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We describe an efficient quantum algorithm for the quantum Schur transform.
The Schur transform is an operation on a quantum computer that maps the
standard computational basis to a basis composed of irreducible representations
of the unitary and symmetric groups. We simplify and extend the algorithm of
Bacon, Chuang, and Harrow, and provide a new practical construction as well as
sharp theoretical and practical analyses. Our algorithm decomposes the Schur
transform on $n$ qubits into $O(n^4 \log(n/{\epsilon}))$ operators in the

Understanding the wave transport and localisation is a major goal in the
study of lattices of different nature. In general, inhibiting the energy
transport on a perfectly periodic and disorder-free system is challenging,
however, some specific lattice geometries allow localisation due to the
presence of dispersionless (flat) bands in the energy spectrum. Here, we report
on the experimental realisation of a quasi-one-dimensional photonic graphene
ribbon supporting four flat-bands. We study the dynamics of fundamental and

We analyze the propagation of quantum states in the presence of weak
disorder. In particular, we investigate the reliable transmittance of quantum
states, as potential carriers of quantum information, through
disorder-perturbed waveguides. We quantify wave-packet distortion,
backscattering, and disorder-induced dephasing, which all act detrimentally on
transport, and identify conditions for reliable transmission. Our analysis
relies on the treatment of the nonequilibrium dynamics of ensemble-averaged

The linear canonical transform (LCT) was extended to complex-valued
parameters, called complex LCT, to describe the complex amplitude propagation
through lossy or lossless optical systems. Bargmann transform is a special case
of the complex LCT. In this paper, we normalize the Bargmann transform such
that it can be bounded near infinity. We derive the relationships of the
normalized Bargmann transform to Gabor transform, Hermite-Gaussian functions,
gyrator transform, and 2D nonseparable LCT. Several kinds of fast and accurate

Simulating quantum contextuality with classical systems requires memory. A
fundamental yet open question is which is the minimum memory needed and,
therefore, the precise sense in which quantum systems outperform classical
ones. Here we make rigorous the notion of classically simulating quantum
state-independent contextuality (QSIC) in the case of a single quantum system
submitted to an infinite sequence of measurements randomly chosen from a finite
QSIC set. We obtain the minimum memory classical systems need to simulate

A useful approach is investigated in order to analyze a class of a stochastic
differential equations that can be encountered in quantum optics problems,
especially, in the case of two photon losses on the driven cavity mode. The
passage to the ordinary coupled differential equations is presented and the
treatment of the obtained coupled system is explored. Generalization of the
problem to stimulate variable coefficients is discussed and the exact solutions

We construct various types of degenerate multi-soliton and multi-breather
solutions for the sine-Gordon equation based on B\"{a}cklund transformations,
Darboux-Crum transformations and Hirota's direct method. We compare the
different solution procedures and study the properties of the solutions. Many
of them exhibit a compound like behaviour on a small timescale, but their
individual one-soliton constituents separate for large time. Exceptions are
degenerate cnoidal kink solutions that we construct via inverse scattering from

We obtain exact solutions to the two-dimensional (2D) Dirac equation for the
one-dimensional P\"oschl-Teller potential which contains an asymmetry term. The
eigenfunctions are expressed in terms of Heun confluent functions, while the
eigenvalues are determined via the solutions of a simple transcendental
equation. For the symmetric case, the eigenfunctions of the supercritical
states are expressed as spheroidal wave functions, and approximate analytical
expressions are obtained for the corresponding eigenvalues. A universal

We study the nonlinear dynamics of trapped-ion models far away from the
Lamb-Dicke regime. This nonlinearity induces a sideband cooling blockade,
stopping the propagation of quantum information along the Hilbert space of the
Jaynes-Cummings and quantum Rabi models. We compare the linear and nonlinear
cases of these models in the ultrastrong and deep strong coupling regimes.
Moreover, we propose a scheme that simulates the nonlinear quantum Rabi model
in all coupling regimes. This can be done via off-resonant nonlinear red and

The realization of quantum field theories on an optical lattice is an
important subject toward the quantum simulation. We argue that such efforts
would lead to the experimental realizations of quantum black holes. The basic
idea is to construct non-gravitational systems which are equivalent to the
quantum gravitational systems via the holographic principle. Here the
`equivalence' means that two theories cannot be distinguished even in
principle. Therefore, if the holographic principle is true, one can create