Improving Quantum Machine Learning via Heat-Bath Algorithmic Cooling

TL;DR

The paper introduces a thermodynamic lens on quantum machine learning, reframing learning as a cooling process and proposing Bidirectional Quantum Refrigerator (BQR) protocols inspired by heat-bath algorithmic cooling to boost qubit polarization. By alternating entropy compression and thermalization, and by recycling qubits, the approach reduces finite sampling errors in both training and prediction without Grover-like or phase-estimation procedures, making it suitable for NISQ devices. The authors provide theoretical results (including optimal single-shot entropy compression and asymptotic polarization formulas) and numerical evidence showing substantial reductions in the number of measurements required to estimate classification scores and gradients. The work offers a versatile framework applicable to variational quantum classifiers and quantum-kernel methods, with practical variants using k-local compressions that balance performance and implementability, and it points to future directions in optimality, coherence-assisted cooling, and kernel estimation contexts.

Abstract

This work introduces an approach rooted in quantum thermodynamics to enhance sampling efficiency in quantum machine learning (QML). We propose conceptualizing quantum supervised learning as a thermodynamic cooling process. Building on this concept, we develop a quantum refrigerator protocol that enhances sample efficiency during training and prediction without the need for Grover iterations or quantum phase estimation. Inspired by heat-bath algorithmic cooling protocols, our method alternates entropy compression and thermalization steps to decrease the entropy of qubits, increasing polarization towards the dominant bias. This technique minimizes the computational overhead associated with estimating classification scores and gradients, presenting a practical and efficient solution for QML algorithms compatible with noisy intermediate-scale quantum devices.

Figures (7)

• Figure 1: Enhanced polarization $\alpha_\textsc{ac}$ resulting from optimal single-shot entropy compression, plotted as a function of the initial $|\alpha|$ for different numbers of qubits. The black dotted line represents the baseline, initial polarization.
• Figure 2: Reduction factor of the error probability bound after enhancing polarization via AC entropy compression, as a function of the initial polarization $|\alpha|$. The results are shown for different values of $n$, using the error probability bound given by Eq. (\ref{['eq:error_predict']}).
• Figure 3: Bidirectional quantum refrigerator protocol circuit operating on $n$ qubits, including $m$ reset qubits ($m=2$ in this figure).
• Figure 4: Enhanced polarization $\alpha_\textsc{qr}$ for the quantum refrigerator operating with $n=5$ as a function of the initial $|\alpha|$ for different number of rounds. The black dotted line represents the baseline for the initial polarization, and the solid black line corresponds to the asymptotic polarization.
• Figure 5: Reduction factor of the error probability bound for the quantum refrigerator operating with $n=5$ qubits, shown in blue for different numbers of rounds as a function of the initial $|\alpha|$. The pink line represents the improvement achieved through single-shot entropy compression for $n=5$, while the yellow dashed line depicts the upper bound from simulations using optimal compressions for the case of $N_{\rm rounds}=9$. Notably, the performance of the BQR closely aligns with the optimal scenario, indicating an almost exact match for the configuration $n=5$, $m=2$, and $N_{\rm rounds}=9$.