3D Topological Quantum Memory with a Power-Law Energy Barrier

2014/06/17 by Kamil Michnicki, Kamil P Michnicki · 1 citation
Chemistry · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Memory and Neural Computing #Chemistry #Code (set theory) #Combinatorics #Computer science #Energy (signal processing) #Geometry #Mathematics #Physics #Power law #Programming language #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Surface (topology) #Theoretical physics #Topology (electrical circuits) #Toric code #Translation (biology) #quant-ph

paper · pdf · doi:10.1103/physrevlett.113.130501

published as Phys. Rev. Lett. 113, 130501 (2014) · 7 pages, 2 figures

arxiv created 2014/06/17 · openalex publication_date 2014/09/24 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3D version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting code is a [[O(L³),1,O(L(4/3))]] stabilizer code with an energy barrier of O(L(2/3)), which is an exponential improvement over the previous highest energy barrier in 3D. No-go results are avoided by breaking microscopic translation invariance.

Citations

• Entanglement and topological entropy of the toric code at finite temperature
• Topological quantum memory
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Local stabilizer codes in three dimensions without string logical operators
• Good Quantum Error-Correcting Codes Exist
• Fault-tolerant quantum computation by anyons

Cited by

• Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata