Exploiting Symmetries in Optimal Quantum Circuit Design

A physical limitation in quantum circuit design is the fact that gates in a quantum system can only act on qubits that are physically adjacent in the architecture. To overcome this problem, SWAP gates need to be inserted to make the circuit physically realizable. The nearest neighbour compliance problem (NNCP) asks for an optimal embedding … Read more

Integer packing sets form a well-quasi-ordering

An integer packing set is a set of non-negative integer vectors with the property that, if a vector x is in the set, then every non-negative integer vector y with y ≤ x is in the set as well. Integer packing sets appear naturally in Integer Optimization. In fact, the set of integer points in … Read more

Invariant semidefinite programs

In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs – SDPs which have symmetry. This was done for a variety of problems and applications. The purpose of this handbook chapter is to give the reader the necessary background for dealing with … Read more

Semidefinite code bounds based on quadruple distances

Let A(n, d) be the maximum number of 0, 1 words of length n, any two having Hamming distance at least d. We prove A(20, 8) = 256, which implies that the quadruply shortened Golay code is optimal. Moreover, we show A(18, 6) ≤ 673, A(19, 6) ≤ 1237, A(20, 6) ≤ 2279, A(23, 6) … Read more