Discretely Parametrized Quantum Circuits as Quantum Classifiers

Parametrized quantum circuits (PQCs) are typically parametrized continuously, whereas low-resolution quantum control motivates restricting circuit parameters to a discrete set. This distinction can become consequential at low resolution, where projecting a continuously optimized circuit onto executable parameter values can substantially perturb the implemented circuit and degrade task performance. We therefore study *discretely parametrized quantum circuits* (DPQCs), whose trainable circuit parameters are defined and optimized directly over a discrete set, in contrast to continuously parametrized quantum circuits (CPQCs). To better preserve input structure under finite resolution, we introduce resolution-aware angular re-uploading, which progressively uploads input information across multiple resolution levels during classical data encoding into the circuit. We further develop spectrum-informed shift-compatible optimization (SISCO), which exploits the spectral structure of Pauli-generated PQCs to optimize discrete circuit parameters. Across multiple benchmarks, our DPQC framework generally outperforms alternative approaches and is particularly effective in the low-resolution regime. With a nominal **5-bit resolution** for circuit parametrization (i.e., \(2^5 = 32\) executable values), our resolution-aware DPQCs trained with SISCO achieve **93.56%**, **77.27%**, and **86.56%** mean accuracy on Imagenette, CIFAR-10, and STL-10, respectively, closely matching the corresponding CPQC references of **92.44%**, **77.43%**, and **86.62%**. These results show that jointly designing data encoding and optimization for DPQCs can retain competitive performance without relying on continuous circuit parametrization, providing an algorithmic framework for variational quantum learning under low resolutions.