  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.
