Noise and Error Correction

Physical qubits are noisy. Fault-tolerant computation encodes one logical qubit across many physical qubits and repairs errors faster than they accumulate.

Learning objectives

Name the main error channels affecting qubits.
Describe how stabiliser measurements detect errors without reading the data.
Explain the threshold concept and its resource cost.

Error channels

Relaxation, dephasing, imperfect control pulses, crosstalk, and readout error each degrade results differently. Reported fidelities should therefore always state which channel was measured.

Stabiliser codes

Codes such as the surface code measure parity checks on groups of qubits. The checks reveal where an error occurred without revealing the encoded value, so correction does not destroy the computation.

Thresholds and overhead

Below a hardware-specific error threshold, adding more physical qubits reduces the logical error rate. Above it, more qubits make things worse. Current overhead estimates are large, which is why logical-qubit counts matter more than physical ones.

Check your understanding

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