*
*Research Articles:

**Quantum deep learning**
(pp0541-0587)

Nathan Wiebe,
Ashish Kapoor and Krysta M. Svore

In recent years, deep learning has had a profound impact on machine
learning and artificial intelligence. At the same time, algorithms for
quantum computers have been shown to efficiently solve some problems
that are intractable on conventional, classical computers. We show that
quantum computing not only reduces the time required to train a deep
restricted Boltzmann machine, but also provides a richer and more
comprehensive framework for deep learning than classical computing and
leads to significant improvements in the optimization of the underlying
objective function. Our quantum methods also permit efficient training
of multiā€“layer and fully connected models.

**Quantum advice enhances social optimality in
three-party conflicting interest games (pp0588-0596)**

Haozhen Situ,
Cai Zhang, and Fang Yu

Quantum pseudo-telepathy games are good examples of explaining the
strangeness of quantum mechanics and demonstrating the advantage of
quantum resources over classical resources. Most of the quantum
pseudo-telepathy games are common interest games, nevertheless
conflicting interest games are more widely used to model real world
situations. Recently Pappa \emph{et al.} (Phys. Rev. Lett. 114, 020401,
2015) proposed the first two-party conflicting interest game where
quantum advice enhances social optimality. In the present paper we give
two new three-party conflicting interest games and show that quantum
advice can enhance social optimality in a three-party setting. The first
game we propose is based on the famous GHZ game which is a common
interest game. The second game we propose is related to the Svetlichny
inequality which demonstrates quantum mechanics cannot be explained by
the local hidden variable model in a three-party setting.

**Quantum feedback control for qubit-qutrit
entanglement
**
(pp0597-0614)

Tiantian Ma,
Jun Jing, Yi Guo, and Ting Yu

We study a hybrid quantum open system consisting of two interacting
subsystems formed by one two-level atom (qubit) and one three-level atom
(qutrit). The quantum open system is coupled to an external environment
(cavity) via the qubit-cavity interaction. It is found that the feedback
control on different parts of the system (qubit or qutrit) gives
dramatically different asymptotical behaviors of the open system
dynamics. We show that the local feedback control mechanism acting on
the qutrit subsystem is superior than that on the qubit in the sense of
improving the entanglement. Particularly, the qutrit-control scheme may
result in an entangled steady state, depending on the initial state.

**The learnability of unknown quantum measurements
**
(pp0615-0656)

Hao-Chung Cheng,
Min-Hsiu Hsieh, and Ping-Cheng Yeh

In this work, we provide an elegant framework to analyze learning
matrices in the Schatten class by taking advantage of a recently
developed methodology---matrix concentration inequalities. We establish
the fat-shattering dimension, Rademacher/Gaussian complexity, and
entropy number of learning bounded operators and trace class operators.
By characterizing the tasks of learning quantum states and two-outcome
quantum measurements into learning matrices in the Schatten-$1$ and $\infty$
classes, our proposed approach directly solves the sample complexity
problems of learning quantum states and quantum measurements. Our main
result in the paper is that, for learning an unknown quantum
measurement, the upper bound, given by the fat-shattering dimension, is
linearly proportional to the dimension of the underlying Hilbert space.
Learning an unknown quantum state becomes a dual problem to ours, and as
a byproduct, we can recover Aaronson's famous result solely using a
classical machine learning technique. In addition, other famous
complexity measures like covering numbers and Rademacher/Gaussian
complexities are derived explicitly under the same framework. We are
able to connect measures of sample complexity with various areas in
quantum information science, e.g. quantum state/measurement tomography,
quantum state discrimination and quantum random access codes, which may
be of independent interest. Lastly, with the assistance of general
Bloch-sphere representation, we show that learning quantum
measurements/states can be mathematically formulated as a neural
network. Consequently, classical ML algorithms can be applied to
efficiently accomplish the two quantum learning tasks.

**General fixed points of quasi-local
frustration-free quantum semigroups: from invariance to stabilization**
(pp0657-0699)

Peter D. Johnson,
Francesco Ticozzi, and Lorenza Viola

We investigate under which conditions a mixed state on a
finite-dimensional multipartite quantum system may be the unique,
globally stable fixed point of frustration-free semigroup dynamics
subject to specified quasi-locality constraints. Our central result is a
linear-algebraic necessary and sufficient condition for a generic
(full-rank) target state to be *frustration-free quasi-locally
stabilizable*, along with an explicit procedure for constructing
Markovian dynamics that achieve stabilization. If the target state is
not full-rank, we establish sufficiency under an additional condition,
which is naturally motivated by consistency with pure-state
stabilization results yet provably not necessary in general.
Several applications are discussed, of relevance to both dissipative
quantum engineering and information processing, and non-equilibrium
quantum statistical mechanics. In particular, we show that a large class
of graph product states (including arbitrary thermal graph states) as
well as Gibbs states of commuting Hamiltonians are frustration-free
stabilizable relative to natural quasi-locality constraints. Likewise,
we provide explicit examples of non-commuting Gibbs states and
non-trivially entangled mixed states that are stabilizable despite the
lack of an underlying commuting structure, albeit scalability to
arbitrary system size remains in this case an open question.

**An n-bit general implementation of Shor's quantum
period-finding algorithm for quantum information and computation**
(pp0700-0718)

J.T. Davies,
Christopher J. Rickerd, Mike A. Grimes, and Durduo Guney

The goal of this paper is to outline a general-purpose scalable
implementation of Shor's period-finding algorithm using fundamental
quantum gates, and to act as a blueprint for linear optical
implementations of Shor's algorithm for both general and specific values
of $N$. This offers a broader view of a problem often overlooked in
favour of compiled versions of the algorithm.