Add dbi notebooks to documentation

doc/source/code-examples/applications-by-algorithm.rst

@@ -76,4 +76,13 @@ Diagonalization Algorithms
 .. toctree::
     :maxdepth: 1
 
-    tutorials/dbi/dbi.ipynb
+    tutorials/dbi/README.md
+
+    tutorials/dbi/dbi_cost_functions.ipynb
+    tutorials/dbi/dbi_gradient_descent_strategies.ipynb
+    tutorials/dbi/dbi_group_commutator_tests.ipynb
+    tutorials/dbi/dbi_scheduling.ipynb
+    tutorials/dbi/dbi_strategies_compare.ipynb
+    tutorials/dbi/dbi_strategy_Ising_model.ipynb
+    tutorials/dbi/dbi_strategy_Pauli-Z.ipynb
+    tutorials/dbi/dbi_tutorial_basic_intro.ipynb

doc/source/code-examples/applications-by-topic.rst

@@ -61,7 +61,6 @@ Quantum Physics
     tutorials/bell-variational/README.md
     tutorials/falqon/README.md
     tutorials/grover/README.md
-    tutorials/dbi/dbi.ipynb
 
 Quantum Machine Learning
 ^^^^^^^^^^^^^^^^^^^^^^^^

doc/source/code-examples/applications.rst

@@ -69,8 +69,6 @@ Quantum Physics
     tutorials/bell-variational/README.md
     tutorials/falqon/README.md
     tutorials/grover/README.md
-    tutorials/dbi/dbi.ipynb
-
 
 Quantum Machine Learning
 ^^^^^^^^^^^^^^^^^^^^^^^^

doc/source/code-examples/tutorials/dbi/README.md

@@ -0,0 +1 @@
+../../../../../examples/dbi/README.md

doc/source/code-examples/tutorials/dbi/dbi_cost_functions.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_cost_functions.ipynb

doc/source/code-examples/tutorials/dbi/dbi_gradient_descent_strategies.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_gradient_descent_strategies.ipynb

doc/source/code-examples/tutorials/dbi/dbi_group_commutator_tests.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_group_commutator_tests.ipynb

doc/source/code-examples/tutorials/dbi/dbi_scheduling.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_scheduling.ipynb

doc/source/code-examples/tutorials/dbi/dbi_strategies_compare.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_strategies_compare.ipynb

doc/source/code-examples/tutorials/dbi/dbi_strategy_Ising_model.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_strategy_Ising_model.ipynb

doc/source/code-examples/tutorials/dbi/dbi_strategy_Pauli-Z.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_strategy_Pauli-Z.ipynb

doc/source/code-examples/tutorials/dbi/dbi_tutorial_basic_intro.ipynb

@@ -0,0 +1 @@
+../../../../../examples/dbi/dbi_tutorial_basic_intro.ipynb

examples/dbi/README.md

@@ -0,0 +1,54 @@
+# Double-bracket quantum algorithms
+
+Qibo features a model implementing double-bracke quantum algorithms (DBQAs) which are helpful for approximating eigenstates based on the ability to run the evolution under the input Hamiltonian.
+
+More specifically, given a Hamiltonian $H_0$, how can we find a circuit which after applying to the reference state (usually $|0\rangle^{\otimes L}$ for $L$ qubits) will approximate an eigenstate?
+
+A standard way is to run variational quantum circuits. For example, Qibo already features  the `VQE` model [2] which provides the implementation of the variational quantum eigensolver framework.
+DBQAs allow to go beyond VQE in that they take a different approach to compiling the quantum circuit approximating the eigenstate.
+
+## What is the unitary of DBQA?
+
+Given $H_0$ we begin by assuming that we were given a diagonal and hermitian operator $D_0$ and a time $s_0$.
+The `dbi` module provides numerical strategies for selecting them.
+For any such choice we define the bracket
+$$ W_0 = [D_0, H_0]$$
+and the double-bracket rotation (DBR) of the input Hamiltonian to time $s$
+$$H_0(s) = e^{sW} H e^{- s W}$$
+
+### Why are double-bracket rotations useful?
+We can show that the magnitude of the off-diagonal norms will decrease.
+For this let us set the notation that $\sigma(A)$ is the restriction to the off-diagonal of the matrix A.
+In `numpy` this can be implemented by `\sigma(A) = A-np.diag(A)`. In Qibo we implement this as
+https://github.com/qiboteam/qibo/blob/8c9c610f5f2190b243dc9120a518a7612709bdbc/src/qibo/models/dbi/double_bracket.py#L145-L147
+which is part of the basic `DoubleBracketIteration` class in the `dbi` module.
+
+With this notation we next use the Hilbert-Schmidt scalar product and norm to measure the progress of diagonalization
+ $$||\sigma(H_0(s))||^2- ||\sigma (H_0 )||^2= -2s \langle W, [H,\sigma(H)\rangle+O(s^2)$$
+This equation tells us that as long as the scalar product $\langle W, [H,\sigma(H)\rangle$ is positive then after the DBR the magnitude of the off-diagonal couplings in $H_0(s)$ is less than in $H_0$.
+
+For the implementation of the DBR unitary $U_0(s) = e^{-s W_0}$ see
+https://github.com/qiboteam/qibo/blob/363a6e5e689e5b907a7602bd1cc8d9811c60ee69/src/qibo/models/dbi/double_bracket.py#L68
+
+### How to choose $D$?
+
+For theoretical considerations the canonical bracket is useful.
+For this we need the notation of the dephasing channel $\Delta(H)$ which is equivalent to `np.diag(h)`.
+ $M = [\Delta(H),\sigma(H)]= [H,\sigma(H)]= [\Delta(H),H]$
+ The canonical bracket appears on its own in the monotonicity relation above and gives an unconditional reduction of the magnitude of the off-diagonal terms
+ $$||\sigma(H_0(s))||^2- ||\sigma (H_0 )||^2= -2s \|M\|^2+O(s^2)$$
+- the multi qubit Pauli Z generator with $Z(\mu) = (Z_1)^{\mu_1}\ldots (Z_L)^{\mu_L}$ where we optimize over all binary strings $\mu\in \{0,1\}^L$
+- the magnetic field $D = \sum_i B_i Z_i$
+- the two qubit Ising model $D  = \sum_i B_i Z_i + \sum_{i,j} J_{i,j} Z_i Z_j$, please follow the tutorial by Matteo and use the QIBO ising model for that with $h=0$
+
+
+### How to choose s?
+
+
+
+
+
+
+[1] https://arxiv.org/abs/2206.11772
+
+[2] https://github.com/qiboteam/vqe-sun

examples/dbi/dbi_gradient_descent_strategies.ipynb

@@ -19,9 +19,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from qibo.models.dbi.double_bracket import *\n",
-    "from qibo.models.dbi.utils import *\n",
-    "from qibo.models.dbi.utils_dbr_strategies import *\n",
+    "from qibo.models.dbi.double_bracket import DoubleBracketIteration, DoubleBracketGeneratorType, DoubleBracketScheduling, DoubleBracketCostFunction\n",
+    "from qibo.models.dbi.utils import generate_pauli_operator_dict, decompose_into_pauli_basis, params_to_diagonal_operator, ParameterizationTypes\n",
+    "from copy import deepcopy\n",
+    "from qibo.models.dbi.utils_dbr_strategies import gradient_descent\n",
     "import numpy as np\n",
     "from qibo import set_backend, hamiltonians\n",
     "from qibo.hamiltonians import Hamiltonian\n",
@@ -44,7 +45,7 @@
     "    except TypeError:\n",
     "        im = ax.imshow(np.absolute(matrix.get()), cmap=\"inferno\")\n",
     "    fig.colorbar(im, ax=ax)\n",
-    "    \n",
+    "\n",
     "def s_hist_to_plot(s_hist):\n",
     "    # convert list of step durations taken to plotable\n",
     "    s_plot = [0] * len(s_hist)\n",
@@ -103,7 +104,7 @@
     "pauli_operator_dict = generate_pauli_operator_dict(nqubits)\n",
     "pauli_operators = list(pauli_operator_dict.values())\n",
     "# let initial d be approximation of $\\Delta(H)\n",
-    "d_coef_pauli = decompose_into_Pauli_basis(dbi.diagonal_h_matrix, pauli_operators=pauli_operators)\n",
+    "d_coef_pauli = decompose_into_pauli_basis(dbi.diagonal_h_matrix, pauli_operators=pauli_operators)\n",
     "d_pauli = sum([d_coef_pauli[i]*pauli_operators[i] for i in range(nqubits)])\n",
     "\n",
     "# Computational basis\n",
@@ -136,7 +137,7 @@
    "outputs": [],
    "source": [
     "# 1. Pauli-basis\n",
-    "NSTEPS = 10\n",
+    "NSTEPS = 5\n",
     "dbi_pauli = deepcopy(dbi)\n",
     "loss_hist_pauli, d_params_hist_pauli, s_hist_pauli = gradient_descent(dbi_pauli, NSTEPS, d_coef_pauli, ParameterizationTypes.pauli, pauli_operator_dict=pauli_operator_dict)"
    ]
@@ -227,7 +228,7 @@
     "pauli_operator_dict = generate_pauli_operator_dict(nqubits)\n",
     "pauli_operators = list(pauli_operator_dict.values())\n",
     "# let initial d be approximation of $\\Delta(H)\n",
-    "d_coef_pauli = decompose_into_Pauli_basis(dbi.diagonal_h_matrix, pauli_operators=pauli_operators)\n",
+    "d_coef_pauli = decompose_into_pauli_basis(dbi.diagonal_h_matrix, pauli_operators=pauli_operators)\n",
     "d_pauli = sum([d_coef_pauli[i]*pauli_operators[i] for i in range(nqubits)])\n",
     "\n",
     "# Computational basis\n",
@@ -249,7 +250,7 @@
    "outputs": [],
    "source": [
     "# 1. Pauli-basis\n",
-    "NSTEPS = 10\n",
+    "NSTEPS = 3\n",
     "dbi_pauli = deepcopy(dbi)\n",
     "loss_hist_pauli, d_params_hist_pauli, s_hist_pauli = gradient_descent(dbi_pauli, NSTEPS, d_coef_pauli, ParameterizationTypes.pauli, pauli_operator_dict=pauli_operator_dict)"
    ]
@@ -334,34 +335,9 @@
     ")\n",
     "assert (operator_element.diagonal() == params).all()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "DBF_qibo",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.11.7"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }

examples/dbi/dbi_group_commutator_tests.ipynb

@@ -12,9 +12,7 @@
     "import matplotlib.pyplot as plt\n",
     "\n",
     "from qibo import hamiltonians, set_backend\n",
-    "from qibo.models.dbi.double_bracket import DoubleBracketGeneratorType, DoubleBracketScheduling, DoubleBracketIteration, DoubleBracketCostFunction\n",
-    "from qibo.models.dbi.utils import *\n",
-    "from qibo.models.dbi.utils_scheduling import *"
+    "from qibo.models.dbi.double_bracket import DoubleBracketGeneratorType, DoubleBracketScheduling, DoubleBracketIteration, DoubleBracketCostFunction"
    ]
   },
   {
@@ -61,8 +59,8 @@
     "    dbi_eval.mode = DoubleBracketGeneratorType.single_commutator\n",
     "    dbi_eval(s_space[s],d=d)\n",
     "    off_diagonal_norm_diff[s,0] = dbi_eval.off_diagonal_norm\n",
-    "   \n",
-    "    \n",
+    "\n",
+    "\n",
     "\n",
     "plt.figure()\n",
     "plt.plot(s_space, off_diagonal_norm_diff[:,0],label=r'$e^{sW}$')\n",
@@ -118,31 +116,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "dbi",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.11.7"
-  },
-  "orig_nbformat": 4,
-  "vscode": {
-   "interpreter": {
-    "hash": "43f1f904380137ff38e17e8a93371c4872e6bababc18e270d8a0497ea5c7ea38"
-   }
-  }
- },
+ "metadata": {},
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }

examples/dbi/dbi_scheduling.ipynb

@@ -29,8 +29,10 @@
     "\n",
     "from qibo import hamiltonians, set_backend\n",
     "from qibo.models.dbi.double_bracket import DoubleBracketGeneratorType, DoubleBracketScheduling, DoubleBracketIteration\n",
-    "from qibo.models.dbi.utils import *\n",
-    "from qibo.models.dbi.utils_scheduling import *"
+    "from qibo.hamiltonians import SymbolicHamiltonian\n",
+    "from qibo.models.dbi.utils import str_to_symbolic, generate_Z_operators\n",
+    "from qibo.models.dbi.utils_scheduling import polynomial_step\n",
+    "from qibo.models.dbi.utils_dbr_strategies import select_best_dbr_generator"
    ]
   },
   {
@@ -326,7 +328,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "NSTEPS = 8\n",
+    "NSTEPS = 3\n",
     "scheduling_list = [DoubleBracketScheduling.grid_search,\n",
     "                   DoubleBracketScheduling.hyperopt,\n",
     "                   DoubleBracketScheduling.polynomial_approximation,\n",
@@ -424,32 +426,30 @@
     "    print(n, step)\n",
     "print(dbi.choose_step(n=1))"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.11.7"
-  },
-  "vscode": {
-   "interpreter": {
-    "hash": "48caf7dabad7b721a854729228548373f17e53f40870080394d552284aea7c35"
-   }
-  }
- },
+ "metadata": {},
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }