Machine learning (ML) models are trained using historical data to classify
new, unseen data. However, traditional computing resources often struggle to
handle the immense amount of data, commonly known as Big Data, within a
reasonable timeframe. Quantum computing (QC) provides a novel approach to
information processing. Quantum algorithms have the potential to process
classical data exponentially faster than classical computing. By mapping
quantum machine learning (QML) algorithms into the quantum mechanical domain,
we can potentially achieve exponential improvements in data processing speed,
reduced resource requirements, and enhanced accuracy and efficiency. In this
article, we delve into both the QC and ML fields, exploring the interplay of
ideas between them, as well as the current capabilities and limitations of
hardware. We investigate the history of quantum computing, examine existing QML
algorithms, and aim to present a simplified procedure for setting up
simulations of QML algorithms, making it accessible and understandable for
readers. Furthermore, we conducted simulations on a dataset using both machine
learning and quantum machine learning approaches. We then proceeded to compare
their respective performances by utilizing a quantum simulator.

利用量子计算和量子机器学习算法在数据处理方面取得了指数级的提速、资源需求的减少以及准确度和效率的提高，本文对量子计算、机器学习和量子机器学习算法进行了探讨，并提供了一个简化的步骤，可以帮助读者建立量子机器学习算法的模拟。此外，通过在数据集上利用机器学习和量子机器学习方法进行模拟，利用量子模拟器对它们的性能进行了比较。

量子辅助模拟：在量子计算领域设计机器学习模型的框架

Quantum-Assisted Simulation: A Framework for Designing Machine Learning  Models in the Quantum Computing Domain

Variational quantum approaches have shown great promise in finding
near-optimal solutions to computationally challenging tasks. Nonetheless,
enforcing constraints in a disciplined fashion has been largely unexplored. To
address this gap, this work proposes a hybrid quantum-classical algorithmic
paradigm termed VQEC that extends the celebrated VQE to handle optimization
with constraints. As with the standard VQE, the vector of optimization
variables is captured by the state of a variational quantum circuit (VQC). To
deal with constraints, VQEC optimizes a Lagrangian function classically over
both the VQC parameters as well as the dual variables associated with
constraints. To comply with the quantum setup, variables are updated via a
perturbed primal-dual method leveraging the parameter shift rule. Among a wide
gamut of potential applications, we showcase how VQEC can approximately solve
quadratically-constrained binary optimization (QCBO) problems, find stochastic
binary policies satisfying quadratic constraints on the average and in
probability, and solve large-scale linear programs (LP) over the probability
simplex. Under an assumption on the error for the VQC to approximate an
arbitrary probability mass function (PMF), we provide bounds on the optimality
gap attained by a VQC. Numerical tests on a quantum simulator investigate the
effect of various parameters and corroborate that VQEC can generate
high-quality solutions.

基于 VQEC 算法模型，采用量子变分法和经典算法结合的方式进行带约束的优化，通过量子模拟器进行数值测试验证和参数优化，展示了其在近似解决复杂优化问题方面的优势。

变分量子特征求解器 (VQEC)：通过 VQE 求解约束优化问题

Variational Quantum Eigensolver with Constraints (VQEC): Solving  Constrained Optimization Problems via VQE

To explore the possibilities of a near-term intermediate-scale quantum
algorithm and long-term fault-tolerant quantum computing, a fast and versatile
quantum circuit simulator is needed. Here, we introduce Qulacs, a fast
simulator for quantum circuits intended for research purpose. We show the main
concepts of Qulacs, explain how to use its features via examples, describe
numerical techniques to speed-up simulation, and demonstrate its performance
with numerical benchmarks.

本研究介绍了一种用于量子电路模拟器的快速和多功能的 Qulacs，旨在探索中等规模的近期计算算法和长期的容错量子计算。通过数字基准测试得出其性能，并介绍使用示例和数值技术以加快模拟。