A note on QUBO instances defined on Chimera graphs

McGeoch and Wang (2013) recently obtained optimal or near-optimal solutions to some quadratic unconstrained boolean optimization (QUBO) problem instances using a 439 qubit D-Wave Two quantum computing system in much less time than with the IBM ILOG CPLEX mixed-integer quadratic programming (MIQP) solver. The problems studied by McGeoch and Wang are defined on subgraphs -- with up to 439 nodes -- of Chimera graphs. We observe that after a standard reformulation of the QUBO problem as a mixed-integer linear program (MILP), the specific instances used by McGeoch and Wang can be solved to optimality with the CPLEX MILP solver in much less time than the time reported in McGeoch and Wang for the CPLEX MIQP solver. However, the solution time is still more than the time taken by the D-Wave computer in the McGeoch-Wang tests.Comment: Version 1 discussed computational results with random QUBO instances. McGeoch and Wang made an error in describing the instances they used; they did not use random QUBO instances but rather random Ising Model instances with fields (mapped to QUBO instances). The current version of the note reports on tests with the precise instances used by McGeoch and Wan

Cayley graphs generated by small degree polynomials over finite fields

We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields

Yinuo Wang, Piano

Sonata in E minor, Op. 90 / Ludwig van Beethoven; Canon in D minor; Prelude in F-sharp minor, Op. 23, No. 1; Daisies, Op. 38, No. 3; Prelude in D minor, Op. 23, No. 3; Prelude in B minor, Op. 32, No. 10; Prelude in G-flat major, Op. 23, No. 10; Etude in D minor, Op. 39, No. 8; Etude in D major, Op. 39, No. 9; Rhapsody on a Theme of Paganini / Sergei Rachmaninof

Chao Wang, Flute

Introduction and Variations, D. 802 / Franz Schubert; Hamburger Sonata in G major / Carl Philippe Emanuel Bach; Sonata in D major, for flute and piano Opus 94 / Sergei Prokofie