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

# All

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