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.

翻译：深度度量学习近期在经典数据领域展现出极具前景的结果，能够创建良好分离的特征空间。这一思想也通过量子度量学习（QMeL）被适配到量子计算机上。QMeL包含两步过程：首先使用经典模型压缩数据以适配有限的量子比特数量，然后训练参数化量子电路（PQC）在希尔伯特空间中实现更好的分离。然而，在噪声中等规模量子（NISQ）设备上，QMeL解决方案导致电路宽度和深度过高，两者均限制了可扩展性。我们提出量子极坐标度量学习（QPMeL），该方法利用经典模型学习量子比特极坐标形式的参数。随后，我们使用包含$R_y$和$R_z$门的浅层PQC创建量子态，并通过可训练的$ZZ(\theta)$门层学习纠缠。该电路还通过SWAP测试计算保真度，用于我们提出的保真度三元组损失函数，该函数同时训练经典和量子组件。与QMeL方法相比，QPMeL在多类分离方面提升了3倍，同时仅使用一半的量子门数量和电路深度。我们还证明，QPMeL在类似配置下性能优于经典网络，为未来研究完全经典模型与量子损失函数的结合提供了有前景的方向。