Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

2017/08/23 by Aleksander Kubica, Michael E. Beverland, Fernando G. S. L. Brandão +3 · 3 citations
Computer Science · Engineering · Physics and Astronomy · #Blind Source Separation Techniques #Cellular Automata and Applications #Code (set theory) #Computer science #Image Processing Techniques and Applications #Physics #Programming language #Statistical physics #cond-mat.dis-nn #quant-ph

paper · pdf · doi:10.1103/physrevlett.120.180501

published as Phys. Rev. Lett. 120, 180501 (2018) · 4+7 pages, 6 figures, 1 table

arxiv created 2017/08/23 · openalex publication_date 2018/05/04 · arxiv updated 2018/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p_3DCC⁽¹⁾≃1.9% and p_3DCC⁽²⁾≃27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Citations

• Universality Class of the Nishimori Point in the 2D±JRandom-Bond Ising Model
• Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• String-net condensation: A physical mechanism for topological phases
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Topological quantum memory
• Good Quantum Error-Correcting Codes Exist
• An introduction to lattice gauge theory and spin systems
• Fault-tolerant quantum computation by anyons
• Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model

Cited by

• Fault-tolerant fermionic quantum computation based on color code
• Quantum error correction with the toric Gottesman-Kitaev-Preskill code
• Triangular color codes on trivalent graphs with flag qubits