Frontier physics

Quantum error correction and decoherence

Quantum codes protect states without directly measuring encoded information, using compatible syndrome measurements.

Quantum codes protect states without directly measuring encoded information, using compatible syndrome measurements.

Model and interpretation

The three-qubit repetition code encodes |0_L⟩=|000⟩ and |1_L⟩=|111⟩ to detect a single bit flip. Measuring parities Z₁Z₂ and Z₂Z₃ yields a syndrome without distinguishing logical states. It does not correct phase flips; a full code must protect against both.

Quick check

A three-qubit repetition code illustrates syndrome measurement: checks $Z_1Z_2$ and $Z_2Z_3$ locate a bit flip without directly measuring the logical bit. A quantum code must protect against both bit and phase errors; stabilizer checks commute and enable syndrome-based recovery. The error-correction threshold depends on the noise model and architecture. Adding physical qubits is useful only when logical error rates decrease as code size grows.

Quantum error correction does not copy an unknown state; instead, several physical qubits encode one logical qubit in a protected subspace. Syndrome measurements reveal error indicators without exposing logical phase, and a decoder selects a recovery. Real devices must repeat syndrome extraction over time and correct measurement faults too, so code design balances code distance, hardware connectivity, and gate overhead.

A code of distance $d$ can detect up to $d-1$ errors and correct up to $\lfloor(d-1)/2\rfloor$ in the relevant error model; logical information is distributed so no single physical qubit reveals the state. Below threshold, increasing code size can lower logical failure probability, enabling fault-tolerant computation.