Modeling chemical reactions and complicated molecular systems has been
proposed as the `killer application' of a future quantum computer. Accurate
calculations of derivatives of molecular eigenenergies are essential towards
this end, allowing for geometry optimization, transition state searches,
predictions of the response to an applied electric or magnetic field, and
molecular dynamics simulations.In this work, we survey methods to calculate
energy derivatives, and present two new methods: one based on quantum phase

The relationship between quantum physics and discrete mathematics is reviewed
in this article. The Boolean functions unitary representation is considered.
The relationship between Zhegalkin polynomial, which defines the algebraic
normal form of Boolean function, and quantum logic circuits is described. It is
shown that quantum information approach provides simple algorithm to construct
Zhegalkin polynomial using truth table. Developed methods and algorithms have

The method of many body Green's functions is used to describe an arbitrary
system of electrons and nuclei in a rigorous manner given the Hamiltonian of
Coulombic interactions and kinetic energies. The theory given resolves the
problem arising from the translational and rotational invariance of the
Hamiltonian afflicting the existing theory based on the same technique. As a
result, we derive a coupled set of exact equations for the electron and nuclei
Green's functions giving a systematic way to potentially compute various

We introduce a model to study the collisions of two ultracold diatomic
molecules in one dimension interacting via pairwise potentials. We present
results for this system, and argue that it offers lessons for real molecular
collisions in three dimensions. We analyze the distribution of the adiabatic
potentials in the hyperspherical coordinate representation as well as the
distribution of the four-body bound states in the adiabatic approximation (i.e.
no coupling between adiabatic channels). It is found that while the adiabatic

We measure the population distribution in one of the atomic twin beams
generated by four-wave mixing in an optical lattice.

Although the produced two-mode squeezed vacuum state is pure, each individual
mode is described as a statistical mixture.

We confirm the prediction that the particle number follows an exponential
distribution when only one spatio-temporal mode is selected.

We also show that this distribution accounts well for the contrast of an
atomic Hong--Ou--Mandel experiment.

The quantum measurement procedure based on the Lorentz transformation
formalism and weak perturbation of the system is considered. In the simple case
of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation
along with ordinary 3-dimension rotations on the Bloch sphere. These
pseudo-rotations are similar to the Lorentz transformation in special
relativity theory. The extension of the Lorentz transformation for many-qubit
systems is also considered. The quantum measurement protocols based on the

Recently, the study of non-Hermitian physics has attracted considerable
attention. The modified bulk-boundary correspondence has been proposed to
understand topological edge states in non-Hermitian static systems. Here we
report a new experimental observation of edge states in non-Hermitian
periodically driven systems. Some unconventional edge states are found not to
be satisfied with the bulk-boundary correspondence when the system belongs to
the broken parity-time (PT) symmetric phase. The experiments are performed in

We analyse quasi-periodically driven quantum systems that can be mapped
exactly to periodically driven ones and find Floquet Time Spirals in analogy
with spatially incommensurate spiral magnetic states. Generalising the
mechanism to many-body systems we discover that a form of discrete
time-translation symmetry breaking can also occur in quasi-periodically driven
systems. We construct a discrete time quasi-crystal stabilised by many-body
localisation, which persists also under perturbations that break the

Author(s): H. Chau Nguyen, Huy-Viet Nguyen, and Otfried Gühne
Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications such as quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky, and Rosen (EPR) used these correlations to argue against the ...
[Phys. Rev. Lett. 122, 240401] Published Mon Jun 17, 2019

Author(s): Quirin Hummel, Juan Diego Urbina, and Klaus Richter
Because of the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with r...
[Phys. Rev. Lett. 122, 240601] Published Mon Jun 17, 2019