Characterizing and developing bosonic error-correcting codes

Presenting Author: Victor V. Albert, California Institute of Technology
Contributing Author(s): R. T. Brierley, Michel H. Devoret, Kasper Duivenvoorden, S. M. Girvin, Alexander Grimm, Liang Jiang, Linshu Li, Shantanu O. Mundhada, Kyungjoo Noh, Philip Reinhold, Chao Shen, Barbara M. Terhal, Steven Touzard, Christophe Vuillot, Dylan J. Young

Continuous-variable or bosonic quantum information processing is a field concerned with using one or more harmonic oscillators to protect, manipulate, and transport quantum information. The large oscillator Hilbert space provides alternative encodings that are currently outperforming encodings into registers of many qubits: break-even error correction has been achieved with the bosonic cat codes but not yet with a many-qubit system. However, an analysis of theoretical capabilities of bosonic codes is missing. We have undertaken a program identifying (1) Which codes are able to protect against dominant noise in realistic bosonic systems? (2) Why those codes perform so well? and (3) How to extend codes to multiple modes advantageously? We provide answers to all these questions. First, we calculate the error-correction conditions of single-mode codes, showing that Gottesman-Kitaev-Preskill (GKP) codes offer the best performance. Second, we prove that GKP codes achieve the quantum capacity (up to a constant offset) of the thermal loss channel. Third, we present a multimode extension of the cat codes that increases both experimental feasibility and theoretically achievable performance.

Read this article online: https://drive.google.com/file/d/1PBONYwxVfWtazgCVDp0f0ihqZCt5Ccn1/view?usp=sharing

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