Quantum error correction

Qubits are sensitive to interactions with their environment and to imperfect control operations. These effects can alter stored quantum information before a computation is complete. Unlike a classical bit error, a quantum error may involve changes analogous to bit flips, phase flips, or combinations of them. Long computations therefore need methods that detect and manage errors while preserving the quantum information being processed.

A quantum error-correcting code encodes a logical qubit in a larger group of physical qubits. Rather than measuring the encoded state directly, a computer measures selected properties of the group, called error syndromes. These measurements provide clues about what kind of error may have occurred without revealing the logical qubit's encoded value. A recovery operation can then correct the inferred error, or the information can be decoded later. Quantum error correction cannot simply copy an unknown qubit: it uses carefully structured correlations among qubits instead.

The Shor code, introduced in 1995, was an early quantum code and uses nine physical qubits to encode one logical qubit while correcting single-qubit errors. Other codes include the seven-qubit Steane code and surface codes, which arrange qubits and checks in a two-dimensional pattern. In fault-tolerant computing, information processing and error correction are designed so that errors introduced during the correction process do not overwhelm the protection. A code's threshold is the level of physical noise below which increasing the code size can reduce logical errors, subject to the assumptions and noise model of that code.

Logical qubits require multiple physical qubits, repeated measurements and classical processing to interpret syndromes. This resource cost, often called overhead, can be substantial and varies by code, hardware and intended operation. Researchers are developing codes and decoders that reduce these costs and demonstrating improved logical memories. In a 2025 Nature paper, Google Quantum AI and collaborators reported distance-5 and distance-7 surface-code memories operating below a threshold in their experimental system; the result was evidence of error suppression in that platform, not a general solution to the overhead or scalability challenge.

Quantum error correction and quantum error mitigation are related but distinct. Error correction encodes logical information, detects error syndromes and aims to suppress errors in a way that can scale toward fault tolerance. Error mitigation uses methods such as repeated sampling or noise characterization to estimate more accurate results from a noisy computation, generally without fully correcting each error during the computation. Both are active areas of research for making near-term quantum experiments more reliable.