Editing Quantum decoherence (section)

==== Quantum Error Correction (QEC) ====
{{Only primary sources|date=December 2024}}
One of the most powerful tools for combating quantum decoherence is '''[[Quantum error correction|Quantum Error Correction]]''' (QEC). QEC schemes encode quantum information redundantly across multiple physical qubits, allowing for the detection and correction of errors without directly measuring the quantum state. These QEC protocols rely on the assumption that errors affect only a small fraction of qubits at any given time, enabling the detection and correction of errors through redundant encoding. Here are some representative QEC protocols.

* [[Shor code|Shor Code]]:<ref>{{Cite journal |last=Shor |first=Peter W. |date=1995-10-01 |title=Scheme for reducing decoherence in quantum computer memory |url=http://dx.doi.org/10.1103/physreva.52.r2493 |journal=Physical Review A |volume=52 |issue=4 |pages=R2493–R2496 |doi=10.1103/physreva.52.r2493 |bibcode=1995PhRvA..52.2493S |issn=1050-2947}}</ref> One of the first quantum error correction codes, it encodes a single qubit into nine physical qubits to protect against both bit-flip and phase-flip errors.

* [[Steane code|Steane Code]]:<ref>{{Cite journal |last=Steane |first=A. M. |date=1996-07-29 |title=Error Correcting Codes in Quantum Theory |url=http://dx.doi.org/10.1103/physrevlett.77.793 |journal=Physical Review Letters |volume=77 |issue=5 |pages=793–797 |doi=10.1103/physrevlett.77.793 |pmid=10062908 |bibcode=1996PhRvL..77..793S |issn=0031-9007}}</ref> A 7-qubit code that provides error correction for arbitrary errors.

* Surface Codes:<ref>{{Cite journal |last1=Dennis |first1=Eric |last2=Kitaev |first2=Alexei |last3=Landahl |first3=Andrew |last4=Preskill |first4=John |date=2002-09-01 |title=Topological quantum memory |url=http://dx.doi.org/10.1063/1.1499754 |journal=Journal of Mathematical Physics |volume=43 |issue=9 |pages=4452–4505 |doi=10.1063/1.1499754 |arxiv=quant-ph/0110143 |bibcode=2002JMP....43.4452D |issn=0022-2488}}</ref> A more scalable error correction code that uses a 2D lattice of qubits with high threshold for errors.

* [[Quantum error correction#Bosonic codes|Bosonic Codes]]: A type of quantum error-correcting code designed specifically to protect quantum information in continuous-variable systems.{{cn|date=December 2024}}

However, QEC comes at a significant cost: it requires a large number of physical qubits to encode a single logical qubit, and fault-tolerant error correction methods introduce additional computational overhead.