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38 changes: 18 additions & 20 deletions docs/tutorials/repetition-codes.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -23,8 +23,6 @@
"\n",
"To enable real-time quantum error correction (QEC), you need to be able to dynamically control quantum program flow during execution so that quantum gates can be conditioned on measurement results. This tutorial runs the bit-flip code, which is a very simple form of QEC. It demonstrates a dynamic quantum circuit that can protect an encoded qubit from a single bit-flip error, and then evaluates the bit-flip code performance.\n",
"\n",
"You can exploit additional ancilla qubits and entanglement to measure *stabilizers* that do not transform encoded quantum information, while still informing you of some classes of errors that might have occurred. A quantum stabilizer code encodes $k$ logical qubits into $n$ physical qubits. Stabilizer codes critically focus on correcting a discrete error set with support from the Pauli group $\\Pi^n$.\n",
"\n",
"For more information about QEC, refer to [Quantum Error Correction for Beginners.](https://arxiv.org/abs/0905.2794)"
]
},
Expand Down Expand Up @@ -75,24 +73,6 @@
"service = QiskitRuntimeService()"
]
},
{
"cell_type": "markdown",
"id": "4d01e8d3",
"metadata": {},
"source": [
"## Step 1. Map classical inputs to a quantum problem"
]
},
{
"cell_type": "markdown",
"id": "cdee0b18",
"metadata": {},
"source": [
"### Build a bit-flip stabilizer circuit\n",
"\n",
"The bit-flip code is among the simplest examples of a stabilizer code. It protects the state against a single bit-flip (X) error on any of the encoding qubits. Consider the action of bit-flip error $X$, which maps $|0\\rangle \\rightarrow |1\\rangle$ and $|1\\rangle \\rightarrow |0\\rangle$ on any of our qubits, then we have $\\epsilon = \\{E_0, E_1, E_2 \\} = \\{IIX, IXI, XII\\}$. The code requires five qubits: three are used to encode the protected state, and the remaining two are used as stabilizer measurement ancillas."
]
},
{
"cell_type": "code",
"execution_count": null,
Expand All @@ -110,6 +90,24 @@
")"
]
},
{
"cell_type": "markdown",
"id": "4d01e8d3",
"metadata": {},
"source": [
"## Step 1. Map classical inputs to a quantum problem"
]
},
{
"cell_type": "markdown",
"id": "cdee0b18",
"metadata": {},
"source": [
"### Build a bit-flip stabilizer circuit\n",
"\n",
"The bit-flip code protects the state against a single bit-flip (X) error on any of the encoding qubits. Consider the action of bit-flip error $X$, which maps $|0\\rangle \\rightarrow |1\\rangle$ and $|1\\rangle \\rightarrow |0\\rangle$ on any of our qubits, then we have $\\epsilon = \\{E_0, E_1, E_2 \\} = \\{IIX, IXI, XII\\}$. The code requires five qubits: three are used to encode the protected state, and the remaining two are used as stabilizer measurement ancillas."
]
},
{
"cell_type": "code",
"execution_count": null,
Expand Down
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