2012/06/30 by N. E. Bonesteel, David P. DiVincenzo, D. P. DiVincenzo · 37 citations
Computer Science · Mathematics · Physics and Astronomy · #Arithmetic #Computer science #Construct (python library) #Discrete mathematics #Electronic circuit #Fibonacci number #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum circuit #Quantum error correction #Quantum gate #Quantum mechanics #Qubit #Set (abstract data type) #Toffoli gate #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1103/physrevb.86.165113
published in Physical Review B 86(16) (American Physical Society) · 12 pages, 13 figures; published version
openalex publication_date 2012/10/10 · arxiv created 2012/10/16 · arxiv updated 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct quantum circuits for measuring the commuting set of vertex and plaquette operators that appear in the Levin-Wen model for doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum error-correcting code defined by the ground states of this model (the Fibonacci code). We quantify the complexity of these circuits with gate counts using different universal gate sets and find these measurements become significantly easier to perform if n-qubit Toffoli gates with n=3,\phantom\rule0.28em0ex4, and 5 can be carried out directly. In addition to measurement circuits, we construct simplified quantum circuits requiring only a few qubits that can be used to verify that certain self-consistency conditions, including the pentagon equation, are satisfied by the Fibonacci code.