The framework of noiseless subsystems has been developed as a tool to preserve fragile

quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...

against

decoherence Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...

. In brief, when a

quantum register In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register. Definition ...

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

) is subjected to decoherence due to an interaction with an external and uncontrollable environment, information stored in the register is, in general, degraded. It has been shown that when the source of decoherence exhibits some symmetries, certain subsystems of the quantum register are unaffected by the interactions with the environment and are thus noiseless. These noiseless subsystems are therefore very natural and robust tools that can be used for processing quantum information.

References

{{reflist, refs= {{citation , last1 = Kempe , first1 = J. , author1-link = Julia Kempe , last2 = Bacon , first2 = D. , last3 = Lidar , first3 = D. A. , author3-link = Daniel Lidar , last4 = Whaley , first4 = K. B. , arxiv = quant-ph/0004064 , doi = 10.1103/physreva.63.042307 , issue = 4 , journal =

Physical Review A ''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost (Max Planck Ins ...

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Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journa ...

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, pages = 2594–2597 , title = Decoherence-free subspaces for quantum computation , volume = 81 , year = 1998, bibcode = 1998PhRvL..81.2594L, s2cid = 13979882 {{citation , last1 = Zanardi , first1 = P. , last2 = Rasetti , first2 = M. , arxiv = quant-ph/9705044 , doi = 10.1103/physrevlett.79.3306 , issue = 17 , journal = Physical Review Letters , pages = 3306–3309 , title = Noiseless quantum codes , volume = 79 , year = 1997, bibcode = 1997PhRvL..79.3306Z , s2cid = 44477408 Quantum information science

See also

References