Discriminating Quantum States with Quantum Machine Learning

TL;DR

This paper introduces a quantum k-means algorithm leveraging quantum speedups for the task of quantum state discrimination, demonstrating high fidelity results on IBM quantum hardware and analyzing device-specific cross-talk effects.

Contribution

It presents a low-complexity quantum k-means algorithm for quantum state discrimination, implemented on real hardware, and analyzes qubit cross-talk effects.

Findings

Achieved up to 98.7% assignment fidelity on IBMQ Bogota.

Quantum k-means performance closely matches classical k-means.

Identified qubit cross-talk effects affecting discrimination accuracy.

Abstract

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.