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The distillation circuit for |Y> state can be implemented using the 7-qubit Steane code. The 7-qubit Steane is one of the quantum error correction codes. This circuit consists of initialization of |0> and |+>, multi-target CNOTs, logical S gate teleportation, and X-basis measurements. In this circuit, seven qubits are encoded in Steane code and entangled with qubit 8 using the multi-target CNOTs. After that, seven encoded qubits are each rotated with an S gate using |Y> state. The |Y> state used is either the injected state in the first round or the state distilled in a prior round. The output state on qubit 8 is interpreted by evaluating the X-basis measurement outcomes of the seven qubits and eigenvalues of the Steane code X stabilizers. If the two conditions are satisfied, the output is considered purified |Y> state. Otherwise, the state is discarded, and the subsequent distillation rounds are performed. |
IEEE/ICACT20240330 Slide.09
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