2006/10/19 by Sergey Bravyi, Robert Raussendorf
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Code (set theory) #Combinatorics #Computation #Computer science #Graph #Ising model #Lattice (music) #Mathematics #Physics #Planar #Planar graph #Planarity testing #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum many-body systems #Quantum mechanics #Qubit #Statistical physics #Theoretical computer science #Toric code #quant-ph
paper · pdf · doi:10.1103/physreva.76.022304
published as Phys. Rev. A 76, 022304 (2007) · 9 pages, 5 figures
arxiv created 2006/10/19 · openalex publication_date 2007/08/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study measurement-based quantum computation (MQC) using as a quantum resource the planar code state on a two-dimensional square lattice (planar analog of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice. The simulation scheme is built upon Barahona's algorithm for computing the partition function of the Ising model on a planar graph. Our results provide a simulation method for MQC centered around planarity of graphs.