Quantum Error Correction

Quantum error correction studies how to protect quantum information from noise, a prerequisite for long computations and reliable quantum computers. It encodes logical qubits in stabilizer codes such as surface and quantum low-density parity-check (LDPC) codes, repeatedly measures error syndromes, and designs fault-tolerant gates and syndrome-extraction circuits. Decoders range from minimum-weight matching and belief propagation with ordered-statistics decoding to tensor-network and neural methods; code discovery also uses algebraic search, optimization, and learned proposals, sometimes tailored to hardware noise. The central challenge is to improve logical accuracy while keeping qubit overhead, decoding latency, and calibration manageable on real devices, where simulated noise models may not predict hardware performance.