Examples.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f35018b6-ff6d-43e4-aba0-4d8bbc6f85b6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "import qcopt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "28ed8c37-5134-4586-a6da-707b5295754b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = qcopt.graph_funcs.graph_from_file('benchmark_graphs/N10_d3_graphs/G1.txt')\n",
    "nx.draw_circular(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "89c7f87d-8e41-4026-ab4d-1c444b8378e9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "85cb1055-cc06-4c09-84d1-67b741866bc6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">      ░ ┌───────┐                                                                                        ░ ┌────────┐ ░ \n",
       "q_0: ─░─┤ Rx(2) ├──────────────────────o──────────────────o─────────o────────────────────────────────────░─┤ Rz(22) ├─░─\n",
       "      ░ └───┬───┘┌───────┐             │                  │         │                                    ░ ├────────┤ ░ \n",
       "q_1: ─░─────┼────┤ Rx(4) ├────o────────┼──────────────────┼─────────┼─────────o─────────o────────────────░─┤ Rz(22) ├─░─\n",
       "      ░     │    └───┬───┘┌───┴───┐    │                  │         │         │         │                ░ ├────────┤ ░ \n",
       "q_2: ─░─────┼────────o────┤ Rx(6) ├────┼──────────────────o─────────o─────────┼─────────┼────────────────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │    └───┬───┘┌───┴───┐              │         │         │         │                ░ ├────────┤ ░ \n",
       "q_3: ─░─────o────────┼────────┼────┤ Rx(8) ├──────────────o─────────┼─────────┼─────────┼─────────o──────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │        │    └───┬───┘┌────────┐    │         │         │         │         │      ░ ├────────┤ ░ \n",
       "q_4: ─░─────┼────────┼────────┼────────┼────┤ Rx(10) ├────┼─────────o─────────o─────────┼─────────o──────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │        │        │    └───┬────┘┌───┴────┐    │         │         │         │      ░ ├────────┤ ░ \n",
       "q_5: ─░─────o────────┼────────o────────o────────┼─────┤ Rx(12) ├────┼─────────┼─────────┼─────────┼──────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │        │        │        │     └────────┘┌───┴────┐    │         │         │      ░ ├────────┤ ░ \n",
       "q_6: ─░─────o────────┼────────o────────┼────────o───────────────┤ Rx(14) ├────┼─────────┼─────────┼──────░─┤ Rz(22) ├─░─\n",
       "      ░              │                 │        │               └────────┘┌───┴────┐    │         │      ░ ├────────┤ ░ \n",
       "q_7: ─░──────────────o─────────────────┼────────o─────────────────────────┤ Rx(16) ├────o─────────┼──────░─┤ Rz(22) ├─░─\n",
       "      ░              │                 │        │                         └───┬────┘┌───┴────┐    │      ░ ├────────┤ ░ \n",
       "q_8: ─░──────────────o─────────────────┼────────┼─────────────────────────────o─────┤ Rx(18) ├────o──────░─┤ Rz(22) ├─░─\n",
       "      ░                                │        │                                   └───┬────┘┌───┴────┐ ░ ├────────┤ ░ \n",
       "q_9: ─░────────────────────────────────o────────o───────────────────────────────────────o─────┤ Rx(20) ├─░─┤ Rz(22) ├─░─\n",
       "      ░                                                                                       └────────┘ ░ └────────┘ ░ </pre>"
      ],
      "text/plain": [
       "      ░ ┌───────┐                                                                                        ░ ┌────────┐ ░ \n",
       "q_0: ─░─┤ Rx(2) ├──────────────────────o──────────────────o─────────o────────────────────────────────────░─┤ Rz(22) ├─░─\n",
       "      ░ └───┬───┘┌───────┐             │                  │         │                                    ░ ├────────┤ ░ \n",
       "q_1: ─░─────┼────┤ Rx(4) ├────o────────┼──────────────────┼─────────┼─────────o─────────o────────────────░─┤ Rz(22) ├─░─\n",
       "      ░     │    └───┬───┘┌───┴───┐    │                  │         │         │         │                ░ ├────────┤ ░ \n",
       "q_2: ─░─────┼────────o────┤ Rx(6) ├────┼──────────────────o─────────o─────────┼─────────┼────────────────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │    └───┬───┘┌───┴───┐              │         │         │         │                ░ ├────────┤ ░ \n",
       "q_3: ─░─────o────────┼────────┼────┤ Rx(8) ├──────────────o─────────┼─────────┼─────────┼─────────o──────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │        │    └───┬───┘┌────────┐    │         │         │         │         │      ░ ├────────┤ ░ \n",
       "q_4: ─░─────┼────────┼────────┼────────┼────┤ Rx(10) ├────┼─────────o─────────o─────────┼─────────o──────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │        │        │    └───┬────┘┌───┴────┐    │         │         │         │      ░ ├────────┤ ░ \n",
       "q_5: ─░─────o────────┼────────o────────o────────┼─────┤ Rx(12) ├────┼─────────┼─────────┼─────────┼──────░─┤ Rz(22) ├─░─\n",
       "      ░     │        │        │        │        │     └────────┘┌───┴────┐    │         │         │      ░ ├────────┤ ░ \n",
       "q_6: ─░─────o────────┼────────o────────┼────────o───────────────┤ Rx(14) ├────┼─────────┼─────────┼──────░─┤ Rz(22) ├─░─\n",
       "      ░              │                 │        │               └────────┘┌───┴────┐    │         │      ░ ├────────┤ ░ \n",
       "q_7: ─░──────────────o─────────────────┼────────o─────────────────────────┤ Rx(16) ├────o─────────┼──────░─┤ Rz(22) ├─░─\n",
       "      ░              │                 │        │                         └───┬────┘┌───┴────┐    │      ░ ├────────┤ ░ \n",
       "q_8: ─░──────────────o─────────────────┼────────┼─────────────────────────────o─────┤ Rx(18) ├────o──────░─┤ Rz(22) ├─░─\n",
       "      ░                                │        │                                   └───┬────┘┌───┴────┐ ░ ├────────┤ ░ \n",
       "q_9: ─░────────────────────────────────o────────o───────────────────────────────────────o─────┤ Rx(20) ├─░─┤ Rz(22) ├─░─\n",
       "      ░                                                                                       └────────┘ ░ └────────┘ ░ "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you can turn individual_partial_mixers on or off to change whether the mixer is parameterized by 1 or many angles\n",
    "qaoa_circuit = qcopt.qao_ansatz.gen_qaoa(\n",
    "    G=G,\n",
    "    P=1,\n",
    "    mixer_order=None,\n",
    "    params=np.arange(1,len(G)+2,1), # need 1 angle for each mixer (= number of nodes) plus 1 more for the phase separate Rz rotations\n",
    "    init_state='0'*len(G.nodes),\n",
    "    individual_partial_mixers=True,\n",
    "    barriers=1,\n",
    "    decompose_toffoli=0\n",
    ")\n",
    "qaoa_circuit.draw(fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "69261ed2-5f2a-4359-b04f-59c223938f00",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐ ░                                                                    ░ ┌────────┐ ░                                ░ \n",
       "q_0: ┤ X ├─░────────────────────────────────o────────────────────────────o──────░─┤ Rz(16) ├─░────────────────────────────────░─\n",
       "     └───┘ ░ ┌───────┐                      │                            │      ░ ├────────┤ ░ ┌────────┐                     ░ \n",
       "q_1: ──────░─┤ Rx(2) ├────o────────o────────┼────────────────────────────┼──────░─┤ Rz(16) ├─░─┤ Rx(18) ├────o─────────o──────░─\n",
       "     ┌───┐ ░ └───┬───┘    │        │        │                            │      ░ ├────────┤ ░ └───┬────┘    │         │      ░ \n",
       "q_2: ┤ X ├─░─────o────────┼────────┼────────o────────────────────────────┼──────░─┤ Rz(16) ├─░─────o─────────┼─────────┼──────░─\n",
       "     └───┘ ░     │        │        │        │                        ┌───┴────┐ ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_3: ──────░─────┼────────┼────────┼────────┼──────────────────o─────┤ Rx(14) ├─░─┤ Rz(16) ├─░─────┼─────────┼─────────┼──────░─\n",
       "           ░     │        │        │        │    ┌────────┐    │     └───┬────┘ ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_4: ──────░─────┼────────┼────────o────────o────┤ Rx(10) ├────o─────────┼──────░─┤ Rz(16) ├─░─────┼─────────┼─────────o──────░─\n",
       "     ┌───┐ ░     │        │        │        │    └───┬────┘    │         │      ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_5: ┤ X ├─░─────┼────────┼────────┼────────┼────────┼─────────┼─────────o──────░─┤ Rz(16) ├─░─────┼─────────┼─────────┼──────░─\n",
       "     └───┘ ░     │        │        │    ┌───┴───┐    │         │         │      ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_6: ──────░─────┼────────┼────────┼────┤ Rx(8) ├────o─────────┼─────────┼──────░─┤ Rz(16) ├─░─────┼─────────┼─────────┼──────░─\n",
       "           ░     │        │    ┌───┴───┐└───────┘    │         │         │      ░ ├────────┤ ░     │         │     ┌───┴────┐ ░ \n",
       "q_7: ──────░─────o────────o────┤ Rx(6) ├─────────────o─────────┼─────────┼──────░─┤ Rz(16) ├─░─────o─────────o─────┤ Rx(22) ├─░─\n",
       "           ░     │    ┌───┴───┐└───┬───┘             │         │         │      ░ ├────────┤ ░     │     ┌───┴────┐└───┬────┘ ░ \n",
       "q_8: ──────░─────o────┤ Rx(4) ├────o─────────────────┼─────────o─────────┼──────░─┤ Rz(16) ├─░─────o─────┤ Rx(20) ├────o──────░─\n",
       "           ░          └───┬───┘                      │     ┌───┴────┐    │      ░ ├────────┤ ░           └───┬────┘           ░ \n",
       "q_9: ──────░──────────────o──────────────────────────o─────┤ Rx(12) ├────o──────░─┤ Rz(16) ├─░───────────────o────────────────░─\n",
       "           ░                                               └────────┘           ░ └────────┘ ░                                ░ </pre>"
      ],
      "text/plain": [
       "     ┌───┐ ░                                                                    ░ ┌────────┐ ░                                ░ \n",
       "q_0: ┤ X ├─░────────────────────────────────o────────────────────────────o──────░─┤ Rz(16) ├─░────────────────────────────────░─\n",
       "     └───┘ ░ ┌───────┐                      │                            │      ░ ├────────┤ ░ ┌────────┐                     ░ \n",
       "q_1: ──────░─┤ Rx(2) ├────o────────o────────┼────────────────────────────┼──────░─┤ Rz(16) ├─░─┤ Rx(18) ├────o─────────o──────░─\n",
       "     ┌───┐ ░ └───┬───┘    │        │        │                            │      ░ ├────────┤ ░ └───┬────┘    │         │      ░ \n",
       "q_2: ┤ X ├─░─────o────────┼────────┼────────o────────────────────────────┼──────░─┤ Rz(16) ├─░─────o─────────┼─────────┼──────░─\n",
       "     └───┘ ░     │        │        │        │                        ┌───┴────┐ ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_3: ──────░─────┼────────┼────────┼────────┼──────────────────o─────┤ Rx(14) ├─░─┤ Rz(16) ├─░─────┼─────────┼─────────┼──────░─\n",
       "           ░     │        │        │        │    ┌────────┐    │     └───┬────┘ ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_4: ──────░─────┼────────┼────────o────────o────┤ Rx(10) ├────o─────────┼──────░─┤ Rz(16) ├─░─────┼─────────┼─────────o──────░─\n",
       "     ┌───┐ ░     │        │        │        │    └───┬────┘    │         │      ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_5: ┤ X ├─░─────┼────────┼────────┼────────┼────────┼─────────┼─────────o──────░─┤ Rz(16) ├─░─────┼─────────┼─────────┼──────░─\n",
       "     └───┘ ░     │        │        │    ┌───┴───┐    │         │         │      ░ ├────────┤ ░     │         │         │      ░ \n",
       "q_6: ──────░─────┼────────┼────────┼────┤ Rx(8) ├────o─────────┼─────────┼──────░─┤ Rz(16) ├─░─────┼─────────┼─────────┼──────░─\n",
       "           ░     │        │    ┌───┴───┐└───────┘    │         │         │      ░ ├────────┤ ░     │         │     ┌───┴────┐ ░ \n",
       "q_7: ──────░─────o────────o────┤ Rx(6) ├─────────────o─────────┼─────────┼──────░─┤ Rz(16) ├─░─────o─────────o─────┤ Rx(22) ├─░─\n",
       "           ░     │    ┌───┴───┐└───┬───┘             │         │         │      ░ ├────────┤ ░     │     ┌───┴────┐└───┬────┘ ░ \n",
       "q_8: ──────░─────o────┤ Rx(4) ├────o─────────────────┼─────────o─────────┼──────░─┤ Rz(16) ├─░─────o─────┤ Rx(20) ├────o──────░─\n",
       "           ░          └───┬───┘                      │     ┌───┴────┐    │      ░ ├────────┤ ░           └───┬────┘           ░ \n",
       "q_9: ──────░──────────────o──────────────────────────o─────┤ Rx(12) ├────o──────░─┤ Rz(16) ├─░───────────────o────────────────░─\n",
       "           ░                                               └────────┘           ░ └────────┘ ░                                ░ "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# basically the same circuit as qaoa, but turns off partial mixers where init_state=1,\n",
    "# however it always keeps the total number of partial mixers, so the extras are added after the phase separator\n",
    "dqva_circuit = qcopt.dqva.gen_dqva(\n",
    "    G=G,\n",
    "    P=1,\n",
    "    mixer_order=None,\n",
    "    params=np.arange(1,len(G)+2,1), # need 1 angle for each mixer (= number of nodes) plus 1 more for the phase separate Rz rotations\n",
    "    init_state='0000100101',\n",
    "    barriers=1,\n",
    "    decompose_toffoli=0\n",
    ")\n",
    "dqva_circuit.draw(fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dbb836a6-8a2f-4481-a639-9e2516bdafb2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">      ░                                                           ░ ┌───────┐ ░ \n",
       "q_0: ─░──────────────────────────────────────────o─────────o──────░─┤ Rz(2) ├─░─\n",
       "      ░ ┌───────┐                                │         │      ░ ├───────┤ ░ \n",
       "q_1: ─░─┤ Rx(4) ├────o────────o────────o─────────┼─────────┼──────░─┤ Rz(2) ├─░─\n",
       "      ░ └───┬───┘┌───┴───┐    │        │         │         │      ░ ├───────┤ ░ \n",
       "q_2: ─░─────o────┤ Rx(6) ├────┼────────┼─────────o─────────o──────░─┤ Rz(2) ├─░─\n",
       "      ░     │    └───┬───┘    │        │         │         │      ░ ├───────┤ ░ \n",
       "q_3: ─░─────┼────────┼────────┼────────┼─────────┼─────────o──────░─┤ Rz(2) ├─░─\n",
       "      ░     │        │        │        │         │         │      ░ ├───────┤ ░ \n",
       "q_4: ─░─────┼────────┼────────┼────────o─────────o─────────┼──────░─┤ Rz(2) ├─░─\n",
       "      ░     │        │        │        │         │     ┌───┴────┐ ░ ├───────┤ ░ \n",
       "q_5: ─░─────┼────────o────────┼────────┼─────────┼─────┤ Rx(14) ├─░─┤ Rz(2) ├─░─\n",
       "      ░     │        │        │        │     ┌───┴────┐└────────┘ ░ ├───────┤ ░ \n",
       "q_6: ─░─────┼────────o────────┼────────┼─────┤ Rx(12) ├───────────░─┤ Rz(2) ├─░─\n",
       "      ░     │                 │    ┌───┴────┐└────────┘           ░ ├───────┤ ░ \n",
       "q_7: ─░─────o─────────────────o────┤ Rx(10) ├─────────────────────░─┤ Rz(2) ├─░─\n",
       "      ░     │             ┌───┴───┐└───┬────┘                     ░ ├───────┤ ░ \n",
       "q_8: ─░─────o─────────────┤ Rx(8) ├────o──────────────────────────░─┤ Rz(2) ├─░─\n",
       "      ░                   └───┬───┘                               ░ ├───────┤ ░ \n",
       "q_9: ─░───────────────────────o───────────────────────────────────░─┤ Rz(2) ├─░─\n",
       "      ░                                                           ░ └───────┘ ░ </pre>"
      ],
      "text/plain": [
       "      ░                                                           ░ ┌───────┐ ░ \n",
       "q_0: ─░──────────────────────────────────────────o─────────o──────░─┤ Rz(2) ├─░─\n",
       "      ░ ┌───────┐                                │         │      ░ ├───────┤ ░ \n",
       "q_1: ─░─┤ Rx(4) ├────o────────o────────o─────────┼─────────┼──────░─┤ Rz(2) ├─░─\n",
       "      ░ └───┬───┘┌───┴───┐    │        │         │         │      ░ ├───────┤ ░ \n",
       "q_2: ─░─────o────┤ Rx(6) ├────┼────────┼─────────o─────────o──────░─┤ Rz(2) ├─░─\n",
       "      ░     │    └───┬───┘    │        │         │         │      ░ ├───────┤ ░ \n",
       "q_3: ─░─────┼────────┼────────┼────────┼─────────┼─────────o──────░─┤ Rz(2) ├─░─\n",
       "      ░     │        │        │        │         │         │      ░ ├───────┤ ░ \n",
       "q_4: ─░─────┼────────┼────────┼────────o─────────o─────────┼──────░─┤ Rz(2) ├─░─\n",
       "      ░     │        │        │        │         │     ┌───┴────┐ ░ ├───────┤ ░ \n",
       "q_5: ─░─────┼────────o────────┼────────┼─────────┼─────┤ Rx(14) ├─░─┤ Rz(2) ├─░─\n",
       "      ░     │        │        │        │     ┌───┴────┐└────────┘ ░ ├───────┤ ░ \n",
       "q_6: ─░─────┼────────o────────┼────────┼─────┤ Rx(12) ├───────────░─┤ Rz(2) ├─░─\n",
       "      ░     │                 │    ┌───┴────┐└────────┘           ░ ├───────┤ ░ \n",
       "q_7: ─░─────o─────────────────o────┤ Rx(10) ├─────────────────────░─┤ Rz(2) ├─░─\n",
       "      ░     │             ┌───┴───┐└───┬────┘                     ░ ├───────┤ ░ \n",
       "q_8: ─░─────o─────────────┤ Rx(8) ├────o──────────────────────────░─┤ Rz(2) ├─░─\n",
       "      ░                   └───┬───┘                               ░ ├───────┤ ░ \n",
       "q_9: ─░───────────────────────o───────────────────────────────────░─┤ Rz(2) ├─░─\n",
       "      ░                                                           ░ └───────┘ ░ "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_params = 6 + 1 # 5 partial mixers + 1 phase separator angle\n",
    "qlsa_circuit = qcopt.qlsa.gen_qlsa(\n",
    "    G=G,\n",
    "    P=1,\n",
    "    mixer_order=None,\n",
    "    params=np.arange(1,num_params+1),\n",
    "    init_state='0'*len(G),\n",
    "    barriers=1,\n",
    "    decompose_toffoli=0,\n",
    "    param_lim=num_params, # this controls number of mixers, have to remember to add 1 angle for the phase separator\n",
    ")\n",
    "qlsa_circuit.draw(fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ac2e603b-2de2-470d-94b6-88dfc6c26fcd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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