Quantum computing method and a quantum computer

A quantum computing method comprising:

• operating a two-qubit gate on two qubits, the two-qubit gate having failure information related to success and failure (the failure information suggesting success is S, the failure information suggesting failure is F);
• when the failure information is F(S), defining failure information of the two qubits as F(S);
• executing an error-correction by an error-correcting teleportation, using the Knill code (at level 1:
• one-qubit-error-detecting code to encode four qubits into one qubit pair, at level equal to or larger than 2:
• one-qubit-pair-error-detecting code to encode three qubit pairs into one qubit pair) as an error-correcting code;
• executing a CNOT gate (called an encoded CNOT gate) to two encoded qubits by the error-correcting teleportation using |χ>≡|0000>+|0011>+|1101>+|1110>;
• when a measurement result of non-encoded qubits (called physical qubits, a gate of the physical qubit is called a physical gate) is processed in Bell measurement of the error-correcting teleportation, determining the measurement result and defining the failure information of an encoded qubit pair of each level by (1)˜(4),
• (1) If all failure information of the four physical qubits of level 1 have failure information S, error-detection is performed. If an error is not detected, the measured value of the encoded qubit pair of level 1 is determined, and failure information of the encoded qubit pair of level 1 is defined as S. If the error is detected, failure information of the encoded qubit pair is defined as F.
• (2) If the number of four physical qubits of level 1 with failure information F is one, one physical qubit having the failure information F is regarded as an erasure error. The erasure error of the one physical qubit is corrected, the measured value of the encoded qubit pair of level 1 is determined, and failure information of the encoded qubit pair of level 1 is defined as S.
• (3) If the number of four physical qubits with failure information F is at least two, failure information of the encoded qubit pair of level 1 is defined as F.
• (4) If all of the three encoded qubit pairs of level l (l:
• an integral number equal to or larger than one) composing an encoded qubit pair of level (l+1) have failure information S, error detection is performed. If an error is not detected, the measured value of the encoded qubit pair of level (l+1) is determined, and failure information of the encoded qubit pair of level (l+1) is defined as S. If the error is detected, the failure information of the encoded qubit pair of level (l+1) is defined as F.
• (5) If the number of the three encoded qubit pairs of level l with failure information F composing an encoded qubit pair of level (l+1) is one, one physical qubit having the failure information F is regarded as an erasure error. The erasure error of the one physical qubit is corrected, a measured value of an encoded qubit pair of level (l+1) is determined, and failure information of the encoded qubit pair of level (l+1) is defined as S.
• (6) If the number of the three encoded qubit pairs of level l with failure information F composing an encoded qubit pair of level (l+1) is at least two, failure information of the encoded qubit pair of level (l+1) is defined as F.;
• wherein the measurement result of a logical qubit pair as the encoded qubit pair of the highest level is determined.