02_Introduction_to_spin_chains_and_quantum_gates_implementation.ipynb

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    "# Implementing quantum gates from scratch: Simulating circuits and qubit gates\n",
    "\n",
    "## Exact representation of spin-1/2 operators on a chain\n",
    "\n",
    "### The starting point is to implement the Pauli spin chain operators on a spin-$1/2$ chain with $L$ spins.\n",
    "### The Pauli spin operators $X_i,Y_i,Z_i$ acting on $i$-th spin are defined as:\n",
    "### \\begin{equation}\n",
    " \\begin{split}\n",
    " X_i  &= \\mathbb{1}_1\\otimes\\dots\\mathbb{1}_{i-1}\\otimes\\hat{\\sigma}^x\\otimes\\mathbb{1}_{i+1}\\dots\\mathbb{1}_{L},\\\\\n",
    " Y_i  &= \\mathbb{1}_1\\otimes\\dots\\mathbb{1}_{i-1}\\otimes\\hat{\\sigma}^y\\otimes\\mathbb{1}_{i+1}\\dots\\mathbb{1}_{L},\\\\\n",
    " Z_i  &= \\mathbb{1}_1\\otimes\\dots\\mathbb{1}_{i-1}\\otimes\\hat{\\sigma}^z\\otimes\\mathbb{1}_{i+1}\\dots\\mathbb{1}_{L},\n",
    " \\end{split}\n",
    "\\end{equation}\n",
    "### where $\\hat{\\sigma}^{x,y,z}$ are $2\\times2$ Pauli operators.\n",
    "\n",
    "\n",
    "## spin-1/2 $\\equiv$ qubit\n",
    "\n",
    "### In a similar manner we can define Hadamard matrix $H_i$ acting on $i$-th spin, i.e.\n",
    "### \\begin{equation}\n",
    "H_i = \\mathbb{1}_1\\otimes\\dots\\mathbb{1}_{i-1}\\otimes H\\otimes\\mathbb{1}_{i+1}\\dots\\mathbb{1}_{L},\n",
    "\\end{equation}\n",
    "### where $H = \\frac{\\hat{\\sigma}^x + \\hat{\\sigma}^z}{\\sqrt{2}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b4a6e0e",
   "metadata": {},
   "source": [
    "## PyTorch implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd6bde61",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import torch as pt\n",
    "from torch import matrix_exp as expm\n",
    "from torch.linalg import eigh as eigh\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "967192a8",
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   "outputs": [],
   "source": [
    "def get_Identity(k):  # returns k-tensor product of the identity operator, ie. Id^k\n",
    "    Id = id_local\n",
    "    for i in range(0, k-1):\n",
    "        Id = pt.kron(Id, id_local)\n",
    "    return Id\n",
    "       \n",
    "def get_chain_operator(A, L, i):\n",
    "    Op = A\n",
    "    if(i == 1):\n",
    "        Op = pt.kron(A,get_Identity(L-1))\n",
    "        return Op\n",
    "    if(i == L):\n",
    "        Op = pt.kron(get_Identity(L-1),A)\n",
    "        return Op\n",
    "    if(i>0 and i<L):\n",
    "        Op = pt.kron(get_Identity(i-1), pt.kron(Op, get_Identity(L-i)))\n",
    "        return Op\n",
    "\n",
    "def get_chain_operators(L):\n",
    "    \n",
    "    Id = get_chain_operator(id_local, L, 1)\n",
    "    X = {}\n",
    "    Y = {}\n",
    "    Z = {}\n",
    "\n",
    "    for qubit_i in range(1, L+1):    # Loop over indices on a 2-dimensional grid (i_x,i_y)\n",
    "        X[qubit_i] = get_chain_operator(sigma_x, L, qubit_i)        # Define operator X_i acting on spin (i_x,i_y)\n",
    "        Y[qubit_i] = get_chain_operator(sigma_y, L, qubit_i)        # Define operator Y_i acting on spin (i_x,i_y)\n",
    "        Z[qubit_i] = get_chain_operator(sigma_z, L, qubit_i)        # Define operator Z_i acting on spin (i_x,i_y)\n",
    "    return Id, X, Y, Z\n",
    "\n",
    "\n",
    "id_local = pt.tensor([[1.,0],[0,1.]])\n",
    "sigma_x = pt.tensor([[0,1.],[1.,0]])\n",
    "sigma_y = 1j*pt.tensor([[0,-1.],[1.,0]])\n",
    "sigma_z = pt.tensor([[1.,0],[0,-1.]])\n",
    "hadamard = 1.0/pt.sqrt(pt.tensor(2))*pt.tensor([[1,1],[1,-1]])+1j*0    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88d9a44e",
   "metadata": {},
   "source": [
    "## Operators are expressed in the diagonal basis of the $Z = \\sum_{i=1}^{L} Z_i$ operator\n",
    "\n",
    "\n",
    "### \\begin{equation}\n",
    " \\begin{split}\n",
    "   |v_1\\rangle & = |\\uparrow \\uparrow \\dots \\uparrow \\rangle \\\\\n",
    "   |v_2\\rangle & = |\\uparrow \\uparrow \\dots \\downarrow \\rangle \\\\\n",
    "   & \\vdots \\\\\n",
    "   |v_D\\rangle & = |\\downarrow \\downarrow \\dots \\downarrow \\rangle \\\\\n",
    " \\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "### \\begin{equation}\n",
    "\\begin{split}\n",
    "   X & = \\sum_{k,l} <v_k|X|v_l>|v_k\\rangle\\langle v_l| \\\\\n",
    "   Y & = \\sum_{k,l} <v_k|Y|v_l>|v_k\\rangle\\langle v_l| \\\\\n",
    "   Z & = \\sum_{k,l} <v_k|Z|v_l>|v_k\\rangle\\langle v_l| \\delta_{k,l},\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "## In the following we denote: $\\uparrow \\equiv 1$, $\\downarrow \\equiv -1$.\n",
    "\n",
    "\n",
    "### Let's us construct our spin-$1/2$ chain Hilbert space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7a397bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|v_000> = | 1  1  1  1  1 >\n",
      "|v_001> = | 1  1  1  1 -1 >\n",
      "|v_002> = | 1  1  1 -1  1 >\n",
      "|v_003> = | 1  1  1 -1 -1 >\n",
      "|v_004> = | 1  1 -1  1  1 >\n",
      "|v_005> = | 1  1 -1  1 -1 >\n",
      "|v_006> = | 1  1 -1 -1  1 >\n",
      "|v_007> = | 1  1 -1 -1 -1 >\n",
      "|v_008> = | 1 -1  1  1  1 >\n",
      "|v_009> = | 1 -1  1  1 -1 >\n",
      "|v_010> = | 1 -1  1 -1  1 >\n",
      "|v_011> = | 1 -1  1 -1 -1 >\n",
      "|v_012> = | 1 -1 -1  1  1 >\n",
      "|v_013> = | 1 -1 -1  1 -1 >\n",
      "|v_014> = | 1 -1 -1 -1  1 >\n",
      "|v_015> = | 1 -1 -1 -1 -1 >\n",
      "|v_016> = |-1  1  1  1  1 >\n",
      "|v_017> = |-1  1  1  1 -1 >\n",
      "|v_018> = |-1  1  1 -1  1 >\n",
      "|v_019> = |-1  1  1 -1 -1 >\n",
      "|v_020> = |-1  1 -1  1  1 >\n",
      "|v_021> = |-1  1 -1  1 -1 >\n",
      "|v_022> = |-1  1 -1 -1  1 >\n",
      "|v_023> = |-1  1 -1 -1 -1 >\n",
      "|v_024> = |-1 -1  1  1  1 >\n",
      "|v_025> = |-1 -1  1  1 -1 >\n",
      "|v_026> = |-1 -1  1 -1  1 >\n",
      "|v_027> = |-1 -1  1 -1 -1 >\n",
      "|v_028> = |-1 -1 -1  1  1 >\n",
      "|v_029> = |-1 -1 -1  1 -1 >\n",
      "|v_030> = |-1 -1 -1 -1  1 >\n",
      "|v_031> = |-1 -1 -1 -1 -1 >\n"
     ]
    }
   ],
   "source": [
    "L = 5\n",
    "D = 2**L\n",
    "Id, X, Y, Z = get_chain_operators(L)\n",
    "\n",
    "basis = pt.zeros((D,L)) \n",
    "for v_i in range(0,D):\n",
    "    fock_state = pt.zeros(D) \n",
    "    fock_state[v_i] = 1\n",
    "    for i in range(1,L+1):\n",
    "        basis[v_i,i-1] = pt.vdot(fock_state, Z[i]@fock_state)\n",
    "\n",
    "for v_i in range(0,D):  \n",
    "    string_fock_vector = \"|v_\" + \"{:03d}\".format(v_i) + \"> = |\"\n",
    "    for i in range(1,L+1):\n",
    "        tmp = int(basis[v_i,i-1].item())\n",
    "        if(tmp==1):\n",
    "            string_plus_minus = \" {:1d}\".format(tmp)\n",
    "        if(tmp==-1):\n",
    "            string_plus_minus = \"{:1d}\".format(tmp)\n",
    "            \n",
    "         \n",
    "        string_fock_vector = string_fock_vector + string_plus_minus + \" \"\n",
    "    string_fock_vector = string_fock_vector + \">\"\n",
    "    print(string_fock_vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7052676e",
   "metadata": {},
   "source": [
    "### The many-body wave-function $|\\psi\\rangle$  decomposed in the Fock basis:\n",
    "\n",
    "### \\begin{equation}\n",
    "|\\psi\\rangle = \\sum_{k} \\psi_k |v_k\\rangle,\n",
    "\\end{equation}\n",
    "### with $\\sum_k |\\psi_k|^2 = 1$.\n",
    "\n",
    "### As such, the state of the system is encoded in a vector:\n",
    "\n",
    "### \\begin{equation}\n",
    "   |\\psi\\rangle    \\Leftrightarrow \\begin{pmatrix} \\psi_1 \\\\ \n",
    "                               \\psi_2 \\\\\n",
    "                               \\vdots \\\\ \n",
    "                               \\psi_D \n",
    "                \\end{pmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92646cde",
   "metadata": {},
   "source": [
    "### Let's construct a quantum Heisenberg Hamiltonian:\n",
    "\n",
    "### \\begin{equation}\n",
    " \\hat{H} = -\\frac{1}{2}\\sum_i J_x X_iX_{i+1} + J_y Y_iY_{i+1} + J_z Z_iZ_{i+1} + h\\sum_iZ_i\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2f1a449",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_H(parameters):\n",
    "    Jx,Jy,Jz, h = parameters\n",
    "    H = pt.zeros(D,D)\n",
    "    for i in range(1,L):\n",
    "        H = H - Jx/2*X[i]@X[i+1] - Jy/2*Y[i]@Y[i+1] - Jz/2*Z[i]@Z[i+1]\n",
    "    for i in range(1,L+1):\n",
    "        H = H + h*Z[i]\n",
    "    return H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9240eb36",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ground state energy is E_0 = -2.73\n"
     ]
    }
   ],
   "source": [
    "Jx = 1\n",
    "Jy = -1\n",
    "Jz = 0\n",
    "h = 0\n",
    "parameters = [Jx, Jy, Jz, h]\n",
    "H = get_H(parameters)\n",
    "\n",
    "E, P = eigh(H)\n",
    "E_GS = E[0]\n",
    "psi_GS = P[:,0]\n",
    "print(\"Ground state energy is E_0 = \" + \"{:2.2f}\".format(E_GS))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4b44adb",
   "metadata": {},
   "source": [
    "### Let's have a look at groundstate decomposition in a Fock states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c53188e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|psi|^2 = \n",
      "0.25 | 1  1  1  1  1 >\n",
      "0.00 | 1  1  1  1 -1 >\n",
      "0.00 | 1  1  1 -1  1 >\n",
      "0.16 | 1  1  1 -1 -1 >\n",
      "0.00 | 1  1 -1  1  1 >\n",
      "0.00 | 1  1 -1  1 -1 >\n",
      "0.08 | 1  1 -1 -1  1 >\n",
      "0.00 | 1  1 -1 -1 -1 >\n",
      "0.00 | 1 -1  1  1  1 >\n",
      "0.01 | 1 -1  1  1 -1 >\n",
      "0.00 | 1 -1  1 -1  1 >\n",
      "0.00 | 1 -1  1 -1 -1 >\n",
      "0.08 | 1 -1 -1  1  1 >\n",
      "0.00 | 1 -1 -1  1 -1 >\n",
      "0.00 | 1 -1 -1 -1  1 >\n",
      "0.08 | 1 -1 -1 -1 -1 >\n",
      "0.00 |-1  1  1  1  1 >\n",
      "0.00 |-1  1  1  1 -1 >\n",
      "0.01 |-1  1  1 -1  1 >\n",
      "0.00 |-1  1  1 -1 -1 >\n",
      "0.00 |-1  1 -1  1  1 >\n",
      "0.00 |-1  1 -1  1 -1 >\n",
      "0.00 |-1  1 -1 -1  1 >\n",
      "0.00 |-1  1 -1 -1 -1 >\n",
      "0.16 |-1 -1  1  1  1 >\n",
      "0.00 |-1 -1  1  1 -1 >\n",
      "0.00 |-1 -1  1 -1  1 >\n",
      "0.08 |-1 -1  1 -1 -1 >\n",
      "0.00 |-1 -1 -1  1  1 >\n",
      "0.00 |-1 -1 -1  1 -1 >\n",
      "0.08 |-1 -1 -1 -1  1 >\n",
      "0.00 |-1 -1 -1 -1 -1 >\n"
     ]
    }
   ],
   "source": [
    "def get_density_decomposition(psi):\n",
    "    rho = pt.abs(psi)**2\n",
    "    print(\"|psi|^2 = \")\n",
    "    for v_i in range(0,D):  \n",
    "        string_fock_vector = \"{:2.2f}\".format(rho[v_i])\n",
    "        string_fock_vector = string_fock_vector + \" |\"\n",
    "        for i in range(1,L+1):\n",
    "            tmp = int(basis[v_i,i-1].item())\n",
    "            if(tmp==1):\n",
    "                string_plus_minus = \" {:1d}\".format(tmp)\n",
    "            if(tmp==-1):\n",
    "                string_plus_minus = \"{:1d}\".format(tmp)\n",
    "\n",
    "\n",
    "            string_fock_vector = string_fock_vector + string_plus_minus + \" \"\n",
    "        string_fock_vector = string_fock_vector + \">\"\n",
    "        \n",
    "        print(string_fock_vector)\n",
    "        \n",
    "get_density_decomposition(P[:,0])        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1551361",
   "metadata": {},
   "source": [
    "# Quantum gates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b7572b3",
   "metadata": {},
   "source": [
    "### We can consider each spin-$1/2$ as a qubit, so it is straightforward to implement quantum gates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db504adc",
   "metadata": {},
   "outputs": [],
   "source": [
    "pt.set_printoptions(edgeitems=1, precision=0)\n",
    "L = 2\n",
    "Id, X, Y, Z = get_chain_operators(L)"
   ]
  },
  {
   "attachments": {
    "1000px-Quantum_Logic_Gates.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "e903535c",
   "metadata": {},
   "source": [
    "![1000px-Quantum_Logic_Gates.png](attachment:1000px-Quantum_Logic_Gates.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "041bf092",
   "metadata": {},
   "source": [
    "## Rotational gates acting on $j$-th qubit\n",
    "### \\begin{equation}\n",
    " \\begin{split}\n",
    " R^x_j(\\theta) = e^{-i\\frac{\\theta}{2} X_j} \\\\\n",
    " R^y_j(\\theta) = e^{-i\\frac{\\theta}{2} Y_j} \\\\\n",
    " R^z_j(\\theta) = e^{-i\\frac{\\theta}{2} Z_j} \\\\\n",
    " \\end{split}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b10b8016",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Rx(theta, j):\n",
    "    return expm(-1j*theta/2*X[j])\n",
    "\n",
    "def Ry(theta, j):\n",
    "    return expm(-1j*theta/2*Y[j])\n",
    "\n",
    "def Rz(theta, j):\n",
    "    return expm(-1j*theta/2*Z[j])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f13ba62b",
   "metadata": {},
   "source": [
    "## Phase gate\n",
    "\n",
    "### \\begin{equation}\n",
    " P_j(\\theta) = e^{i\\frac{\\theta}{2}}R^z_j(\\theta)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18830562",
   "metadata": {},
   "source": [
    "## Two-qubit gates\n",
    "\n",
    "### CNOT\n",
    "\n",
    "### \\begin{equation}\n",
    " {\\rm CNOT}_{i,j} = e^{i\\frac{\\pi}{4}(\\mathbb{1} - Z[i])(\\mathbb{1}-X[j])}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81331b00",
   "metadata": {},
   "outputs": [],
   "source": [
    "def CNOT(i,j):\n",
    "    return  expm(pt.pi/4*(Id - X[i])@(Id - Z[j])*1j) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7fcf2afc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1, 0, 0, 0],\n",
      "        [0, 1, 0, 0],\n",
      "        [0, 0, 0, 1],\n",
      "        [0, 0, 1, 0]])\n"
     ]
    }
   ],
   "source": [
    "print(CNOT(2,1).real)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "847a55ca",
   "metadata": {},
   "source": [
    "### Interaction gate\n",
    "\n",
    "### \\begin{equation}\n",
    " R^{XX}_{i,j}(\\theta) = e^{-i\\frac{\\theta}{2}X_i\\otimes X_j}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe89f24c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def RXX(i,j,theta):\n",
    "    return expm(-theta/2*X[i]@X[j]*1j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f62ad1d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1+0j, 0+0j, 0+0j, 0-1j],\n",
      "        [0+0j, 1+0j, 0-1j, 0+0j],\n",
      "        [0+0j, 0-1j, 1+0j, 0+0j],\n",
      "        [0-1j, 0+0j, 0+0j, 1+0j]])\n"
     ]
    }
   ],
   "source": [
    "print(RXX(1,2,pt.pi/2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d3b3799",
   "metadata": {},
   "source": [
    "### SWAP gate\n",
    "\n",
    "### \\begin{equation}\n",
    "{\\rm SWAP}_{ij} = \\frac{1}{2}(\\mathbb{1}\\otimes\\mathbb{1} + X_i\\otimes X_j + Y_i\\otimes Y_j + Z_i\\otimes Z_j)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d05a41f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def SWAP(i,j):\n",
    "    return 0.5*(Id@Id + X[i]@X[j] + Y[i]@Y[j] + Z[i]@Z[j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "934690c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1., 0., 0., 0.],\n",
      "        [0., 0., 1., 0.],\n",
      "        [0., 1., 0., 0.],\n",
      "        [0., 0., 0., 1.]])\n"
     ]
    }
   ],
   "source": [
    "print(SWAP(1,2).real)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98b7825e",
   "metadata": {},
   "source": [
    "## Three-qubits gate\n",
    "\n",
    "### Toffoli gate\n",
    "\n",
    "### \\begin{equation}\n",
    " {\\rm Toff}_{ijk} = e^{-i\\frac{\\pi}{8}(\\mathbb{1} - Z_i)(\\mathbb{1} - Z_j)(\\mathbb{1} - X_k)}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "512da9f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Toff(i,j,k):\n",
    "    return expm(pt.pi/8*(Id - Z[i])@(Id - Z[j])@(Id - X[k])*1j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d200b070",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1, 0, 0, 0, 0, 0, 0, 0],\n",
      "        [0, 1, 0, 0, 0, 0, 0, 0],\n",
      "        [0, 0, 1, 0, 0, 0, 0, 0],\n",
      "        [0, 0, 0, 1, 0, 0, 0, 0],\n",
      "        [0, 0, 0, 0, 1, 0, 0, 0],\n",
      "        [0, 0, 0, 0, 0, 1, 0, 0],\n",
      "        [0, 0, 0, 0, 0, 0, 0, 1],\n",
      "        [0, 0, 0, 0, 0, 0, 1, 0]])\n"
     ]
    }
   ],
   "source": [
    "L = 3\n",
    "Id, X, Y, Z = get_chain_operators(L)\n",
    "print(Toff(1,2,3).real)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}