community/algorithms/simon_algorithm.ipynb

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   "source": [
    "<img src=\"../../images/qiskit-heading.gif\" 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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   "cell_type": "markdown",
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   "source": [
    "## _*The Simon Algorithm*_ \n",
    "\n",
    "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n",
    "\n",
    "The Simon algorithm is an example that shows a quantum algorithm can solve a problem exponentially efficient than any classical algorithms. Like the Grover search, it depends on the existence of a blackbox (or, oracle) function that returns a predefined output over specific input or query. In the query-complexity setting, one cares only about how many queries are required to solve a specific problem, but does not care how the blackbox is realized. However, in this tutorial we have to implement it using the unit gates available in QISKit, just like we have done with the Grover search.\n",
    "\n",
    "We first describe the problem addressed by the Simon algorithm, show the steps of the algorithm and the construction of the blackbox function, and present the experimental results on simulators and real devices. \n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Rudy Raymond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Problem <a id='introduction'></a>\n",
    "\n",
    "The Simon algorithm deals with finding a hidden integer $s \\in \\{0,1\\}^n$ from an oracle $f_s$ that satisfies $f_s(x) = f_s(y)$ if and only if $y = x \\oplus s$ for all $x \\in \\{0,1\\}^n$.  Here, the $\\oplus$ is the bitwise XOR operation. Thus, if $s = 0\\ldots 0$, i.e., the all-zero bitstring, then $f_s$ is a 1-to-1 (or, permutation) function. Otherwise, if $s \\neq 0\\ldots 0$, then $f_s$ is a 2-to-1 function. \n",
    "\n",
    "The Simon algorithm can find the hidden integer using only $O(n)$ queries to the blackbox function, while any classical algorithms require $\\Omega(\\sqrt{2^n})$ queries. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Algorithm to Find the Hidden Integer\n",
    "\n",
    "The Simon algorithm finds the hidden integer by combining quantum algorithm with postprocessing on classical computers as below. \n",
    "\n",
    "1. Prepare two quantum registers each of length $n$ that are initialized to all-zero bitstring: the first one as input and the second one as output of the blackbox function.\n",
    "$$\n",
    "|0\\rangle |0\\rangle\n",
    "$$\n",
    "\n",
    "2. Apply Hadamard gates to the first register to create superposition of all possible inputs. \n",
    "$$\n",
    "H^{\\otimes n} |0\\rangle |0\\rangle = \\frac{1}{\\sqrt{2^n}} \\sum_{x=0}^{2^n-1} |x\\rangle |0\\rangle\n",
    "$$\n",
    "\n",
    "3. Query the blackbox function to obtain the answer to queries on the second register.\n",
    "$$\n",
    "\\frac{1}{\\sqrt{2^n}} \\sum_{x=0}^{2^n-1} U_{f_s}|x\\rangle |0\\rangle = \\frac{1}{\\sqrt{2^n}} \\sum_{x=0}^{2^n-1} |x\\rangle |f_s(x)\\rangle\n",
    "$$\n",
    "\n",
    "4. Apply Hadamard gates to the first register. \n",
    "$$\n",
    "\\frac{1}{\\sqrt{2^n}} \\sum_{x=0}^{2^n-1} H^{\\otimes n}|x\\rangle |f_s(x)\\rangle = \\frac{1}{2^n} \\sum_{y=0}^{2^n-1}\\sum_{x=0}^{2^n-1} (-1)^{x \\cdot y}|y\\rangle |f_s(x)\\rangle = \\frac{1}{2^n} \\sum_{y=0}^{2^n-1} |y\\rangle \\sum_{x=0}^{2^n-1} ( (-1)^{x \\cdot y} + (-1)^{(x\\oplus s) \\cdot y} )  |f_s(x)\\rangle\n",
    "$$\n",
    "\n",
    "    Notice that at the right-hand side of the above equation, because $(-1)^{(x\\oplus s) \\cdot y} = (-1)^{x\\cdot y +  s \\cdot y}$ we can conclude that the probability amplitude of the basis state $|y\\rangle |f_s(x)\\rangle$ is $(-1)^{x\\cdot y} (1 + (-1)^{s \\cdot y}  )$, which is zero if and only if $s \\cdot y = 1$. Thus, measuring the first register will always give $y$ such that $s \\cdot y = 0$. Moreover, we can obtain many different $y$'s by repeating Step 1 to 4. \n",
    "\n",
    "5. Repeat Step 1 to 4 for $m$ times to obtain $y_1, y_2, \\ldots, y_m$. \n",
    "\n",
    "6. **(Classical post-processing)** Let $\\mathbf{Y}$ be an $m\\times n$ matrix whose $i$-th row is $y_i$ in Step 5, and $\\vec{s}$ be the column vector whose $j$-th element is the $j$-th bit of $s$. Solve the following system of linear equations to obtain $s$. \n",
    "$$\n",
    "\\mathbf{Y} \\vec{s} = 0 \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Circuit <a id=\"circuit\"></a>\n",
    "\n",
    "We now implement the Simon algorithm with Qiskit by first preparing the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:51:35.519392Z",
     "start_time": "2018-09-25T18:51:35.501393Z"
    }
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   "outputs": [],
   "source": [
    "#initialization\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import BasicAer, IBMQ\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:50:06.948246Z",
     "start_time": "2018-09-25T18:50:06.016456Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load the saved IBMQ accounts\n",
    "IBMQ.load_accounts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then set the hidden bitstring $s$ that will be used to construct the circuit of the blackbox function (whose details will be given later). The number of qubits used in the experiment is twice the length of the bitstring $s$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:47:05.431217Z",
     "start_time": "2018-09-25T18:47:05.428155Z"
    }
   },
   "outputs": [],
   "source": [
    "s = \"010101\" # the hidden bitstring\n",
    "\n",
    "assert 1 < len(s) < 20, \"The length of s must be between 2 and 19\"\n",
    "\n",
    "for c in s:\n",
    "    assert c == \"0\" or c == \"1\", \"s must be a bitstring of '0' and '1'\"\n",
    "    \n",
    "n = len(s) #the length of the bitstring"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then use Qiskit to create the circuit of the Simon algorithm prior the querying the blackbox function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:47:05.439545Z",
     "start_time": "2018-09-25T18:47:05.433240Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.barrier.Barrier at 0xa17f90f28>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 1\n",
    "# Creating registers\n",
    "# qubits for querying the oracle and recording its output\n",
    "qr = QuantumRegister(2*n)\n",
    "# for recording the measurement on the first register of qr\n",
    "cr = ClassicalRegister(n)\n",
    "\n",
    "circuitName = \"Simon\"\n",
    "simonCircuit = QuantumCircuit(qr, cr)\n",
    "\n",
    "# Step 2\n",
    "# Apply Hadamard gates before querying the oracle\n",
    "for i in range(n):\n",
    "    simonCircuit.h(qr[i])\n",
    "\n",
    "# Apply barrier to mark the beginning of the blackbox function\n",
    "simonCircuit.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing a Circuit for the Blackbox Function\n",
    "\n",
    "We now details the construction of 1-to-1 and 2-to-1 permutation circuit of the blackbox function. Let us assume the blackbox function receive $|x\\rangle|0\\rangle$ as input. With regards to a predetermined $s$, the blackbox function writes its output to the second register so that it transforms the input to $|x\\rangle|f_s(x)\\rangle$ such that $f(x) = f(x\\oplus s)$ for all $x \\in \\{0,1\\}^n$. \n",
    "\n",
    "Such a blackbox function can be realized by the following procedures.\n",
    "\n",
    "-  Copy the content of the first register to the second register.\n",
    "$$\n",
    "|x\\rangle|0\\rangle \\rightarrow |x\\rangle|x\\rangle\n",
    "$$\n",
    "\n",
    "-  **(Creating 1-to-1 or 2-to-1 mapping)** If $s$ is not all-zero, then there is the least index $j$ so that $s_j = 1$. If $x_j = 0$, then XOR the second register with $s$. Otherwise, do not change the second register.\n",
    "$$\n",
    "|x\\rangle|x\\rangle \\rightarrow |x\\rangle|x \\oplus s\\rangle~\\mbox{if}~x_j = 0~\\mbox{for the least index j}\n",
    "$$\n",
    "\n",
    "-  **(Creating random permutation)** Randomly permute and flip the qubits of the second register.\n",
    "$$\n",
    "|x\\rangle|y\\rangle \\rightarrow |x\\rangle|f_s(y)\\rangle\n",
    "$$\n",
    "\n",
    "Below is the circuit of the blacbox function based on the above procedures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:47:05.449055Z",
     "start_time": "2018-09-25T18:47:05.441604Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.barrier.Barrier at 0xa17faf390>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 3 query the blackbox function\n",
    "# copy the content of the first register to the second register\n",
    "for i in range(n):\n",
    "    simonCircuit.cx(qr[i], qr[n+i])\n",
    "\n",
    "# get the least index j such that s_j is \"1\"\n",
    "j = -1\n",
    "for i, c in enumerate(s):\n",
    "    if c == \"1\":\n",
    "        j = i\n",
    "        break\n",
    "\n",
    "# Creating 1-to-1 or 2-to-1 mapping with the j-th qubit of x as control to XOR the second register with s\n",
    "for i, c in enumerate(s):\n",
    "    if c == \"1\" and j >= 0:\n",
    "        simonCircuit.cx(qr[j], qr[n+i]) #the i-th qubit is flipped if s_i is 1\n",
    "\n",
    "# get random permutation of n qubits\n",
    "perm = list(np.random.permutation(n))\n",
    "\n",
    "#initial position\n",
    "init = list(range(n))\n",
    "i = 0\n",
    "while i < n:\n",
    "    if init[i] != perm[i]:\n",
    "        k = perm.index(init[i])\n",
    "        simonCircuit.swap(qr[n+i], qr[n+k]) #swap qubits\n",
    "        init[i], init[k] = init[k], init[i] #marked swapped qubits\n",
    "    else:\n",
    "        i += 1\n",
    "        \n",
    "# randomly flip the qubit\n",
    "for i in range(n):\n",
    "    if np.random.random() > 0.5:\n",
    "        simonCircuit.x(qr[n+i])\n",
    "\n",
    "# Apply the barrier to mark the end of the blackbox function\n",
    "simonCircuit.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can continue with the steps of the Simon algorithm: applying the Hadamard gates to the first register and measure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:47:08.221872Z",
     "start_time": "2018-09-25T18:47:05.450515Z"
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   "outputs": [
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa17fa04a8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 4 apply Hadamard gates to the first register\n",
    "for i in range(n):\n",
    "    simonCircuit.h(qr[i])\n",
    "    \n",
    "# Step 5 perform measurement on the first register\n",
    "for i in range(n):\n",
    "    simonCircuit.measure(qr[i], cr[i])\n",
    "\n",
    "#draw the circuit\n",
    "simonCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimenting with Simulators\n",
    "\n",
    "We show the experiments of finding the hidden integer with simulators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:47:10.099909Z",
     "start_time": "2018-09-25T18:47:08.226926Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1e420160>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use local simulator\n",
    "backend = BasicAer.get_backend(\"qasm_simulator\")\n",
    "# the number of shots is twice the length of the bitstring\n",
    "shots = 2*n\n",
    "job = execute(simonCircuit, backend=backend, shots=shots)\n",
    "answer = job.result().get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the results of the measurements are the basis whose inner product with the hidden string $s$ are zero. \n",
    "\n",
    "*(Notice that the basis on the label of the x-axis in the above plot are numbered from right to left instead of from left to right that we used for $s$)*\n",
    "\n",
    "Gathering the measurement results, we proceed to post-processing with computations that can be done on classical computers. \n",
    "\n",
    "### Post Processing with Gaussian Elimination\n",
    "\n",
    "The post processing is done with Gaussian elimination to solve the system of linear equations to determine $s$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:47:10.109591Z",
     "start_time": "2018-09-25T18:47:10.101528Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The hidden bistring s[ 0 ], s[ 1 ]....s[ 5 ] is the one satisfying the following system of linear equations:\n",
      "s[ 0 ] = 0\n",
      "s[ 1 ] + s[ 5 ] = 0\n",
      "s[ 2 ] = 0\n",
      "s[ 3 ] + s[ 5 ] = 0\n",
      "s[ 4 ] = 0\n"
     ]
    }
   ],
   "source": [
    "# Post-processing step\n",
    "# Constructing the system of linear equations Y s = 0\n",
    "# By k[::-1], we reverse the order of the bitstring\n",
    "lAnswer = [ (k[::-1],v) for k,v in answer.items() if k != \"0\"*n  ] #excluding the trivial all-zero\n",
    "#Sort the basis by their probabilities\n",
    "lAnswer.sort(key = lambda x: x[1], reverse=True)\n",
    "\n",
    "Y = []\n",
    "for k, v in lAnswer:\n",
    "    Y.append( [ int(c) for c in k ] )\n",
    "\n",
    "\n",
    "#import tools from sympy\n",
    "from sympy import Matrix, pprint, MatrixSymbol, expand, mod_inverse\n",
    "\n",
    "\n",
    "Y = Matrix(Y)\n",
    "\n",
    "#pprint(Y)\n",
    "\n",
    "#Perform Gaussian elimination on Y\n",
    "Y_transformed = Y.rref(iszerofunc=lambda x: x % 2==0) # linear algebra on GF(2) \n",
    "\n",
    "#to convert rational and negatives in rref of linear algebra on GF(2)\n",
    "def mod(x,modulus):\n",
    "    numer, denom = x.as_numer_denom()\n",
    "    return numer*mod_inverse(denom,modulus) % modulus\n",
    "\n",
    "Y_new = Y_transformed[0].applyfunc(lambda x: mod(x,2)) #must takecare of negatives and fractional values\n",
    "#pprint(Y_new)\n",
    "\n",
    "print(\"The hidden bistring s[ 0 ], s[ 1 ]....s[\",n-1,\"] is the one satisfying the following system of linear equations:\")\n",
    "rows, cols = Y_new.shape\n",
    "for r in range(rows):\n",
    "    Yr = [ \"s[ \"+str(i)+\" ]\" for i, v in enumerate(list(Y_new[r,:])) if v == 1 ]\n",
    "    if len(Yr) > 0:\n",
    "        tStr = \" + \".join(Yr)\n",
    "        print(tStr, \"= 0\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As seen above, the system of linear equations is satisfied by the hidden integer $s$. Notice that there can be more than one solutions to the system. In fact, all-zero bitstring is a trivial solution to the system of linear equations. But by having more samples one can narrow down the candidates of the solution, and then test the solution by querying the blackbock in the classical manner.\n",
    "\n",
    "## Experimenting with Real Devices\n",
    "\n",
    "We see how one can still find out the hidden integer by running the Simon algorithm on real devices. Due to imperfect quantum computers, obtaining the conclusion is not as easy as done with the simulator of perfect quantum computers.\n",
    "\n",
    "We first register the token and query the available backends. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:50:10.894408Z",
     "start_time": "2018-09-25T18:50:10.886028Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<QasmSimulatorPy('qasm_simulator') from BasicAer()>,\n",
       " <StatevectorSimulatorPy('statevector_simulator') from BasicAer()>,\n",
       " <UnitarySimulatorPy('unitary_simulator') from BasicAer()>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BasicAer.backends()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<IBMQBackend('ibmqx4') from IBMQ()>,\n",
       " <IBMQBackend('ibmq_16_melbourne') from IBMQ()>,\n",
       " <IBMQBackend('ibmq_qasm_simulator') from IBMQ()>,\n",
       " <IBMQBackend('ibmq_20_tokyo') from IBMQ(ibm-q-melbourne, internal, default)>,\n",
       " <IBMQBackend('ibmq_qasm_simulator') from IBMQ(ibm-q-melbourne, internal, default)>,\n",
       " <IBMQBackend('ibmq_20_tokyo') from IBMQ(ibm-q-internal, research, melbourne)>,\n",
       " <IBMQBackend('ibmq_qasm_simulator') from IBMQ(ibm-q-internal, research, melbourne)>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IBMQ.backends()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:52:15.659234Z",
     "start_time": "2018-09-25T18:52:14.298564Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status of ibmq_16_melbourne is BackendStatus(backend_name='ibmq_16_melbourne', backend_version='1.0.0', operational=True, pending_jobs=0, status_msg='active')\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3f7b7a2e8c1643b5b4053ae6d21f4baf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HTML(value=\"<p style='font-size:16px;'>Job Status: job is being initialized </p>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Use one of the available backends \n",
    "backend = IBMQ.get_backend(\"ibmq_16_melbourne\")\n",
    "\n",
    "# show the status of the backend\n",
    "print(\"Status of\", backend, \"is\", backend.status())\n",
    "\n",
    "shots = 10*n #run more experiments to be certain\n",
    "max_credits = 3          # Maximum number of credits to spend on executions. \n",
    "\n",
    "job_exp = execute(simonCircuit, backend=backend, shots=shots, max_credits=max_credits)\n",
    "job_monitor(job_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T14:28:21.410640Z",
     "start_time": "2018-09-26T14:28:20.585612Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa17b0f8d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = job_exp.result()\n",
    "answer = results.get_counts(simonCircuit)\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The hidden bistring s[ 0 ], s[ 1 ]....s[ 5 ] is the one satisfying the following system of linear equations:\n",
      "s[ 0 ] = 0\n",
      "s[ 1 ] = 0\n",
      "s[ 2 ] = 0\n",
      "s[ 3 ] = 0\n",
      "s[ 4 ] = 0\n",
      "s[ 5 ] = 0\n"
     ]
    }
   ],
   "source": [
    "# Post-processing step\n",
    "# Constructing the system of linear equations Y s = 0\n",
    "# By k[::-1], we reverse the order of the bitstring\n",
    "lAnswer = [ (k[::-1][:n],v) for k,v in answer.items() ] #excluding the qubits that are not part of the inputs\n",
    "#Sort the basis by their probabilities\n",
    "lAnswer.sort(key = lambda x: x[1], reverse=True)\n",
    "\n",
    "Y = []\n",
    "for k, v in lAnswer:\n",
    "    Y.append( [ int(c) for c in k ] )\n",
    "\n",
    "Y = Matrix(Y)\n",
    "\n",
    "#Perform Gaussian elimination on Y\n",
    "Y_transformed = Y.rref(iszerofunc=lambda x: x % 2==0) # linear algebra on GF(2)\n",
    "Y_new = Y_transformed[0].applyfunc(lambda x: mod(x,2)) #must takecare of negatives and fractional values\n",
    "#pprint(Y_new)\n",
    "\n",
    "print(\"The hidden bistring s[ 0 ], s[ 1 ]....s[\",n-1,\"] is the one satisfying the following system of linear equations:\")\n",
    "rows, cols = Y_new.shape\n",
    "for r in range(rows):\n",
    "    Yr = [ \"s[ \"+str(i)+\" ]\" for i, v in enumerate(list(Y_new[r,:])) if v == 1 ]\n",
    "    if len(Yr) > 0:\n",
    "        tStr = \" + \".join(Yr)\n",
    "        print(tStr, \"= 0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## References\n",
    "\n",
    "[1] \"[On the power of quantum computation](https://epubs.siam.org/doi/abs/10.1137/S0097539796298637)\", Daniel R. Simon, SIAM J. Comput., 26(5), 1474–1483 (1997) "
   ]
  }
 ],
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   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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