Performance and structure of single-mode bosonic codes
Autor: | Liang Jiang, R. T. Brierley, Christophe Vuillot, Philip Reinhold, Kyungjoo Noh, Victor V. Albert, Barbara M. Terhal, Steven Girvin, Chao Shen, Linshu Li, Kasper Duivenvoorden, Dylan Young |
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Přispěvatelé: | Yale Quantum Institute, Yale University [New Haven], JARA-Institute for Quantum Information (JARA-IQI), JARA-IQI, RWTH Aachen University, Departments of Applied Physics [New Haven] |
Jazyk: | angličtina |
Předmět: |
Physics
Quantum Physics Binomial (polynomial) Generalization Hash function FOS: Physical sciences Monotonic function Quantum entanglement 01 natural sciences 010305 fluids & plasmas [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Qubit 0103 physical sciences Code (cryptography) Limit (mathematics) 010306 general physics Quantum Physics (quant-ph) Algorithm |
Zdroj: | Physical Review A Physical Review A, American Physical Society, 2018, 97 (3), pp.032346. ⟨10.1103/PhysRevA.97.032346⟩ |
ISSN: | 2469-9934 2469-9926 1050-2947 1094-1622 |
DOI: | 10.1103/physreva.97.032346 |
Popis: | The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce new codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat/binomial/GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multi-qubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a new multi-qudit code. 34 pages, 11 figures, 4 tables. v3: published version. See related talk at https://absuploads.aps.org/presentation.cfm?pid=13511 |
Databáze: | OpenAIRE |
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