• Publications
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A practical heuristic for finding graph minors
We present a heuristic algorithm for finding a graph $H$ as a minor of a graph $G$ that is practical for sparse $G$ and $H$ with hundreds of vertices. We also explain the practical importance of
Next-Generation Topology of D-Wave Quantum Processors
This paper presents an overview of the topology of D-Wave's next-generation quantum processors. It provides examples of minor embeddings and discusses performance of embedding algorithms for the new
Discrete optimization using quantum annealing on sparse Ising models
TLDR
A way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware are proposed.
Weighted complex projective 2-designs from bases : Optimal state determination by orthogonal measurements
We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then
Fast clique minor generation in Chimera qubit connectivity graphs
TLDR
A combinatorial class of native clique minors in Chimera graphs with vertex images of uniform, near minimal size are defined and a polynomial-time algorithm is provided that finds a maximumnative clique minor in a given induced subgraph of a Chimera graph.
Unitary designs and codes
TLDR
In this paper, irreducible representations of the unitary group are used to find a general lower bound on the size of a unitary t-design in U(d), for any d and t.
Complex lines with restricted angles
This thesis is a study of large sets of unit vectors in Cn such that the absolute value of their standard inner products takes on only a small number of values. We begin with bounds: what is the
Mapping Constrained Optimization Problems to Quantum Annealing with Application to Fault Diagnosis
TLDR
A new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and two new decomposition algorithms for solving problems too large to map directly into hardware are proposed.
Bounds for codes and designs in complex subspaces
  • Aidan Roy
  • Mathematics, Computer Science
  • 13 June 2008
TLDR
Using Delsarte’s linear programming techniques, the bounds for real subspaces recently found by Bachoc, Bannai, Coulangeon and Nebe are found and the bounds generalize those ofDelsarte, Goethals and Seidel for codes and designs on the complex unit sphere.
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