Deep metric learning has recently shown extremely promising results in the
classical data domain, creating well-separated feature spaces. This idea was
also adapted to quantum computers via Quantum Metric Learning(QMeL). QMeL
consists of a 2 step process with a classical model to compress the data to fit
into the limited number of qubits, then train a Parameterized Quantum
Circuit(PQC) to create better separation in Hilbert Space. However, on Noisy
Intermediate Scale Quantum (NISQ) devices. QMeL solutions result in high
circuit width and depth, both of which limit scalability. We propose Quantum
Polar Metric Learning (QPMeL) that uses a classical model to learn the
parameters of the polar form of a qubit. We then utilize a shallow PQC with
$R_y$ and $R_z$ gates to create the state and a trainable layer of
$ZZ(\theta)$-gates to learn entanglement. The circuit also computes fidelity
via a SWAP Test for our proposed Fidelity Triplet Loss function, used to train
both classical and quantum components. When compared to QMeL approaches, QPMeL
achieves 3X better multi-class separation, while using only 1/2 the number of
gates and depth. We also demonstrate that QPMeL outperforms classical networks
with similar configurations, presenting a promising avenue for future research
on fully classical models with quantum loss functions.

基于深度度量学习和量子计算的研究，提出了一种新的量子极化度量学习 (QPMeL) 方法，通过使用经典模型学习极坐标形式的量子比特参数，并结合浅层的参数化量子电路和可训练的量子门层进行训练，以实现更好的多类别分离效果。在与现有量子度量学习方法和经典网络相比较时，QPMeL 方法取得了较好的性能表现，为未来基于经典模型和量子损失函数的研究提供了有前景的方向。

量子极化度量学习：高效经典学习的量子嵌入

Quantum Polar Metric Learning: Efficient Classically Learned Quantum  Embeddings

Quantum classifiers are trainable quantum circuits used as machine learning
models. The first part of the circuit implements a quantum feature map that
encodes classical inputs into quantum states, embedding the data in a
high-dimensional Hilbert space; the second part of the circuit executes a
quantum measurement interpreted as the output of the model. Usually, the
measurement is trained to distinguish quantum-embedded data. We propose to
instead train the first part of the circuit -- the embedding -- with the
objective of maximally separating data classes in Hilbert space, a strategy we
call quantum metric learning. As a result, the measurement minimizing a linear
classification loss is already known and depends on the metric used: for
embeddings separating data using the l1 or trace distance, this is the Helstrom
measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple
overlap measurement. This approach provides a powerful analytic framework for
quantum machine learning and eliminates a major component in current models,
freeing up more precious resources to best leverage the capabilities of
near-term quantum information processors.

该论文提出了一种称为量子度量学习的新策略，通过训练可训练的量子电路的第一部分来实现数据类最大分离的嵌入，从而消除了当前模型中的一个主要部分。