  Quantum machine learning (QML) algorithms have obtained great relevance in
the machine learning (ML) field due to the promise of quantum speedups when
performing basic linear algebra subroutines (BLAS), a fundamental element in
most ML algorithms. By making use of BLAS operations, we propose, implement and
analyze a quantum k-means (qk-means) algorithm with a low time complexity of
$\mathcal{O}(NKlog(D)I/C)$ to apply it to the fundamental problem of
discriminating quantum states at readout. Discriminating quantum states allows
the identification of quantum states $|0\rangle$ and $|1\rangle$ from low-level
in-phase and quadrature signal (IQ) data, and can be done using custom ML
models. In order to reduce dependency on a classical computer, we use the
qk-means to perform state discrimination on the IBMQ Bogota device and managed
to find assignment fidelities of up to 98.7% that were only marginally lower
than that of the k-means algorithm. Inspection of assignment fidelity scores
resulting from applying both algorithms to a combination of quantum states
showed concordance to our correlation analysis using Pearson Correlation
coefficients, where evidence shows cross-talk in the (1, 2) and (2, 3)
neighboring qubit couples for the analyzed device.
