Stabilizer Codes and Quantum Bits
The concept behind quantum error correction is to encode quantum information in a way that allows for error detection and correction. Stabilizer codes are used to do this, encoding many qubits into a larger quantum state and generating redundancy that enables error detection and repair. While the physical qubits they are recorded within are known as "data qubits," the qubits employed for error correction are frequently referred to as "logical qubits." These logical qubits perform detection events for error and implement solutions as such within the logical qubits.
Syndrome Measurement
Syndromes are measurement results from certain measurements on the encoded qubits that are used in quantum error correction. These symptoms suggest the existence of faults without outlining their precise nature. Errors in the quantum state must be found and located using syndrome measurements. These measurements provide information about the error but not what is within the qubit itself, which is a benefit and hindrance to information at the same time. On one hand, superposition would be destroyed if all the information about the qubit was extracted, but without it, there is a lack in specification of error, leading to potentially harder development of error correction.
Quantum Error Detection and Correction
A combination of error detection and correction techniques are used in quantum error correction. Error detection uses measurements of syndromes to find errors when they are present. To undo the consequences of faults and return the encoded qubits to their intended quantum state, error correction operations are undertaken, guided by the syndromes. Refer to Fig. 10, which displays a visual for how error detection and correction works, with syndrome qubits being spaced separately, for more efficient and even coverage. For practicality purposes, most experts suggest an error rate of about one in a million, but the best error rates achievable as of now are around one in one thousand. There certainly is more progress necessary to attain a practical system of correction.