2011/12/14 by Sergey Bravyi, Jeongwan Haah · 305 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Decoding methods #Inverse #Lattice (music) #Mathematics #Monte Carlo method #Physics #Quantum #Quantum and electron transport phenomena #Quantum computer #Quantum many-body systems #Quantum mechanics #Quantum memory #Quantum network #Quantum simulator #Statistical physics #Statistics #Topological Materials and Phenomena #Toric code #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevlett.111.200501
published in Physical Review Letters 111(20), 200501 (American Physical Society) · 40 pages, 6 figures
arxiv created 2011/12/14 · openalex publication_date 2013/11/12 · arxiv updated 2013/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A big open question in the quantum information theory concerns the feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction, if the memory is in contact with a cold enough thermal bath. Here we report analytic and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code. We prove that its memory time is at least L(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient. However, this bound applies only if the lattice size L does not exceed a critical value which grows exponentially with β. In that sense, the model can be called a partially self-correcting memory. We also report a Monte Carlo simulation indicating that our analytic bounds on the memory time are tight up to constant coefficients. To model the readout step we introduce a new decoding algorithm, which can be implemented efficiently for any topological stabilizer code. A longer version of this work can be found in Bravyi and Haah, arXiv:1112.3252.