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

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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

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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