Recent work has proposed and explored using coreset techniques for quantum
algorithms that operate on classical data sets to accelerate the applicability
of these algorithms on near-term quantum devices. We apply these ideas to
Quantum Boltzmann Machines (QBM) where gradient-based steps which require Gibbs
state sampling are the main computational bottleneck during training. By using
a coreset in place of the full data set, we try to minimize the number of steps
needed and accelerate the overall training time. In a regime where
computational time on quantum computers is a precious resource, we propose this
might lead to substantial practical savings. We evaluate this approach on 6x6
binary images from an augmented bars and stripes data set using a QBM with 36
visible units and 8 hidden units. Using an Inception score inspired metric, we
compare QBM training times with and without using coresets.

使用 coreset 技术加速量子算法在量子计算机上的训练时间，尤其是应用于 Quantum Boltzmann Machines 时的梯度下降算法，以减少计算时间并提高实际效益。

用 Coresets 训练量子 Boltzmann 机

Training Quantum Boltzmann Machines with Coresets

DNA sequencing allows for the determination of the genetic code of an
organism, and therefore is an indispensable tool that has applications in
Medicine, Life Sciences, Evolutionary Biology, Food Sciences and Technology,
and Agriculture. In this paper, we present several novel methods of performing
classical-to-quantum data encoding inspired by various mathematical fields, and
we demonstrate these ideas within Bioinformatics. In particular, we introduce
algorithms that draw inspiration from diverse fields such as Electrical and
Electronic Engineering, Information Theory, Differential Geometry, and Neural
Network architectures. We provide a complete overview of the existing data
encoding schemes and show how to use them in Genomics. The algorithms provided
utilise lossless compression, wavelet-based encoding, and information entropy.
Moreover, we propose a contemporary method for testing encoded DNA sequences
using Quantum Boltzmann Machines. To evaluate the effectiveness of our
algorithms, we discuss a potential dataset that serves as a sandbox environment
for testing against real-world scenarios. Our research contributes to
developing classical-to-quantum data encoding methods in the science of
Bioinformatics by introducing innovative algorithms that utilise diverse fields
and advanced techniques. Our findings offer insights into the potential of
Quantum Computing in Bioinformatics and have implications for future research
in this area.

本文介绍了在生物信息学中使用多种数学领域的算法进行古典到量子数据编码的新颖方法，其中包括无损压缩、小波编码和信息熵技术，并提出了基于量子玻尔兹曼机的 DNA 序列编码测试方法，为量子计算在生物信息学中的发展提供了新的思路和应用。

基因组学中的经典到量子序列编码

Classical-to-Quantum Sequence Encoding in Genomics

This work presents a novel realization approach to Quantum Boltzmann Machines
(QBMs). The preparation of the required Gibbs states, as well as the evaluation
of the loss function's analytic gradient is based on Variational Quantum
Imaginary Time Evolution, a technique that is typically used for ground state
computation. In contrast to existing methods, this implementation facilitates
near-term compatible QBM training with gradients of the actual loss function
for arbitrary parameterized Hamiltonians which do not necessarily have to be
fully-visible but may also include hidden units. The variational Gibbs state
approximation is demonstrated with numerical simulations and experiments run on
real quantum hardware provided by IBM Quantum. Furthermore, we illustrate the
application of this variational QBM approach to generative and discriminative
learning tasks using numerical simulation.

本文提出一种基于虚时间演化的变分量子 Gibbs 状态逼近方法，实现了与临近中期的量子计算机兼容的量子 Boltzmann 机械训练方法，同时支持任意参数哈密顿量的梯度下降求解，适用于生成学习与判别学习任务。

变分量子玻尔兹曼机

Variational Quantum Boltzmann Machines

We present a representation for linguistic structure that we call a
Fock-space representation, which allows us to embed problems in language
processing into small quantum devices. We further develop a formalism for
understanding both classical as well as quantum linguistic problems and phrase
them both as a Harmony optimization problem that can be solved on a quantum
computer which we show is related to classifying vectors using quantum
Boltzmann machines. We further provide a new training method for learning
quantum Harmony operators that describe a language. This also provides a new
algorithm for training quantum Boltzmann machines that requires no
approximations and works in the presence of hidden units. We additionally show
that quantum language processing is BQP-complete, meaning that it is
polynomially equivalent to the circuit model of quantum computing which implies
that quantum language models are richer than classical models unless BPP=BQP.
It also implies that, under certain circumstances, quantum Boltzmann machines
are more expressive than classical Boltzmann machines. Finally, we examine the
performance of our approach numerically for the case of classical harmonic
grammars and find that the method is capable of rapidly parsing even
non-trivial grammars. This suggests that the work may have value as a quantum
inspired algorithm beyond its initial motivation as a new quantum algorithm.

该论文介绍了一种语言结构的 Fock 空间表示法，其允许我们将语言处理中的问题嵌入到小型量子设备中，并提供了一种新的算法来训练描述语言的量子 和训练量子 Boltzmann 机的算法。此外，该论文表明了量子语言处理是 BQP 完全的，意味着它在多项式时间内等效于量子计算电路模型，暗示了量子语言模型比经典模型更丰富。