 | Review waiting, please be patient.
This may take 6 weeks or more, since drafts are reviewed in no specific order. There are 2,070 pending submissions waiting for review.
Where to get help
How to improve a draft
You can also browse Wikipedia:Featured articles and Wikipedia:Good articles to find examples of Wikipedia's best writing on topics similar to your proposed article. Improving your odds of a speedy review To improve your odds of a faster review, tag your draft with relevant WikiProject tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the Biography, Astronomy, and Women scientists tags. Editor resources
Reviewer tools
|
Comment: Might be LLM-generated —pythoncoder (talk | contribs) 02:01, 29 August 2025 (UTC)
| Open-system formulations | |
|---|---|
| Field | Quantum computing |
| Applications | Noise modeling, Decoherence, Error correction |
| Related topics | Open quantum system, Quantum decoherence |
Open-system formulations in quantum computing are theoretical frameworks for describing the interaction of qubits with their surrounding environment. Such interactions lead to effects including noise and decoherence. Master equation approaches such as the Lindblad equation and the Redfield equation are widely used to represent these processes mathematically.[1][2][3]
Background
editIn an isolated system, the quantum state \(\psi\) evolves unitarily according to a time-dependent Hamiltonian \(H(t)\):
![{\displaystyle U(t)={\mathcal {T}}\exp \!\left[-{\frac {i}{\hbar }}\int _{0}^{t}H(t')\,dt'\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4af4c945f4e9f0028b34bae5b2fcbecf1ab5bf79)
where {T} is the time-ordering operator, H is the reduced Planck constant, and U(t) is the time evolution operator.
Realistic quantum devices are not perfectly isolated. Interactions with external degrees of freedom—such as phonons, photons, and control electronics—introduce errors that alter qubit states.[2] These effects can be described in terms of quantum channels or modifications to the system’s effective dynamics.
Formulations
editSeveral mathematical approaches exist for modeling open-system dynamics, depending on the noise characteristics and the system–environment coupling.
- Lindblad equation (Markovian noise): For weak and memoryless noise, the evolution of the density matrix \(\rho\) is given by:
![{\displaystyle {\frac {d\rho }{dt}}=-{\frac {i}{\hbar }}[H,\rho ]+\sum _{k}\left(L_{k}\rho L_{k}^{\dagger }-{\tfrac {1}{2}}\{L_{k}^{\dagger }L_{k},\rho \}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/17f0b36e479d22e008de0285e036dae57f96201a)
where represent specific noise processes such as dephasing. The commutator is and the anticommutator is .[4][5]
![{\displaystyle [A,B]=AB-BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a3b93b316dd0b6b0ab2c71e486c901ddfe6e79a)
- Redfield equation (non-Markovian noise): For environments with memory effects, the Redfield equation is used:
![{\displaystyle {\frac {d\rho (t)}{dt}}=-{\frac {i}{\hbar }}[H_{S},\rho (t)]-\int _{0}^{t}d\tau \,\operatorname {Tr} _{E}\left[H_{I}(t),[H_{I}(\tau ),\rho (t)\otimes \rho _{E}]\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02efaf220c5b5482437a9bfc0bd6edf100bea62d)
where is the interaction Hamiltonian and is the environment density matrix.
- Collisional decoherence: Environmental particle collisions can reduce spatial coherence:
![{\displaystyle C(t)\approx \exp[-\Gamma t],\quad \Gamma \propto n\,v\,\sigma _{\rm {decoh}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0add0c48bcfda453cd8d6e10a014456e99a72546)
where is the effective cross-section for decoherence.
Relevance to quantum computing
editOpen-system models are central to understanding error processes such as dephasing and relaxation in qubit devices. The dominant sources of noise depend on the underlying platform (e.g., trapped ion qubits, neutral atom qubits, or superconducting circuits).[1][2][3] By providing a unified framework, open-system methods guide both experimental characterization and the design of error-correction strategies.
See also
editReferences
edit- ^ a b Breuer, Heinz-Peter; Petruccione, Francesco (2002). The Theory of Open Quantum Systems. Oxford University Press. ISBN 978-0199213900.
- ^ a b c Rivas, Ángel; Huelga, Susana F. (2012). Open Quantum Systems: An Introduction. Springer Briefs in Physics. Springer. arXiv:1104.5242. doi:10.1007/978-3-642-23354-8. ISBN 978-3-642-23353-1.
- ^ a b Gneiting, Clemens; Nori, Franco (2017). "Quantum evolution in open systems: Master equations and dynamical maps". Journal of Statistical Physics. 168 (6): 1223–1240. doi:10.1007/s10955-017-1901-0.
- ^ Lindblad, Göran (1976). "On the generators of quantum dynamical semigroups". Communications in Mathematical Physics. 48 (2): 119–130. Bibcode:1976CMaPh..48..119L. doi:10.1007/BF01608499.
- ^ Gorini, Vittorio; Kossakowski, Andrzej; Sudarshan, E. C. G. (1976). "Completely positive dynamical semigroups of N-level systems". Journal of Mathematical Physics. 17 (5): 821–825. Bibcode:1976JMP....17..821G. doi:10.1063/1.522979.
Further reading
edit- Breuer, H.-P.; Laine, E.-M.; Piilo, J.; Vacchini, B. (2016). "Colloquium: Non-Markovian dynamics in open quantum systems". Reviews of Modern Physics. 88 (2): 021002. arXiv:1505.01385. Bibcode:2016RvMP...88b1002B. doi:10.1103/RevModPhys.88.021002. hdl:2434/387123.
 | This technology-related article is a stub. You can help Wikipedia by expanding it. |