Physical Review A

Given an arbitrary 2w×2w unitary matrix U, a powerful matrix decomposition can be applied, leading to four different syntheses of a w-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. Führ and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates (w=1) to gates with arbitrary value of w. The synthesized circuit consists of controlled one-qubit gates, such as negator gates and phasor gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled not gates in the case that U is a permutation matrix.

The isoelectronic series of Be, Ne and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple and quadruple zeta basis sets.

We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving a self-consistent set of single-particle equations. The method can be viewed as a nontrivial extension of the Kohn-Sham scheme (which is embedded as a special case). It is based on separating the Green’s function into a quasiparticle part and a background part, and expressing only the background part as a functional of the density matrix. The calculated single-particle energies and wave functions have a clear physical interpretation as quasiparticle energies and orbitals.

We consider low-dimensional model systems with a fixed two-body interaction and a variable (nonlocal) one-body potential. It is shown explicitly that an extended domain of allowed (N-representable) one-body density matrices cannot be generated in this way, the excluded domain depending on the two-body interaction under consideration. This stands in contrast to the behavior of the diagonal part of the density matrix.

series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known correction is a scalar term related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well (pseudoquadrupole effect, isotopologue anomaly, etc.).