Preparation of qubits

1. A quantum error correction method performed at a quantum computing system comprising a control system and a quantum processing unit having a plurality of qubits, the method comprising:

preparing, by the control system, at least one syndrome qubit and a plurality of auxiliary qubits of the plurality of qubits in respective initial states, wherein each of the at least one syndrome qubit and the plurality of auxiliary qubits has a respective probability greater than zero and less than one half of being prepared with an error;

performing, by the control system, a plurality of non-measurement multi-qubit quantum logic operations that propagate errors between the at least one syndrome qubit and the plurality of auxiliary qubits so as to reduce the probability of an error affecting the at least one syndrome qubit; and,

performing, by the control system, syndrome extraction using the at least one syndrome qubit.

2. The method of claim 1 , wherein performing the plurality of non-measurement multi-qubit quantum logic operations comprises performing, by the control system, the following gates:

a first CNOT gate controlled by the at least one syndrome qubit and acting on a first auxiliary qubit of the plurality of auxiliary qubits;

a second CNOT gate controlled by the at least one data qubit and acting on a second auxiliary qubit of the plurality of auxiliary qubits; and,

a Toffoli gate controlled by the first and second auxiliary qubits and acting on the at least one syndrome qubit.

3. The method of claim 1 , wherein performing the plurality of non-measurement multi-qubit quantum logic operations comprises performing, by the control system, the following gates:

a first CNOT gate controlled by the at least one syndrome qubit and acting on a first auxiliary qubit of the plurality of auxiliary qubits; then

a first Toffoli gate controlled by the at least one syndrome qubit and the first auxiliary qubit and acting on a second auxiliary qubit of the plurality of auxiliary qubits; and then,

a Toffoli gate controlled by the first and second auxiliary qubits and acting on the at least one syndrome qubit.

4. The method of claim 1 , wherein performing the plurality of non-measurement multi-qubit quantum logic operations comprises performing, by the control system, gate sequences logically equivalent to the gate sequences in any of FIG. 3 a , 3 b , 4 , 5 a , 5 b , 6 , 7 , 11 or 13 .

5. The method of claim 1 , further comprising concatenating the plurality of non-measurement multi-qubit quantum logic operations.

6. The method of claim 1 , wherein the respective initial states are 10> states and wherein the error is a bitflip error.

7. The method of claim 1 , wherein the auxiliary qubits are not measured.

8. A quantum computing system comprising:

a control system; and,

a quantum processing unit having a plurality of qubits,

wherein the control system is configured to:

prepare at least one syndrome qubit and a plurality of auxiliary qubits of the plurality of qubits in respective initial states, wherein each of the at least one syndrome qubit and the plurality of auxiliary qubits has a respective probability greater than zero and less than one half of being prepared with an error;

perform a plurality of non-measurement multi-qubit quantum logic operations that propagate errors between the at least one syndrome qubit and the plurality of auxiliary qubits so as to reduce the probability of an error affecting the at least one syndrome qubit; and

perform syndrome extraction using the at least one syndrome qubit.