Netket development)",
   "language": "python",
   "name": "dev-netket"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}