community/terra/qis_adv/topological_quantum_walk.ipynb

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    "<img src=\"../../../images/qiskit-heading.png\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"500 px\" align=\"left\">"
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   "source": [
    "## _*Topological Quantum Walks on IBM Q*_\n",
    "\n",
    "This notebook is based on the paper of Radhakrishnan Balu, Daniel Castillo, and George Siopsis, \"Physical realization of topological quantum walks on IBM-Q and beyond\" arXiv:1710.03615 \\[quant-ph\\](2017).\n",
    "\n",
    "### Contributors\n",
    "Keita Takeuchi (Univ. of Tokyo) and Rudy Raymond (IBM Research - Tokyo)\n",
    "***"
   ]
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   "source": [
    "## Introduction: challenges in implementing topological walk\n",
    "In this section, we introduce one model of quantum walk called *split-step topological quantum walk*."
   ]
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   "cell_type": "markdown",
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   "source": [
    "We define Hilbert space of quantum walker states and coin states as \n",
    "$\\mathcal{H}_{\\mathcal{w}}=\\{\\vert x \\rangle, x\\in\\mathbb{Z}_N\\}, \\mathcal{H}_{\\mathcal{c}}=\\{\\vert 0 \\rangle, \\vert 1 \\rangle\\}$, respectively. Then, step operator is defined as\n",
    "\n",
    "$$\n",
    "S^+ := \\vert 0 \\rangle_c \\langle 0 \\vert \\otimes L^+ + \\vert 1 \\rangle_c \\langle 1 \\vert \\otimes \\mathbb{I}\\\\\n",
    "S^- := \\vert 0 \\rangle_c \\langle 0 \\vert \\otimes \\mathbb{I} + \\vert 1 \\rangle_c \\langle 1 \\vert \\otimes L^-,\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "L^{\\pm}\\vert x \\rangle_{\\mathcal w} := \\vert (x\\pm1)\\ \\rm{mod}\\ N \\rangle_{\\mathcal w}\n",
    "$$\n",
    "\n",
    "is a shift operator. The boundary condition is included.\n",
    "Also, we define the coin operator as\n",
    "\n",
    "$$\n",
    "T(\\theta):=e^{-i\\theta Y} = \\begin{bmatrix} \\cos\\theta & -\\sin\\theta \\\\ \\sin\\theta & \\cos\\theta \\end{bmatrix}.\n",
    "$$\n",
    "\n",
    "One step of quantum walk is the unitary operator defined as below that uses two mode of coins, i.e., $\\theta_1$ and $\\theta_2$: \n",
    "\n",
    "$$\n",
    "W := S^- T(\\theta_2)S^+ T(\\theta_1).\n",
    "$$\n",
    "\n",
    "Intuitively speaking, the walk consists of flipping coin states and based on the outcome of the coins, the shifting operator is applied to determine the next position of the walk. "
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    "Next, we consider a walk with two phases that depend on the current position:\n",
    "\n",
    "$$\n",
    "(\\theta_1,\\theta_2) = \\begin{cases}\n",
    "    (\\theta_{1}^{-},\\ \\theta_{2}^{-}) & 0 \\leq x < \\frac{N}{2} \\\\\n",
    "    (\\theta_{1}^{+},\\ \\theta_{2}^{+}) & \\frac{N}{2} \\leq x < N.\n",
    "  \\end{cases}\n",
    "$$\n",
    "\n",
    "Then, two coin operators are rewritten as\n",
    "\n",
    "$$\n",
    "\\mathcal T_i = \\sum^{N-1}_{x=0}e^{-i\\theta_i(x) Y_c}\\otimes \\vert x \\rangle_w \\langle x \\vert,\\ i=1,2.\n",
    "$$\n",
    "\n",
    "By using this, one step of quantum walk is equal to\n",
    "\n",
    "$$\n",
    "W = S^- \\mathcal T_2 S^+ \\mathcal T_1.\n",
    "$$"
   ]
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   "source": [
    "In principle, we can execute the quantum walk by multiplying $W$ many times, but then we need many circuit elements to construct it. This is not possible with the current approximate quantum computers due to large errors produced after each application of circuit elements (gates)."
   ]
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   "source": [
    "## Hamiltonian of topological walk\n",
    "\n",
    "Altenatively, we can think of time evolution of the states. The Hamiltonian $H$ is regarded as $H=\\lim_{n \\to \\infty}W^n$(See below for further details.). \n",
    "\n",
    "For example, when $(\\theta_1,\\ \\theta_2) = (0,\\ \\pi/2)$, the Schrödinger equation is\n",
    "\n",
    "$$\n",
    "i\\frac{d}{dt}\\vert \\Psi \\rangle = H_{\\rm I} \\vert \\Psi \\rangle,\\ H_{\\rm I} = -Y\\otimes [2\\mathbb I+L^+ + L^-].\n",
    "$$\n",
    "\n",
    "If Hamiltonian is time independent, the solution of the Schrödinger equation is\n",
    "\n",
    "$$\n",
    "\\vert \\Psi(t) \\rangle = e^{-iHt} \\vert \\Psi(0) \\rangle,\n",
    "$$\n",
    "\n",
    "so we can get the final state at arbitrary time $t$ at once without operating W step by step, if we know the corresponding Hamiltonian.\n",
    "\n",
    "The Hamiltonian can be computed as below.\n",
    "\n",
    "Set $(\\theta_1,\\ \\theta_2) = (\\epsilon,\\ \\pi/2+\\epsilon)$, and $\\epsilon\\to 0$ and the number of step $s\\to \\infty$\n",
    "while $se=t/2$(finite variable). Then,\n",
    "\\begin{align*}\n",
    "    H_I&=\\lim_{n \\to \\infty}W^n\\\\\n",
    "    \\rm{(LHS)} &= \\mathbb{I}-iH_{I}t+O(t^2)\\\\\n",
    "    \\rm{(RHS)} &= \\lim_{\\substack{s\\to \\infty\\\\ \\epsilon\\to 0}}(W^4)^{s/4}=\n",
    "    \\lim_{\\substack{s\\to \\infty\\\\ \\epsilon\\to0}}(\\mathbb{I}+O(\\epsilon))^{s/4}\\\\\n",
    "     &\\simeq \\lim_{\\substack{s\\to \\infty\\\\ \\epsilon\\to 0}}\\mathbb{I}+\\frac{s}{4}O(\\epsilon)\\\\\n",
    "     &= \\lim_{\\epsilon\\to 0}\\mathbb{I}+iY\\otimes [2\\mathbb I+L^+ + L^-]t+O(\\epsilon).\n",
    "\\end{align*}\n",
    "Therefore,\n",
    "$$H_{\\rm I} = -Y\\otimes [2\\mathbb I+L^+ + L^-].$$"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computation model "
   ]
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   "source": [
    "In order to check the correctness of results of the implementation of quantum walk by using IBMQ, we investigate two models, which have different features of coin phases. Let the number of positions on the line $n$ is 4.\n",
    "- $\\rm I / \\rm II:\\ (\\theta_1,\\theta_2) = \\begin{cases}\n",
    "    (0,\\ -\\pi/2) & 0 \\leq x < 2 \\\\\n",
    "    (0,\\ \\pi/2) & 2 \\leq x < 4\n",
    "  \\end{cases}$\n",
    "- $\\rm I:\\ (\\theta_1,\\theta_2)=(0,\\ \\pi/2),\\ 0 \\leq x < 4$\n",
    "\n",
    "That is, the former is a quantum walk on a line with two phases of coins, while the latter is that with only one phase of coins.\n",
    "\n",
    "<img src=\"../images/q_walk_lattice_2phase.png\" width=\"30%\" height=\"30%\">\n",
    "<div style=\"text-align: center;\">\n",
    "Figure 1. Quantum Walk on a line with two phases\n",
    "</div>"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Hamiltonian operators for each of the walk on the line are, respectively, \n",
    "$$\n",
    "H_{\\rm I/II} = Y \\otimes \\mathbb I \\otimes \\frac{\\mathbb I + Z}{2}\\\\\n",
    "H_{\\rm I} = Y\\otimes (2\\mathbb I\\otimes \\mathbb I + \\mathbb I\\otimes X + X \\otimes X).\n",
    "$$\n",
    "\n",
    "Then, we want to implement the above Hamiltonian operators with the unitary operators as product of two-qubit gates CNOTs, CZs, and single-qubit gate rotation matrices. Notice that the CNOT and CZ gates are\n",
    "\\begin{align*}\n",
    "  \\rm{CNOT_{ct}}&=\\left |0\\right\\rangle_c\\left\\langle0\\right | \\otimes I_t + \\left |1\\right\\rangle_c\\left\\langle1\\right | \\otimes X_t\\\\\n",
    "  \\rm{CZ_{ct}}&=\\left |0\\right\\rangle_c\\left\\langle0\\right | \\otimes I_t + \\left |1\\right\\rangle_c\\left\\langle1\\right | \\otimes Z_t.\n",
    "\\end{align*}\n",
    "\n",
    "Below is the reference of converting Hamiltonian into unitary operators useful for the topological quantum walk.\n",
    "<br><br>\n",
    "\n",
    "\n",
    "<div style=\"text-align: center;\">\n",
    "Table 1. Relation between the unitary operator and product of elementary gates\n",
    "</div>\n",
    "\n",
    "|unitary operator|product of circuit elements|\n",
    "|:-:|:-:|\n",
    "|$e^{-i\\theta X_c X_j}$|$\\rm{CNOT_{cj}}\\cdot e^{-i\\theta X_c t}\\cdot \\rm{CNOT_{cj}}$|\n",
    "|$e^{-i\\theta X_c Z_j}$|$\\rm{CZ_{cj}}\\cdot e^{-i\\theta X_c t}\\cdot \\rm{CZ_{cj}}$|\n",
    "|$e^{-i\\theta Y_c X_j}$|$\\rm{CNOT_{cj}}\\cdot e^{i\\theta Y_c t}\\cdot \\rm{CNOT_{cj}}$|\n",
    "|$e^{-i\\theta Y_c Z_j}$|$\\rm{CNOT_{jc}}\\cdot e^{-i\\theta Y_c t}\\cdot \\rm{CNOT_{jc}}$|\n",
    "|$e^{-i\\theta Z_c X_j}$|$\\rm{CZ_{cj}}\\cdot e^{-i\\theta X_j t}\\cdot \\rm{CZ_{cj}}$|\n",
    "|$e^{-i\\theta Z_c Z_j}$|$\\rm{CNOT_{jc}}\\cdot e^{-i\\theta Z_c t}\\cdot \\rm{CNOT_{jc}}$|\n",
    "\n",
    "By using these formula, the unitary operators are represented by only CNOT, CZ, and rotation matrices, so we can implement them by using IBM Q, as below.\n",
    "\n",
    "### Phase I/II:<br><br>\n",
    "\n",
    "\\begin{align*}\n",
    "  e^{-iH_{I/II}t}=~&e^{-itY_c \\otimes \\mathbb I_0 \\otimes \\frac{\\mathbb I_1 + Z_1}{2}}\\\\\n",
    "  =~& e^{-iY_c t}e^{-itY_c\\otimes Z_1}\\\\\n",
    "  =~& e^{-iY_c t}\\cdot\\rm{CNOT_{1c}}\\cdot e^{-i Y_c t}\\cdot\\rm{CNOT_{1c}}\n",
    "\\end{align*}\n",
    "\n",
    "<img src=\"../images/c12.png\" width=\"50%\" height=\"60%\">\n",
    "<div style=\"text-align: center;\">\n",
    "Figure 2. Phase I/II on $N=4$ lattice$(t=8)$ - $q[0]:2^0,\\ q[1]:coin,\\ q[2]:2^1$\n",
    "</div>\n",
    "\n",
    "<br><br>\n",
    "### Phase I:<br><br>\n",
    "\n",
    "\\begin{align*}\n",
    "  e^{-iH_I t}=~&e^{-itY_c\\otimes (2\\mathbb I_0\\otimes \\mathbb I_1 + \\mathbb I_0\\otimes X_1 + X_0 \\otimes X_1)}\\\\\n",
    "  =~&e^{-2itY_c}e^{-itY_c\\otimes X_1}e^{-itY_c\\otimes X_0 \\otimes X_1}\\\\\n",
    "  =~&e^{-2iY_c t}\\cdot\\rm{CNOT_{c1}}\\cdot\\rm{CNOT_{c0}}\\cdot e^{-iY_c t}\\cdot\\rm{CNOT_{c0}}\\cdot e^{-iY_c t}\\cdot\\rm{CNOT_{c1}}\n",
    "\\end{align*}\n",
    "\n",
    "<img src=\"../images/c1.png\" width=\"70%\" height=\"70%\">\n",
    "<div style=\"text-align: center;\">\n",
    "Figure 3. Phase I on $N=4$ lattice$(t=8)$ - $q[0]:2^0,\\ q[1]:2^1,\\ q[2]:coin$\n",
    "</div>"
   ]
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   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialization\n",
    "import sys\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# importing QISKit\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit import Aer, IBMQ, execute\n",
    "\n",
    "from qiskit.wrapper.jupyter import *\n",
    "from qiskit.backends.ibmq import least_busy\n",
    "\n",
    "from qiskit.tools.visualization import matplotlib_circuit_drawer as circuit_drawer\n",
    "from qiskit.tools.visualization import plot_histogram, qx_color_scheme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the best backend is ibmq_16_melbourne with coupling [[1, 0], [1, 2], [2, 3], [4, 3], [4, 10], [5, 4], [5, 6], [5, 9], [6, 8], [7, 8], [9, 8], [9, 10], [11, 3], [11, 10], [11, 12], [12, 2], [13, 1], [13, 12]]\n"
     ]
    }
   ],
   "source": [
    "IBMQ.load_accounts()\n",
    "sim_backend = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "device_backend = least_busy(IBMQ.backends(operational=True, simulator=False))\n",
    "device_coupling = device_backend.configuration()['coupling_map']\n",
    "print(\"the best backend is \" + device_backend.name() + \" with coupling \" + str(device_coupling))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quantum walk, phase I/II on $N=4$ lattice$(t=8)$**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OPENQASM 2.0;\n",
      "include \"qelib1.inc\";\n",
      "qreg q0[3];\n",
      "creg c0[3];\n",
      "x q0[2];\n",
      "u3(8,0,0) q0[1];\n",
      "cx q0[2],q0[1];\n",
      "u3(8,0,0) q0[1];\n",
      "cx q0[2],q0[1];\n",
      "measure q0[0] -> c0[0];\n",
      "measure q0[1] -> c0[2];\n",
      "measure q0[2] -> c0[1];\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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LZul/t3yoB6/9hT6+42n95upB54UaSTKZTOrRrpNeuel3Khjxex09dVwTC1/UZcGhhBof83mwWbRokRITE9WqVStlZGRoypQp1Tc55uXlKTs7W/Hx8QoLC9Ps2bO1bNkylZWVeb0vd2onJycrKChI69at83o/TdFVba0KaxGsZ5d/KfuxUzpUeVKvfLRdeR9t14ys5OpxpeVHNfC595X1QpFuSWrvx449a9XHq1V1TX8ptGXDdxYeKXVN18erVzd8XwGiqR8fq1evloKCpJ43eGaHvW7S/n3fqbS01DP7M6BpK+Zp5a5NeuGGiXq8z6/VvFmwW9tdFhyqY6dPqpk5SJWnTyjIFFDnEAzPp/+333jjDU2ZMkULFixQRUWFhgwZorlz5yo1NVV2u127du1SWlpa9fiEhARZrVZt2LChXnVyc3OVlOTGkwL/Vp/aWVlZWrJkSb36gXusLYL11n9cr/W7DunKRwuUOuMfKtiwW0vu7avrroyqHhfXppU+mDxIRVNv0OQ3jREy7Xa7dpeVSp2S6xzrLteVySopKVFVVZXH9ulPTfn4kKQvvvhC5tirpOYtPLPDzimSpPXr13tmfwbzfmlJ9ZmaO7r1c3u7c/fUtGkZpreHP6pTzjOa9EEeZ8Z8yGfB5tixY5o8ebLy8vLUs2dPmUwmjRs3Tk6nU6mpqaqoqJAkhYXVPHVss9nk+PdsmoMGDVJkZKSefPLJi9bKycmp10Rl7tQ+Z/DgwVq6dKnb+0b99E6I1IeTB+nAc7eqLHeY3rmvv/ok/vBH6+TpH2betYQGq1Vz995BBbrDh/894ZzNgzPDhkfp5IkTOnnypOf26WdN9fiQpEOHD6sqPKruge76976qjz1Uc7lcevzjBboyvJ1yfub+peFzoebcPTV92nfTI71v03s716v4u6+92DF+zGc3DxcVFamqqko33XRT9bIDBw5IklJTUxUaevaa5ZEjNWcOtdvtslrPTjw1f/58vf/++9X3wHiKxWKps/Y5ZWVliomJ8Wj92phMvpmP47rExjXF+rpdh/R4wUYFmU067azS07em+rulakVFRQ3/d5s98eyXO/q7Nxldy5YNu7TVmI4Rwx8fktv/7u6Ou+eee3TPPfc0oKHG7+fRXWt8/9l327SlvExzBo53+/LTT0PNuXtqxiZl6Onit/TahkL9rN1VNbbx2DHRRLh71stnwWb//v2Kiqr5bmPhwoVq27atLr/87FMLMTExWr9+vVJSzp4i3bFjhxwOR/VlpfbtvXO93Gaz1Vn7nIKCAo0YMcIrffyYL05b9uvXT1V7t3q9jif1TojU8gcH+ruNWvXt21crV668pG3PnDmjVhaLTg65W7r3v+reoL9VWnH+5wLVMGOsrvj6U/1rz+5L6klqfMeIUY8PSRozZozyC/4h51vbpbr+GLpzfKxZJj38S61atUrXXXfdJffV2PXr109nth+osWzZjnVqZg7SrZ37uLWPC4Ua6ez9Nr/o1Etvb1ujKleVzD+636ahx0RDFBYWKiMjwy+1vc1nl6K6du2q7du3q6ioSKdOndLChQuVm5ur1NQf3lGNHz9es2bN0s6dO+VwOJSdna3MzEzFxcV5vT93aldWVmrFihUaMmSI1/tB09KsWTMlJyfL9OXnntmhyyXzV+vU49q0useiUUhLS5Pz8AFpn4ceptj6mUwmU43XYJxVsn+HukbE1Pr0009dLNScc+3lneQ4dVw77d97o138hM+CTXp6uh555BENHz5c7du3V3FxsXr27FnjlyonJ0dDhw5Venq6oqOj5XQ6lZ+fX+9aM2fOVLdu3eq1jTu1CwsLlZqa6pN5ddD0/CIrS64tn0llHrgWv2G1qv61U7fcckvD94WAMGTIkLOXLf5Z/9fE8zjPKGj5X9R/wAC1atWq4fszmNIj3+tKNybTcyfUSFKn1u2q9wvv8+lTUU888YQOHjyo/fv3a+7cudq2bVuNYBMUFKRnnnlG5eXlqqio0OLFiy8pRDz88MPasmVLvbZxp3ZBQYGysrLq3Q/gjrvvvlvBISHSgmcbtiOXS6aFzygsPFy33367Z5qD33Xs2FE33XyzzO/OkxyHGraz5X+V8/s9uu9e481O7QkLb3lIj/au+3fnnzvWujX5Xvc2cVrxq/9S+hWdPNkmLsBvMw87HA6VlZXV6zTo2LFjVVxcrJMnT6q4uFjvvPOOFzs8X2xsrCE/WNDXjp06ozteW61jJ8/I2iJE+WN7q3lw0HnjzjirNCG/WKUHK3VT93aamtG1lr1JFSdOa8z8NTp87JTu/nmC7ujZ0ds/gldERUXpoWnT9NRTT0n9h0u9bry0Hf0zX67PP9SM//mfBt847C8cI7Wb+dRTeu/aa6X/mSY98mrd99rUpvw7mf/0sHr2/jln9C6gS0QHt8Y90us23XvNEIWHXvysV6uQUKW2TfBEa3CD32YN2rx5sywWixIS3P/HnjdvnrZs2aLt27c3ONSkpKRozJgx9dpm+vTphvtQQX8o3Pqd0uMi9N6kgbo2trUKv/yu1nHvbtqrTm2t+mDyIH3ybbn2OY7XOu711d9qZFqMlk8aoPmf7NCpM85axzUGjz32mLp1v1rmp8ZJX1/C/CLrVsg0d7L69uunexvxu3GOkdolJyfr9489Jn3wpvTnWVJ9HzI4clDmh0cq+PQJzX99noKCzg+LcJ/JZKoz1MD3/BZsevfuLYfD4bdH3S4l2MAz4tu00rGTZyRJR46fVsRlzWsd93npQQ246uwTc307RWltae2n3z/797ggs1lXR9v09fcV3mncB5o3b65/LH1X0W1ayzx5iPSP/3Xvj5fTKS16Xqb/HKmunTrprb/9TWZz453tlGPkwh599FH95je/kebPlGb9Vjpqd2/DLcUy3zdIzXZ9rSV//7s6deKyCIyp8b7yodFKjLKoeOdBpT35D63fdUg/61j7tWn7sVOyhp6dQ8LaIlhHjp+qddyR4+6NayxiYmK0ZvXH6pOeJj19r0wP3ix99I505vT5g0+dkJb/VaZ7B0h/eliDb8zUqqKViohowIdoBgCOkQszm82aN2+eHn30UZnf/6vMd/WQ/u+/pcMHzh/scklfrpX+a4L0u0xdYTqt95cv54N8YWgEG/hcfvFO3Xx1O6179Gbd2K2d/u/z0lrHhbUIkePE2T/mFcdPn/fhh+dYfzzuxIXHNSbR0dFa8eGHeuGFF3TFwV3S7++QeUh7me4dKD0xRpJk/o++Mg1pL828Rx2dR5Wfn6+CJUvUunVr/zbvARwjF2c2mzVjxgwVf/qprut+lZT3uDQ8QUGjr5F+f8fZQVOzZP5FR2niALX85B09cP/92rp5U5OeswZNA8EGPudySeEtz/5hiWgVIsfx0zrjrNL3jhM1xvXoGKGVX599PLLom/1Ki22t46fO6FBlzY8I6Bl3dpyzqkob99jVua3FNz+Il5nNZk2cOFFlO3eooKBAD0z8D/Vp00IJezZLkvpGh2vag5O0fPlyffP1V7rjjjsMM4spx4h7rr32Wq1csUJbtmzRjBkzNDStuzqXfytJusZUobG/HK7XXntN3+3dqzlz5pw3kzpgRH57KgpN123Xxmr0vE/0f5+VKjjIrD+P7a2yQ5V6dvmXevHXParHDb46WuNLijXwufeV2e0KXRHWQh9+tU+flx5U9o0/zFM0pneCxsxfoz8VbdPYnycopJmxbohs1qyZhg4dqqFDh1YvM5lM+vCDD/zYlXdxjNRP165d1bXrD0+EmUwmrfvcQ5M9Ao0MwQY+Z2sZooL7+tVYtmrbfv0yreYTZ8FBZr0+pleNZVv+dUS3ptX8rC5ri2At/u31XukV/sExAuBSEWwQEH6R6t68EfcP6OzlThCoOEYAuINg08Rt3GtX5hzjXtLwlY177UqJ9ncX3sEx0nBGPj6MYNOBUg1+c7rPa6YmRvq0ZlNBsGnCzn2SORouJdqY/z+N+DP5g1GPDyNo6L/L4cOHFR4eXu/tUhMjOSa8xORy1XfqSgD+ZjKZxK8uLoTjw3cKCwuVkZHh7zbqrbH27Q4e9wYAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIZBsAEAAIbBp3uj2qRJk1RSUuKX2ikpKZozZ45fagPwDF5DEAgINqhWUlKiz9d9rNjOLX1at+zrYz6tB8A7SkpK9MWaz3V1ZJxP6246UOrTeghsBBvUENu5pR57pZtPa864Z4tP6wHwnqsj47R05HSf1hz8pm/rIbBxjw0AADAMgg0AADAMgg0AADAMgg0AADAMgg0AADAMgg0AADAMHvcGAPjFmSqnvj60V5sOlMp+4qiCzGbFh12ulLbximhhrXWbdfu2a6d9n269qo+Pu0Vj0WSDzfz58zV//nytXLnS7W3S0tI0c+ZMZWZmeq8xADC4nfZ9emXDe1q4daXsJytrHdPzis66OzlDwzv1VjNzkKSzoWbY4hmKbGnT0MSeat4s2Jdto5EIqEtRTqdT06ZNU2RkpCwWi0aMGKHy8vKAqZ2VlaWCggKf9NMYnDjm1IQBa1X8/sHqZadOVOnxMZs1Z9o2VVW5/NidsbhcLr399tu64YYbZLWefSeblZWl5cuX+7kzBIqvvvpK9913n9q2bStJSkpK0vPPP6/KytqDgz+cqXJqzudvq+f/TlbehmXqH5OklzPv06ejntOOCa/pq3teVsGI3+ux3rfrwPEjGr/sjxr0l0e0tXxXdahp3cKqJSMeI9TgggIq2OTm5mrJkiUqLi7Wnj17JEmjRo0KmNoEm5pCWwZp8OgrtDhvr1wul6qcLs3N3qbgELPufSpRZrPJ3y0aQlVVle6++24NGzZMH374oSoqKiRJ7777rjIyMpSdnS2XixDZlBUUFCg5OVkvvvii9u/fL0nasmWL7r//fvXu3dtnbxAv5tjpk7p9ySxNX71QN3ZM06axL+j1wQ/qti7X66qI9mrdwqLLLwvX9R26a0qP4Vr7mzl6/eZJ2lNRrr4LszXkb9PVuoVV7976uNpb2vj7x0EA83mwWbRokRITE9WqVStlZGRoypQpGjlypCQpLy9P2dnZio+PV1hYmGbPnq1ly5aprKzM6325Uzs5OVlBQUFat26d1/tpLDJuu1xHDp7SZx8c0qtP7tCh/ac0+blOCg4JqMzcqM2dO1evv/66pLMh55xz/z179mz95S9/8Utv8L/S0lL98pe/1OnTp2sE3HPHx6ZNmzRmzBg/dffvXlxVGrP0OX1QtkFzBo7XG4Mn64pWrS+6jdlk1rBOvfVS5n1yulw6fuaUHut9O6EGdfLpX5833nhDU6ZM0YIFC1RRUaEhQ4Zo7ty5Sk1Nld1u165du5SWllY9PiEhQVarVRs2bKhXndzcXCUlJbk9vj61s7KytGTJknr1Y2ShLYI0eHQ7vfT4t9q6zqGc569Sy1ZN9tYtj3M6nXruuedkMl347JfZbNazzz7rw64QSF566SWdPHnygmftXC6Xli5dqm3btvm4sx+8XLJMhaVfaHb/uzTm6kEXPZ5/bN2+7Rr7j/9We0uEOoa11e8/yteRk3xoLi7OZ8Hm2LFjmjx5svLy8tSzZ0+ZTCaNGzdOTqdTqamp1afXw8LCamxns9nkcDj07bff6vrrr9d1112nPn36aO3atReslZOTo40bN7rdW121f2zw4MFaunSp2/tuKk4er9ItY9opLCLE360YypYtW7Rnz56LXmqqqqrSunXrqi9BoGlx9/K4v1639lUe1hOrFyojLlXjktx/8OLH99T8Y+Qf9OpND+i7ykN6ag1nJ3FxPntrXVRUpKqqKt10003Vyw4cOCBJSk1NVWhoqCTpyJEjNbaz2+2yWq2y2Wz6+9//roiICG3dulUTJkzQRx995JHeLBbLRWv/WFlZmWJiYjxS92LcfUfjaV3SLPUa//HSAyp4fa/6ZUVq2f/tU/9hUZfUe1FRkd9+ZqM4d9MoUJvJkydr8uTJXq/z8+iuNb5/Y9MHOn7mlP6r75h6nak5F2rO3VPT3tJGt111vRZsWaFHe90ua/OWNbbhNcT43L2X0GdnbPbv36+oqKgayxYuXKjTqTxSAAAQ+0lEQVS2bdvq8ssvl81mU0xMjNavX1+9fseOHXI4HEpKSlJERIQiIiIkSc2bN1dQUJDHequr9o8VFBQoKyvLY7UvxOVy+fyrb9++9erxi48P6/XcUk1+trNGPxQnx6HTKl5+6JJ+3r59+/rlZw70rwMHDqhZs7rff1itVp04ccLv/fLl+6/Bgwe79Xq4ePFir/dS22vIgq0rNCAmWQnhV7j1WlBbqDlnXHKmKk+f1JLtn563nb9eQ9577z2/HwNNpW93+SzYdO3aVdu3b1dRUZFOnTqlhQsXKjc3V6mpqdVjxo8fr1mzZmnnzp1yOBzKzs5WZmam4uLiqsc4nU797ne/U05Ojkf7c6d2ZWWlVqxYoSFDhni0dmO0bUOFnv/P7fqPJxLUJc1afa/N4lf28Ji3B7Vp00a33nqrzOYL/6qaTCaNHTtWzZs392FnCBQTJkyQ0+m84HqTyaS2bdv65XVrf6VduxwHNDAu2a3xFws1knRN2wTZml+mtd994412YRA+Czbp6el65JFHNHz4cLVv317FxcXq2bNnjWCTk5OjoUOHKj09XdHR0XI6ncrPz69e73K5NHbsWA0ZMkQ33njjBWvNnDlT3bp1q1d/ddWWpMLCQqWmpqpNm6Z9V/7u7cf09ANf6c7JsUrv/8OTDRm/bCvH4TMqXn7wIlujvp588knZbLZaw43ZbFb79u09HvTReNx8880XPIt87tLMiy++qOBg38/7sqV8lyQpKbJjnWPrCjXS2Z8nOSpemw6UerpVGIhPn4p64okndPDgQe3fv19z587Vtm3bagSboKAgPfPMMyovL1dFRYUWL15cI0Tcf//9SkxM1G9/+9uL1nn44Ye1ZcuWevVWV23Jd5ehAl2HxJZ6ZWW6+g+reWmxeYsgvfR+mnplNu3g52kJCQlas2aN+vQ5fwr5jIwMrVmzhvtrmrCgoCAtWrRIDzzwwHln7eLi4vT2229r+PDhfuktrHlLDe/UW7FhURcd932lXcMWP+nWPDU3dExVn/b1e+OKpsVvz+U6HA6VlZXVCDYXs3LlSuXl5al379764IMP1Lp1ay1evNjLXdYUGxtbPecO4EudOnVSUVGRNm/erLVr18pkMunnP/+5EhMT/d0aAkBISIjmzJmjxx9/XIWFhTp69Kji4+PVt2/fi17G9LZrLk/UvJsn1Tmu7WU2/aHPHbqhY2qd89Tcdw23AuDi/BZsNm/eLIvFooSEBLfG9+vXT6dOnfJY/ZSUlHpPWjV9+nSP1QcuRffu3dW9e3d/t4EAFR4erttuu83fbVySu5Ju8HcLMAi/BZvevXufN0eML6WkpCglJcVv9QEAgOcx7z0AADAMgg0AADAMgg0AADAMgg0AADAMgg0AADAMgg0AADAMvz3ujcBU9vUxzbinfrM2e6JmVJpPSwLwkk0HSjX4zek+r5maGOnTmghcBBtU89e8PlFp/qsNwHMa+nt8+PBhhYeH13u71MRIXkNQjWCDanPmzPF3CwAasYa+hhQWFiojI8ND3aCp4h4bAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGAQbAABgGM383QAAAPC8M2fOaOvWrXK5XLWu37BhQ43vO3TooNatW/uiNa8i2AAAYEDNmjVTcHCwdu/eXev677//vvq/Q0ND1b17d1+15lVcigIAwKASEhLUrFnd5zA6deqkoKAgH3TkfQQbAAAMKiQkRAkJCRcdY7PZ1LZtWx915H0EGwAADKxDhw5q2bLlBddfddVVMplMPuzIuwI62DidTk2bNk2RkZGyWCwaMWKEysvLDV8bAABPMZvN6ty5c63roqOjZbVafdyRdwV0sMnNzdWSJUtUXFysPXv2SJJGjRpl+NoAAHhSmzZtFBERUWNZUFCQEhMT/dSR9wREsFm9erUGDhwoq9Uqm82mkSNHSpLy8vKUnZ2t+Ph4hYWFafbs2Vq2bJnKysq83pM/awMA4Ekmk+m8szYdO3ZU8+bN/dSR9/g92Lz11lsaNmyYJk6cqP3792v37t0aN26c7Ha7du3apbS0tOqxCQkJslqt5z17X5fc3FwlJSW5Pd6TtQEACAStWrVShw4dJJ19vDs2NtbPHXmHX4NNZWWlJkyYoLy8PI0YMUKhoaGyWCzKzMxURUWFJCksLKzGNjabTQ6HQ5KUn5+vXr16qVevXlqxYsUF6+Tk5Gjjxo1u9+VObQAAGptzj38b6fHun/LrBH1FRUUymUzKyso6b53FYpEkHTlypMZyu90uq9Uqu92uZ555Rp9++qmOHj2qQYMGaf369TKbG57V6qoNAEBjFBISouTkZEPMMHwhfg025eXlCg8Pr/UxM5vNppiYGK1fv14pKSmSpB07dsjhcCgpKUnFxcXq27evQkNDFRoaqnbt2qm0tFTx8fEN7quu2r5QWFjokzoAEEga42tfY+y5McrIyHBrnF+DzTXXXKOdO3fqnXfe0eDBg+VwOFRcXKzMzExJ0vjx4zVr1iz1799fERERys7OVmZmpuLi4vTJJ58oPDy8el/h4eE6ePCgR4JNXbV9wd1/QAAwisLCwkb32tcYezY6v95j0717d7366quaOnWqrFarunTpolWrVlWvz8nJ0dChQ5Wenq7o6Gg5nU7l5+dLkiIiInT48OHqsXa7/bxH2c6ZOXOmunXrVq/eLlYbAAAEJpPrQh/7GeDsdrsGDBigNWvWqLKyUgMGDPDYPTYAAN9rjGc/GmPPRtdoP93bZrNp0qRJ6tevnyTp2WefJdQAANDENdpgI0mjR4/W6NGj/d0GAAAIEJziAAAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhkGwAQAAhtHM3w0AAJqOqqoqORyOC6632+01vg8JCVHLli293RYMhGADAPAZk8mkb775RocPH651/WeffVbj+7S0NIIN6oVLUQAAnzGZTLrqqqvcGhsZGamIiAgvdwSjIdgAAHzKYrEoOjr6omNMJpM6d+7so45gJAQbAIDPJSYmKigo6ILrY2JiuASFSxLQwcbpdGratGmKjIyUxWLRiBEjVF5ebvjaAGB0zZs3V3x8fK3rgoODL7gOqEtAB5vc3FwtWbJExcXF2rNnjyRp1KhRhq8NAE1BbGysWrRocd7yK6+8UsHBwX7oCEYQEMFm9erVGjhwoKxWq2w2m0aOHClJysvLU3Z2tuLj4xUWFqbZs2dr2bJlKisr83pP/qwNAE2B2WxWp06daixr1apVnfffABfj92Dz1ltvadiwYZo4caL279+v3bt3a9y4cbLb7dq1a5fS0tKqxyYkJMhqtWrDhg31qpGbm6ukpCS3x3uyNgDgwqKiohQeHl79fefOnWUymfzYERo7vwabyspKTZgwQXl5eRoxYoRCQ0NlsViUmZmpiooKSVJYWFiNbWw2W/XkToMGDVJkZKSefPLJi9bJycnRxo0b3e7LndoAgIb78ePfUVFRPN6NBvPrBH1FRUUymUzKyso6b53FYpEkHTlypMZyu90uq9UqSZo/f77ef//96ntgPMWd2gAAz7BYLOrQoYNiY2P93QoMwK/Bpry8XOHh4bWedrTZbIqJidH69euVkpIiSdqxY4ccDkf1ZaX27dt7pS93antbYWGhT+oAQKDYvXu3v1u4JLxe+0ZGRoZb4/wabK655hrt3LlT77zzjgYPHiyHw6Hi4mJlZmZKksaPH69Zs2apf//+ioiIUHZ2tjIzMxUXF+f13vxZW3L/HxAA4D+FhYW8XgcYv95j0717d7366quaOnWqrFarunTpolWrVlWvz8nJ0dChQ5Wenq7o6Gg5nU7l5+fXu87MmTPVrVu3em3jqdoAAMB3TC6Xy+XvJhpi/vz52rNnjx599FF/twIAaGI4YxN4GvWne48dO1bFxcU6efKkiouL9c477/i7JQAA4EeNOtjMmzfP3y0AAIAA4vcJ+gAAADyFYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAyDYAMAAAzD5HK5XP5uAgCAQLZ3717t3bv3vOV2u102m63GspCQECUlJcls5tyBPzTzdwMAAAS6qKgobdu2TadPnz5vnd1ur/F9165dCTV+xP95AADqEBwcrMTExDrHWSwWRUdH+6AjXAjBBgAAN0RHR6tVq1YXHdO5c2eZTCYfdYTaEGwAAHCD2WxW586dL7g+KipKrVu39mFHqE1ABxun06lp06YpMjJSFotFI0aMUHl5ueFrAwACU0REhCIjI89bbjKZ1KlTJz90hJ8K6GCTm5urJUuWqLi4WHv27JEkjRo1yvC1AQCBq1OnTuddboqNjVXLli391BF+LCCCzerVqzVw4EBZrVbZbDaNHDlSkpSXl6fs7GzFx8crLCxMs2fP1rJly1RWVub1nvxZGwAQuC677DLFxMRUfx8SEqL4+Hg/doQf83uweeuttzRs2DBNnDhR+/fv1+7duzVu3DjZ7Xbt2rVLaWlp1WMTEhJktVq1YcOGetXIzc1VUlKS2+M9WRsAYDzx8fEKDg6WJCUmJqpZM2ZPCRR+DTaVlZWaMGGC8vLyNGLECIWGhspisSgzM1MVFRWSpLCwsBrb2Gw2ORwOffvtt7r++ut13XXXqU+fPlq7du0F6+Tk5Gjjxo1u91VXbQBA03bu8W8e7w48fo2YRUVFMplMysrKOm+dxWKRJB05cqTGcrvdXn3J6u9//7siIiK0detWTZgwQR999JFH+qqrNgAA0dHRstlsPN4dYPwabMrLyxUeHl7rQWGz2RQTE6P169crJSVFkrRjxw45HA4lJSUpIiKiemzz5s0VFBTksb7qqu0LhYWFPqkDAEBjkJGR4dY4v35W1ObNm5WamqrFixdr8ODBcjgcKi4uVmZmpiTpqaee0p///GctW7ZMERERuvvuu1VRUaFly5ZV78PpdOqWW27R/fffrxtvvNFjvblTGwAABBa/3mPTvXt3vfrqq5o6daqsVqu6dOmiVatWVa/PycnR0KFDlZ6erujoaDmdTuXn51evd7lcGjt2rIYMGXLRUDNz5kx169atXr3VVRsAAASeRv3p3vfdd5/atm2rxx57zN+tAACAANBog83KlSuVkZGh3r17S5Jat26txYsX+7krAADgT4022AAAAPyU3yfoAwAA8BSCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMAyCDQAAMIz/BzL9W9BOH17HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa19692668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=8 #time\n",
    "\n",
    "q1_2 = QuantumRegister(3)\n",
    "c1_2 = ClassicalRegister(3)\n",
    "qw1_2 = QuantumCircuit(q1_2, c1_2)\n",
    "\n",
    "qw1_2.x(q1_2[2])\n",
    "qw1_2.u3(t, 0, 0, q1_2[1])\n",
    "qw1_2.cx(q1_2[2], q1_2[1])\n",
    "qw1_2.u3(t, 0, 0, q1_2[1])\n",
    "qw1_2.cx(q1_2[2], q1_2[1])\n",
    "\n",
    "qw1_2.measure(q1_2[0], c1_2[0])\n",
    "qw1_2.measure(q1_2[1], c1_2[2])\n",
    "qw1_2.measure(q1_2[2], c1_2[1])\n",
    "\n",
    "print(qw1_2.qasm())\n",
    "circuit_drawer(qw1_2, style=qx_color_scheme())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the result when executing the circuit on the simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1e4ab6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "job = execute(qw1_2, sim_backend, shots=1000)\n",
    "result = job.result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And below is the result when executing the circuit on the real device."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2ad6363bc5d6409685c7153adafb5757",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HTML(value=\"<p style='font-size:16px;'>Job Status : job is being initialized </p>\"),))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%qiskit_job_status\n",
    "HTMLProgressBar()\n",
    "job = execute(qw1_2, backend=device_backend, coupling_map=device_coupling, shots=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa196cb4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = job.result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion**: The walker is bounded at the initial state, which is the boundary of two phases, when the quantum walk on the line has two phases. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quantum walk, phase I on $N=4$ lattice$(t=8)$**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OPENQASM 2.0;\n",
      "include \"qelib1.inc\";\n",
      "qreg q1[3];\n",
      "creg c1[3];\n",
      "x q1[1];\n",
      "cx q1[2],q1[1];\n",
      "u3(8,0,0) q1[2];\n",
      "cx q1[2],q1[0];\n",
      "u3(8,0,0) q1[2];\n",
      "cx q1[2],q1[0];\n",
      "cx q1[2],q1[1];\n",
      "u3(16,0,0) q1[2];\n",
      "measure q1[0] -> c1[0];\n",
      "measure q1[1] -> c1[1];\n",
      "measure q1[2] -> c1[2];\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa19734358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=8 #time\n",
    "\n",
    "q1 = QuantumRegister(3)\n",
    "c1 = ClassicalRegister(3)\n",
    "qw1 = QuantumCircuit(q1, c1)\n",
    "\n",
    "qw1.x(q1[1])\n",
    "qw1.cx(q1[2], q1[1])\n",
    "qw1.u3(t, 0, 0, q1[2])\n",
    "qw1.cx(q1[2], q1[0])\n",
    "qw1.u3(t, 0, 0, q1[2])\n",
    "qw1.cx(q1[2], q1[0])\n",
    "qw1.cx(q1[2], q1[1])\n",
    "qw1.u3(2*t, 0, 0, q1[2])\n",
    "\n",
    "qw1.measure(q1[0], c1[0])\n",
    "qw1.measure(q1[1], c1[1])\n",
    "qw1.measure(q1[2], c1[2])\n",
    "\n",
    "print(qw1.qasm())\n",
    "circuit_drawer(qw1, style=qx_color_scheme())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the result when executing the circuit on the simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117882b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "job = execute(qw1, sim_backend, shots=1000)\n",
    "result = job.result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And below is the result when executing the circuit on the real device."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d1150f0eb93f449585491c3cb9226f4e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HTML(value=\"<p style='font-size:16px;'>Job Status : job is being initialized </p>\"),))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%qiskit_job_status\n",
    "HTMLProgressBar()\n",
    "job = execute(qw1, backend=device_backend, coupling_map=device_coupling, shots=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa196d4828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = job.result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion**: The walker is unbounded when the quantum walk on the line has one phase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the results from simulators match those from real devices. This hints that IBM Q systems can be used to experiments with topological quantum walk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}