Spectral Characterization of the Hamming Graphs

We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q large enough.Hamming graphs;distance-regular graphs;eigenvalues of graphs

A correction procedure for the errors in single-crystal intensities due to the inhomogeneity of the primary X-ray beam

Graphite monochromators are known to give rise to non-homogeneous primary X-ray beams. When intensities of single crystals are measured the effective cross section of a non-spherical crystal in the X-ray beam depends on its orientation in the beam. Therefore, systematic errors in the measured integrated intensities are introduced by the inhomogeneity of the incoming beam. A correction for these errors can be made, knowing the intensity profile of the primary beam and the dimensions and orientation of the crystal in the beam. The correction can conveniently be applied with the absorption correction. Examples of the corrections are given for crystals with rational boundary planes. It is shown that the intensity of an X-ray reflection as a function of the rotation about the scattering vector ( rotation) can be calculated with fair accuracy. In some cases (large elongated crystals in an inhomogeneous beam) correction for absorption only may give results which are worse than those with no correction at all

Quantum Entanglement and Communication Complexity

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the function with only three bits of communication occurring among the parties, whereas, without quantum entanglement, four bits of communication are necessary. We also show that, for a particular two-party probabilistic communication complexity problem, quantum entanglement results in less communication than is required with only classical random correlations (instead of quantum entanglement). These results are a noteworthy contrast to the well-known fact that quantum entanglement cannot be used to actually simulate communication among remote parties.Comment: 10 pages, latex, no figure

Adiabatic quantum computation and quantum phase transitions

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR

Adiabatic Quantum Computation in Open Systems

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.Comment: v2: 4 pages, 1 figure. Published versio

Improved Error-Scaling for Adiabatic Quantum State Transfer

We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate. These improvements rely only on the judicious choice of the total evolution time. Our technique is error-robust, and hence applicable to existing experiments utilizing adiabatic passage. We give two examples as proofs-of-principle, showing quadratic error reductions for an adiabatic search algorithm and a tunable two-qubit quantum logic gate.Comment: 10 Pages, 4 figures. Comments are welcome. Version substantially revised to generalize results to cases where several derivatives of the Hamiltonian are zero on the boundar