2018/06/30 by Christina Knapp, Michael Beverland, Dmitry I. Pikulin +1 · 1 citation
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Error detection and correction #MAJORANA #Noise (video) #Pauli exclusion principle #Quantum #Quantum computer #Quantum error correction #Quantum noise #Quantum optics and atomic interactions #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.supr-con #quant-ph
paper · pdf · doi:10.22331/q-2018-09-03-88
published as Quantum 2, 88 (2018) · 34 pages, 16 figures v3: updated style
openalex created_date 2018/06/13 · arxiv created 2018/08/24 · openalex publication_date 2018/09/03 · arxiv updated 2018/09/11 · openalex updated_date 2026/08/05
Majorana-based quantum computing seeks to use the non-local nature of Majorana zero modes to store and manipulate quantum information in a topologically protected way. While noise is anticipated to be significantly suppressed in such systems, finite temperature and system size result in residual errors. In this work, we connect the underlying physical error processes in Majorana-based systems to the noise models used in a fault tolerance analysis. Standard qubit-based noise models built from Pauli operators do not capture leading order noise processes arising from quasiparticle poisoning events, thus it is not obvious<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext class="MJX-tex-mathit" mathvariant="italic">a priori</mml:mtext></mml:mrow></mml:math>that such noise models can be usefully applied to a Majorana-based system. We develop stochastic Majorana noise models that are generalizations of the standard qubit-based models and connect the error probabilities defining these models to parameters of the physical system. Using these models, we compute pseudo-thresholds for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:math>Bacon-Shor subsystem code. Our results emphasize the importance of correlated errors induced in multi-qubit measurements. Moreover, we find that for sufficiently fast quasiparticle relaxation the errors are well described by Pauli operators. This work bridges the divide between physical errors in Majorana-based quantum computing architectures and the significance of these errors in a quantum error correcting code.