Stabilizer code: Difference between revisions

Revision as of 20:22, 23 November 2023

Latest revision as of 10:51, 8 August 2025

(3 intermediate revisions by 3 users not shown)

Line 1:

{{Short description|Quantum error correction code}}

{{technical|date=April 2022}}

The theory of [[quantum error correction]] plays a prominent role in the practical realization and engineering of

In [[quantum computing]] and [[quantum communication]], a '''stabilizer code''' is a class of quantum [[code]]s for performing [[quantum error correction]]. The [[toric code]], and [[Toric code#Generalizations|surface codes]] more generally,<ref>{{cite web|access-date=2024-01-12|title=What is the "surface code" in the context of quantum error correction?|url=https://quantumcomputing.stackexchange.com/questions/2106/what-is-the-surface-code-in-the-context-of-quantum-error-correction|website=Quantum Computing Stack Exchange}}</ref> are types of stabilizer codes considered very important for the practical realization of quantum information processing.

[[quantum computing]] and [[quantum communication]] devices. The first quantum

error-correcting codes are strikingly similar to [[error correction|classical block codes]] in their

== Conceptual background ==

operation and performance. Quantum error-correcting codes restore a noisy,

operation and performance. Quantum error-correcting codes restore a noisy,

[[decoherence|decohered]] [[quantum state]] to a pure quantum state. A

[[Group action (mathematics)#Orbits and stabilizers|stabilizer]] quantum error-correcting code appends [[Ancilla (quantum computing)|ancilla qubits]]

Line 12 ⟶ 14:

and [[quantum communication]] practical by providing a way for a sender and

receiver to simulate a noiseless qubit channel given a [[noisy qubit channel]]

whose noise conforms to a particular error model. The first quantum error-correcting codes are strikingly similar to [[error correction|classical block codes]] in their operation and performance.

The stabilizer theory of [[quantum error correction]] allows one to import some

Line 83 ⟶ 85:

The generators are

independent in the sense that none of them isare a product of any other two (up

to a [[Quantum state|global phase]]). The operators <math>g_{1},\ldots,g_{n-k}</math> function in the same

way as a [[parity check matrix]] does for a classical [[linear block code]].

Line 293 ⟶ 295:

==References==

{{Reflist}}

* D. Gottesman, "Stabilizer codes and quantum error correction," quant-ph/9705052, Caltech Ph.D. thesis. https://arxiv.org/abs/quant-ph/9705052