Photons with well-defined energy are highly non-localised and occupy all

available space in one dimension. On the other hand, optical elements, like

mirrors, are highly-localised objects. To model the electromagnetic field in

the presence of optical elements, we therefore introduce annihilation operators

for highly-localised field excitations. These are different from

single-particle annihilation operators and arise naturally, if we quantise the

negative as well as the positive solutions of Maxwell's equations. Moreover,

# All

Matrix product state (MPS) belongs to the most important mathematical models

in, for example, condensed matter physics and quantum information sciences.

However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a

quantum platform is extremely challenging, since it requires high-level qudits

or multi-body gates of two-level qubits to carry the entanglement. In this

work, an efficient method that accurately encodes a given MPS into a quantum

circuit with only one- and two-qubit gates is proposed. The idea is to

Quantum computers provide an opportunity to efficiently sample from

probability distributions that include non-trivial interference effects between

amplitudes. Using a simple process wherein all possible state histories can be

specified by a binary tree, we construct an explicit quantum algorithm that

runs in polynomial time to sample from the process once. The corresponding

naive Markov Chain algorithm does not produce the correct probability

distribution and an explicit classical calculation of the full distribution

Selected states of the $EF\ ^1\Sigma_\mathrm{g}^+$ electronic manifold of the

hydrogen molecule are computed as resonances of the four-body problem.

Systematic improvement of the basis representation for the variational

treatment is achieved through an energy-tracking optimization procedure. The

resulting non-relativistic energy is converged within a few nano Hartree, while

the predissociative width is found to be negligible at this level of accuracy.

The four-particle non-relativistic energies are appended with relativistic and

We employ quantum optimal control theory to realize quantum gates for two

protected superconducting circuits: the heavy-fluxonium qubit and the 0-$\pi$

qubit. Utilizing automatic differentiation facilitates the simultaneous

inclusion of multiple optimization targets, allowing one to obtain

high-fidelity gates with realistic pulse shapes. For both qubits, disjoint

support of low-lying wave functions prevents direct population transfer between

the computational-basis states. Instead, optimal control favors dynamics

Most quantum processors requires pulse sequences for controlling quantum

states. Here, we present an alternative algorithm for computing an optimal

pulse sequence in order to perform a specific task, being an implementation of

a quantum gate or a quantum state preparation. In our method, we reduced

drastically the number of parameters to be fitted, by using a limited number of

functions as the modulations for the amplitude and phase of the radio-frequency

The recently developed Wigner functional theory is used to formulate an

evolution equation for arbitrary multi-photon states, propagating through a

turbulent atmosphere under arbitrary conditions. The resulting evolution

equation, which is obtained from an infinitesimal propagation approach, is in

the form of a Fokker-Planck equation for the Wigner functional of the state and

therefore incorporates functional derivatives. We show consistency with

previously obtained solutions from different approaches and consider possible

The mass-correction function is evaluated for selected excited states of the

hydrogen molecule within a single-state non-adiabatic treatment. Its

qualitative features are studied under the avoided crossing of the $EF$ with

the $GK$ state and also for the outer well of the $H\bar{H}$ state. For the

$H\bar{H}$ state, a negative mass correction is obtained for the vibrational

motion near the outer minimum, which accounts for most of the deviation between

experiment and earlier theoretical work.

In Gaussian quantum key distribution eavesdropping attacks are conventionally

modeled through the universal entangling cloner scheme, which is based on the

premise that the whole environment is under control of the adversary, i.e., the

eavesdropper purifies the system. This assumption implies that the eavesdropper

has either access to an identity (noiseless) channel or infinite amount of

entanglement in order to simulate such an identity channel. In this work, we

challenge the necessity of this assumption, and we propose a

We show that a continuous range of nonclassical states of light can be

generated using conditional measurements on the idler mode of an optical

parametric amplifier. The output state is prepared by introducing a coherent

state in the signal mode of the amplifier with a single photon in the idler

mode, followed by a conditional measurement of a single photon in the output

idler mode. By varying the gain of the amplifier, this approach can produce a

coherent state, a photon-added state, a displaced number state, or a continuous