Noiseless Quantum Codes
Open accessAbstract
In this paper we study a model quantum register $R$ made of $N$ replicas (cells) of a given finite-dimensional quantum system S. Assuming that all cells are coupled with a common environment with equal strength we show that, for $N$ large enough, in the Hilbert space of $R$ there exists a linear subspace ${C}_{N}$ which is dynamically decoupled from the environment. The states in ${C}_{N}$ evolve unitarily and are therefore decoherence-dissipation free. The space ${C}_{N}$ realizes a noiseless quantum code in which information can be stored, in principle, for an arbitrarily long time without being affected by errors.
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For a fixed Ω_R we do not have a simple Lindblad generator (of the type (2.96) in [40]), but rather a more complicated generator with Lindblad operators depending on the Rabi frequency, as in Eq. (47).
“Hence for a fixed Ω R we do in fact not have a simple Lindblad generator (of the type (2.96) in [40]), but rather a more complicated generator with Lindblad operators depending on the Rabi frequency, as in Eq. (47).”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [40]
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- Authors
- Zanardi, P., & Rasetti, M.
- Affiliations
- Politecnico di Torino (IT)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1997-10-27
- Volume
- 79
- Issue
- 17
- Pages
- 3306-3309
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2139625432
- Cited by
- 1,315
- References
- 12
- Citations by year
- 2026: 25 · 2025: 36 · 2024: 42 · 2023: 36 · 2022: 31 · 2021: 33 · 2020: 35 · 2019: 40 · 2018: 43 · 2017: 39 · 2016: 54 · 2015: 50 · 2014: 46 · 2013: 45 · 2012: 51
- FWCI
- 24.06
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum error correction, decoherence, dynamical decoupling, quantum registers, quantum memory, open quantum systems, linear subspaces
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