Quantum machine learning has the potential to enable advances in artificial
intelligence, such as solving problems intractable on classical computers. Some
fundamental ideas behind quantum machine learning are similar to kernel methods
in classical machine learning. Both process information by mapping it into
high-dimensional vector spaces without explicitly calculating their numerical
values. We explore a setup for performing classification on labeled classical
datasets, consisting of a classical neural network connected to a quantum
annealer. The neural network programs the quantum annealer's controls and
thereby maps the annealer's initial states into new states in the Hilbert
space. The neural network's parameters are optimized to maximize the distance
of states corresponding to inputs from different classes and minimize the
distance between quantum states corresponding to the same class. Recent
literature showed that at least some of the "learning" is due to the quantum
annealer, connecting a small linear network to a quantum annealer and using it
to learn small and linearly inseparable datasets. In this study, we consider a
similar but not quite the same case, where a classical fully-fledged neural
network is connected with a small quantum annealer. In such a setting, the
fully-fledged classical neural-network already has built-in nonlinearity and
learning power, and can already handle the classification problem alone, we
want to see whether an additional quantum layer could boost its performance. We
simulate this system to learn several common datasets, including those for
image and sound recognition. We conclude that adding a small quantum annealer
does not provide a significant benefit over just using a regular (nonlinear)
classical neural network.

量子机器学习与经典机器学习中的核方法有相似之处，本研究探索了将经典神经网络与量子退火机连接的设置，并模拟了其在分类问题上的性能，发现加入小型量子退火机并不能显著提高性能。

用于编程量子退火机的神经网络

Neural Networks for Programming Quantum Annealers

The Kemeny Rank Aggregation (KRA) problem is a well-studied problem in the
field of Social Choice with a variety of applications in many different areas
like databases and search engines. Intuitively, given a set of votes over a set
of candidates, the problem asks to find an aggregated ranking of candidates
that minimizes the overall dissatisfaction concerning the votes. Recently, a
diverse version of KRA was considered which asks for a sufficiently diverse set
of sufficiently good solutions. The framework of diversity of solutions is a
young and thriving topic in the field of artificial intelligence. The main idea
is to provide the user with not just one, but with a set of different
solutions, enabling her to pick a sufficiently good solution that satisfies
additional subjective criteria that are hard or impossible to model.
In this work, we use a quantum annealer to solve the KRA problem and to
compute a representative set of solutions. Quantum annealing is a meta search
heuristic that does not only show promising runtime behavior on currently
existing prototypes but also samples the solutions space in an inherently
different way, making use of quantum effects. We describe how KRA instances can
be solved by a quantum annealer and provide an implementation as well as
experimental evaluations. As existing quantum annealers are still restricted in
their number of qubits, we further implement two different data reduction rules
that can split an instance into a set of smaller instances. In our evaluation,
we compare classical heuristics that allow to sample multiple solutions such as
simulated annealing and local search with quantum annealing performed on a
physical quantum annealer. We compare runtime, quality of solution, and
diversity of solutions, with and without applying preceding data reduction
rules.

本文描述并实现了如何使用量子退火器解决 Kemeny Rank Aggregation 问题，并使用 2 种数据缩减规则与模拟退火和局部搜索等经典算法进行对比研究量子退火器的运行时间、解决方案的质量和多样性。

基于量子退火的多样化 Kemeny 排名聚合启发式算法

Heuristic for Diverse Kemeny Rank Aggregation based on Quantum Annealing

We study the relation between the Ising problem Hamiltonian parameters and
the minimum spectral gap (min-gap) of the system Hamiltonian in the Ising-based
quantum annealer. The main argument we use in this paper to assess the
performance of a QA algorithm is the presence or absence of an anti-crossing
during quantum evolution. For this purpose, we introduce a new parametrization
definition of the anti-crossing. Using the Maximum-weighted Independent Set
(MIS) problem in which there are flexible parameters (energy penalties J
between pairs of edges) in an Ising formulation as the model problem, we
construct examples to show that by changing the value of J, we can change the
quantum evolution from one that has an anti-crossing (that results in an
exponential small min-gap) to one that does not have, or the other way around,
and thus drastically change (increase or decrease) the min-gap. However, we
also show that by changing the value of $J$ alone, one can not avoid the
anti-crossing. We recall a polynomial reduction from an Ising problem to an MIS
problem to show that the flexibility of changing parameters without changing
the problem to be solved can be applied to any Ising problem. As an example, we
show that by such a reduction alone, it is possible to remove the anti-crossing
and thus increase the min-gap. Our anti-crossing definition is necessarily
scaling invariant as scaling the problem Hamiltonian does not change the nature
(i.e. presence or absence) of an anti-crossing. As a side note, we show exactly
how the min-gap is scaled if we scale the problem Hamiltonian by a constant
factor.

本研究探讨 Ising 问题与量子退火器中问题哈密顿参量之间的关系，并通过新参数定义的引入，阐述贯穿整个论文的一个观点，即判断 QA 算法性能的关键是量子演化时是否存在 anti-crossing。我们通过最大加权独立集问题构造了例子，并改变参数值，展示了如何在问题不变的情况下改变量子演化的性质以从根本上影响 spectral gap 值。最后，我们通过一个多项式约化，将 Ising 问题约化为最大加权独立集问题，并展示了如何通过此方法消除 anti-crossing，增加最小 spectral gap。

问题哈密顿参数对绝热量子优化的最小谱间隙的影响

The Effects of the Problem Hamiltonian Parameters on the Minimum  Spectral Gap in Adiabatic Quantum Optimization

Quantum technology is maturing to the point where quantum devices, such as
quantum communication systems, quantum random number generators and quantum
simulators, may be built with capabilities exceeding classical computers. A
quantum annealer, in particular, solves hard optimisation problems by evolving
a known initial configuration at non-zero temperature towards the ground state
of a Hamiltonian encoding a given problem. Here, we present results from
experiments on a 108 qubit D-Wave One device based on superconducting flux
qubits. The strong correlations between the device and a simulated quantum
annealer, in contrast with weak correlations between the device and classical
annealing or classical spin dynamics, demonstrate that the device performs
quantum annealing. We find additional evidence for quantum annealing in the
form of small-gap avoided level crossings characterizing the hard problems. To
assess the computational power of the device we compare it to optimised
classical algorithms.

该篇文章介绍了基于超导通量量子位的 108 量子比特 D-Wave One 设备的量子退火实验结果，证明设备能够执行量子退火，作者使用了优化过的经典算法来比较该设备的计算能力。