2012/11/30 by Ross B. McDonald, Helmut G. Katzgraber
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Braid #Braid group #Combinatorics #Computation #Computer science #Genetic algorithm #Heuristic #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum computer #Quantum gate #Quantum many-body systems #Quantum mechanics #Quasiparticle #Set (abstract data type) #Theoretical computer science #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #cs.NE #quant-ph
paper · pdf · doi:10.1103/physrevb.87.054414
published as Phys. Rev. B 87, 054414 (2013) · 6 pages 4 figures
arxiv created 2013/02/13 · openalex publication_date 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In topologically protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well as Leijnse and Flensberg [Phys. Rev. B 86, 104511 (2012)], recently provided schemes for computing quantum gates from quasiparticle braids. Mathematically, the problem of executing a gate becomes that of finding a product of the generators (matrices) in that set that approximates the gate best, up to an error. To date, efficient methods to compute these gates only strive to optimize for accuracy. We explore the possibility of using a generic approach applicable to a variety of braiding problems based on evolutionary (genetic) algorithms. The method efficiently finds optimal braids while allowing the user to optimize for the relative utilities of accuracy and/or length. Furthermore, when optimizing for error only, the method can quickly produce efficient braids.