qc-kmeans: A Quantum Compressive K-Means Algorithm for NISQ Devices

TL;DR

qc-kmeans introduces a hybrid quantum-classical clustering algorithm optimized for NISQ devices, utilizing a Fourier-feature sketch and shallow QAOA circuits to efficiently handle large datasets with limited qubits.

Contribution

It presents a novel quantum compressive k-means algorithm that maintains constant qubit requirements and achieves competitive clustering accuracy on real datasets.

Findings

Achieved low qubit usage (≤9 qubits) in simulations.

Maintained constant peak-qubit usage on large datasets.

Comparable accuracy under IBM noise models.

Abstract

Clustering on NISQ hardware is constrained by data loading and limited qubits. We present \textbf{qc-kmeans}, a hybrid compressive $k$-means that summarizes a dataset with a constant-size Fourier-feature sketch and selects centroids by solving small per-group QUBOs with shallow QAOA circuits. The QFF sketch estimator is unbiased with mean-squared error $O(\varepsilon^2)$ for $B,S=\Theta(\varepsilon^{-2})$, and the peak-qubit requirement $q_{\text{peak}}=\max\{D,\lceil \log_2 B\rceil + 1\}$ does not scale with the number of samples. A refinement step with elitist retention ensures non-increasing surrogate cost. In Qiskit Aer simulations (depth $p{=}1$), the method ran with $\le 9$ qubits on low-dimensional synthetic benchmarks and achieved competitive sum-of-squared errors relative to quantum baselines; runtimes are not directly comparable. On nine real datasets (up to $4.3\times 10^5$ points), the pipeline maintained constant peak-qubit usage in simulation. Under IBM noise models, accuracy was similar to the idealized setting. Overall, qc-kmeans offers a NISQ-oriented formulation with shallow, bounded-width circuits and competitive clustering quality in simulation.