def correct(self, qubits: list[cirq.Qid], ancillas: list[cirq.Qid]) -> cirq.Circuit:
        """Corrects the code word.

        Creates a correction circuit by computing the syndrome on the ancillas, and then using this
        syndrome to correct the qubits.

        Args:
            qubits: a vector of self.n qubits that contains (potentially corrupted) code words
            ancillas: a vector of self.n - self.k qubits that are set to zero and will contain the
                syndrome once the circuit is applied.

        Returns:
            The circuit that both computes the syndrome and uses this syndrome to correct errors.
        """
        circuit = cirq.Circuit()

        gate_dict = {'X': cirq.X, 'Y': cirq.Y, 'Z': cirq.Z}

        # We set the ancillas so that measuring them directly would be the same
        # as measuring the qubits with Pauli strings. In other words, we store
        # the syndrome inside the ancillas.
        for r in range(self.n - self.k):
            for n in range(self.n):
                if self.M[r][n] == 'Z':
                    circuit.append(cirq.ControlledOperation([qubits[n]], cirq.X(ancillas[r])))
                elif self.M[r][n] == 'X':
                    circuit.append(cirq.H(qubits[n]))
                    circuit.append(cirq.ControlledOperation([qubits[n]], cirq.X(ancillas[r])))
                    circuit.append(cirq.H(qubits[n]))
                elif self.M[r][n] == 'Y':
                    circuit.append(cirq.S(qubits[n]) ** -1)
                    circuit.append(cirq.H(qubits[n]))
                    circuit.append(cirq.ControlledOperation([qubits[n]], cirq.X(ancillas[r])))
                    circuit.append(cirq.H(qubits[n]))
                    circuit.append(cirq.S(qubits[n]))

        # At this stage, the ancillas are equal to the syndrome. Now, we apply
        # the errors back to correct the code.

        for syndrome, correction in self.syndromes_to_corrections.items():
            op = gate_dict[correction[0]]
            n = correction[1]

            # We do a Boolean operation on the ancillas (i.e. syndrome).
            for r in range(self.n - self.k):
                if syndrome[r] == 1:
                    circuit.append(cirq.X(ancillas[r]))

            circuit.append(cirq.ControlledOperation(ancillas, op(qubits[n])))

            for r in range(self.n - self.k):
                if syndrome[r] == 1:
                    circuit.append(cirq.X(ancillas[r]))

        return circuit
Corrects the code word.

        Creates a correction circuit by computing the syndrome on the ancillas, and then using this
        syndrome to correct the qubits.

        Args:
            qubits: a vector of self.n qubits that contains (potentially corrupted) code words
            ancillas: a vector of self.n - self.k qubits that are set to zero and will contain the
                syndrome once the circuit is applied.

        Returns:
            The circuit that both computes the syndrome and uses this syndrome to correct errors.
        
examples/stabilizer_code.py