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DOE OSTI · 1611438

Scalable fermionic error correction in Majorana surface codes

Viyuela, Oscar·Vijay, Sagar·Fu, Liang
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Abstract

We study the error correcting properties of Majorana surface codes (MSCs), topological quantum codes constructed out of interacting Majorana fermions, which can be used to store quantum information and perform quantum computation. Furthermore, these quantum memories suffer from purely “fermionic” errors, such as quasiparticle poisoning (QP), that have no analog in conventional platforms with bosonic qubits. In physical realizations where QP dominates, we show that errors can be corrected provided that the poisoning rate is below a threshold of ~11%. When QP is highly suppressed and fermionic bilinear (“bosonic”) errors become dominant, we find an error threshold of ~16%, which is much higher than the threshold for spin-based topological memories like the surface code or the color code. In addition, we derive lattice gauge theories to account for measurement errors. These results, together with the inherent error suppression provided by the superconducting gap in physical realizations of the MSCs, makes this a strong candidate for a robust topological quantum memory.

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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITYMajorana fermionsMaterials SciencePhysicsQuantum memoriesTopological materialsTopological quantum computingTopological superconductors

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Viyuela, Oscar, Vijay, Sagar, Fu, Liang. 2019-05-10. Scalable fermionic error correction in Majorana surface codes. https://doi.org/10.1103/physrevb.99.205114

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