Contextuality and Wigner function negativity in qubit quantum computation

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of quantum computation with magic states on qubits that satisfy three simple postulates. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.Comment: published versio

Three-body forces and shell structure in calcium isotopes

Understanding and predicting the formation of shell structure from nuclear forces is a central challenge for nuclear physics. While the magic numbers N=2,8,20 are generally well understood, N=28 is the first standard magic number that is not reproduced in microscopic theories with two-nucleon forces. In this Letter, we show that three-nucleon forces give rise to repulsive interactions between two valence neutrons that are key to explain 48Ca as a magic nucleus, with a high 2+ excitation energy and a concentrated magnetic dipole transition strength. The repulsive three-nucleon mechanism improves the agreement with experimental binding energies.Comment: 5 pages, 4 figures; improved version and added coupled-cluster benchmark; published versio

Magic wavelengths for the 6s^2\,^1S_0-6s6p\,^3P_1^o transition in ytterbium atom

The static and dynamic electric-dipole polarizabilities of the 6s^2\,^1S_0 and 6s6p\,^3P_1^o states of Yb are calculated by using the relativistic ab initio method. Focusing on the red detuning region to the 6s^2\,^1S_0-6s6p\,^3P_1^o transition, we find two magic wavelengths at 1035.7(2) nm and 612.9(2) nm for the 6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=0 transition and three magic wavelengthes at 1517.68(6) nm, 1036.0(3) nm and 858(12) nm for the 6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=\pm1 transitions. Such magic wavelengths are of particular interest for attaining the state-insensitive cooling, trapping, and quantum manipulation of neutral Yb atom.Comment: 13 pages, 3 figure

Structure of the lightest tin isotopes

We link the structure of nuclei around $^{100}$Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers ($N=Z=50$), to nucleon-nucleon ($NN$) and three-nucleon ($NNN$) forces constrained by data of few-nucleon systems. Our results indicate that $^{100}$Sn is doubly magic, and we predict its quadrupole collectivity. We present precise computations of $^{101}$Sn based on three-particle--two-hole excitations of $^{100}$Sn, and reproduce the small splitting between the lowest $J^\pi=7/2^+$ and $5/2^+$ states. Our results are consistent with the sparse available data.Comment: 8 pages, 4 figure