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   "source": [
    "# Phase Shift\n",
    "Create a circuit that creates an equal superposition of two qubits, where the phase negative (shifted by $\\pi$) when the two qubits are equal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from qiskit import BasicAer, execute\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create quantum/classical registers and a quantum circuit\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Copy the equal2 function from Example 3\n",
    "\n",
    "def equal2(circ, input, output) :\n",
    "    circ.cx(input[0],output)\n",
    "    circ.cx(input[1],output)\n",
    "    circ.x(output)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build the phase shift circuit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulate and show results\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "job = execute(qc, backend, shots=512)  # shots default = 1024\n",
    "result = job.result()\n",
    "print(result.get_counts())\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But where's the phase shift?  It's not noticeable in the measurements, because squaring a negative number is the same as squaring its absolute value.  So we have to use the **statevector_simulator** instead.  There are no measurements allowed, so go back and comment out the measurement -- then skip the box above and run the box below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulate and show results\n",
    "backend = BasicAer.get_backend('statevector_simulator')\n",
    "job = execute(qc, backend) \n",
    "result = job.result()\n",
    "print(result.get_statevector())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the state of all three qubits.  The output bit shows up as the most significant bit in the state.  Since it is always 1 at the end of the circuit, the first four states |0xx> all have amplitude zero.  The remaining four states are equally likely, and you can see the negative magnitude for the cases where the output bits are equal: |100> and |111>."
   ]
  }
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