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。