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# Apply CNOT gates to create entanglement
circ.cx(qreg[0], qreg[1])
circ.cx(qreg[0], qreg[2])
circ.cx(qreg[3], qreg[1])
circ.cx(qreg[3], qreg[2])
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The color code is a type of topological quantum error correction code that is implemented on a two-dimensional lattice of qubits. The lattice is divided into three types of cells, each of which is assigned a color (red, green, or blue). The color code gets its name from this coloring scheme.
The qubits are located at the vertices of the lattice, and each cell of the lattice corresponds to a stabilizer. The stabilizers are chosen so that any error affecting a single qubit will cause a detectable change in the stabilizer measurements.
Here's how you might implement the color code in Qiskit for a 2x2 lattice:
python
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# Apply Hadamard gates to each qubit
for i in range(dim_x * dim_y):
circ.h(qreg[i])
# Apply CNOT gates to create entanglement
for i in range(dim_x * dim_y - 1):
circ.cx(qreg[i], qreg[i + 1])
# Apply additional CNOT gates based on the color of each cell
for i in range(dim_x * dim_y):
if i % 3 == 0: # Red cell
circ.cx(qreg[i], qreg[(i + 1) % (dim_x * dim_y)])
circ.cx(qreg[i], qreg[(i + 2) % (dim_x * dim_y)])
elif i % 3 == 1: # Green cell
circ.cx(qreg[i], qreg[(i + 1) % (dim_x * dim_y)])
circ.cx(qreg[i], qreg[(i + 2) % (dim_x * dim_y)])
else: # Blue cell
circ.cx(qreg[i], qreg[(i + 1) % (dim_x * dim_y)])
circ.cx(qreg[i], qreg[(i + 2) % (dim_x * dim_y)])
This code applies a Hadamard gate to each qubit to create a superposition of states, and then applies CNOT gates to create entanglement between the qubits. The specific pattern of CNOT gates is chosen based on the color of each cell in the lattice.
In the next part, we will implement the error detection process.
