Gaussian Boson sampling (GBS) provides a highly efficient approach to make
use of squeezed states from parametric down-conversion to solve a classically
hard-to-solve sampling problem. The GBS protocol not only significantly
enhances the photon generation probability, compared to standard boson sampling
with single photon Fock states, but also links to potential applications such
as dense subgraph problems and molecular vibronic spectra. Here, we report the

In this paper, we consider the stationary measure of the Hadamard walk on the
one-dimensional integer lattice. Here all the stationary measures given by
solving the eigenvalue problem are completely determined via the transfer
matrix method. Then these stationary measures can be divided into three
classes, i.e., quadratic polynomial, bounded, and exponential types. In
particular, we present an explicit necessary and sufficient condition for the
bounded-type stationary measure to be periodic.

In this work, we extensively study the problem of broadcasting of
entanglement as state dependent versus state independent cloners. We start by
re-conceptualizing the idea of state dependent quantum cloning machine
(SD-QCM), and in that process, we introduce different types of SD-QCMs, namely,
orthogonal and non-orthogonal cloners. We derive the conditions for which the
fidelity of these cloners will become independent of the input state. We note
that such a construction allows us to maximize the cloning fidelity at the cost

The lifetime of trapped ion ensembles corresponds to a crucial parameter
determining the potential scalability of their prospective applications. We
report on the realization of a room-temperature $^{40}{\rm Ca}^{+}$ ion
trapping vacuum apparatus with unprecedentedly low reaction rates of ions with
dominant vacuum contaminant - hydrogen. We present our trap assembly procedures
and hydrogen pressure characterization by analysis of the CaH$^+$ molecule
formation rate.

The characterization of quantum processes, e.g. communication channels, is an
essential ingredient for establishing quantum information systems. For quantum
key distribution protocols, the amount of overall noise in the channel
determines the rate at which secret bits are distributed between authorized
partners. In particular, tomographic protocols allow for the full
reconstruction, and thus characterization, of the channel. Here, we perform
quantum process tomography of high-dimensional quantum communication channels

To understand the fundamental trade-offs between training stability, temporal
dynamics and architectural complexity of recurrent neural networks~(RNNs), we
directly analyze RNN architectures using numerical methods of ordinary
differential equations~(ODEs). We define a general family of RNNs--the
ODERNNs--by relating the composition rules of RNNs to integration methods of
ODEs at discrete time steps. We show that the degree of RNN's functional
nonlinearity $n$ and the range of its temporal memory $t$ can be mapped to the

Discretizing spacetime is often a natural step towards modelling physical
systems. For quantum systems, if we also demand a strict bound on the speed of
information propagation, we get quantum cellular automata (QCAs). These
originally arose as an alternative paradigm for quantum computation, though
more recently they have been proposed as models of periodically driven
(Floquet) quantum systems, where the index theory for QCAs has allowed the
classification of chiral phases of two-dimensional Floquet systems. QCAs have

Quantum cellular automata consist in arrays of identical finite-dimensional
quantum systems, evolving in discrete-time steps by iterating a unitary
operator G. Moreover the global evolution G is required to be causal (it
propagates information at a bounded speed) and translation-invariant (it acts
everywhere the same). Quantum cellular automata provide a model/architecture
for distributed quantum computation. More generally, they encompass most of
discrete-space discrete-time quantum theory. We give an overview of their

We consider classical and quantum algorithms which have a duality property:
roughly, either the algorithm provides some nontrivial improvement over random
or there exist many solutions which are significantly worse than random. This
enables one to give guarantees that the algorithm will find such a nontrivial
improvement: if few solutions exist which are much worse than random, then a
nontrivial improvement is guaranteed. The quantum algorithm is based on a

The preparation of initial superposition states of discrete-time quantum
walks (DTQWs) are necessary for the study and applications of DTQWs. In linear
optics, it is easy to prepare initial superposition states of the coin, which
are always encoded by polarization states; while the preparation of
superposition states of the walker is challenging. Based on a novel encoding
method, we here propose a DTQW protocol in linear optics which enables the
preparation of arbitrary initial superposition states of the walker and the