Quantum Kernel Machine Learning for Autonomous Materials Science

TL;DR

The paper investigates quantum kernel learning as a data-efficient tool for autonomous materials discovery by comparing a quantum kernel, computed via a 150-feature map, against classical kernels on an XRD-based Fe-Ga-Pd composition-spread dataset. Using Huang et al.'s model-complexity framework, it assesses potential quantum advantage through $s_K(N)$ and the geometric difference $g_{CQ}$, and evaluates performance with a Gaussian process classifier on limited training data. Results show the quantum kernel can reveal nuanced similarities and, in simulated settings, outperform a radial-basis-function kernel in certain data-sparse regimes, though a cosine-similarity kernel often performs best due to inductive bias; hardware noise attenuates the advantage. The work emphasizes problem-aware quantum kernel design and metric-learning to tailor feature maps for diffraction-like data, suggesting a path toward practical quantum acceleration in autonomous materials science as quantum hardware matures.

Abstract

Autonomous materials science, where active learning is used to navigate large compositional phase space, has emerged as a powerful vehicle to rapidly explore new materials. A crucial aspect of autonomous materials science is exploring new materials using as little data as possible. Gaussian process-based active learning allows effective charting of multi-dimensional parameter space with a limited number of training data, and thus is a common algorithmic choice for autonomous materials science. An integral part of the autonomous workflow is the application of kernel functions for quantifying similarities among measured data points. A recent theoretical breakthrough has shown that quantum kernel models can achieve similar performance with less training data than classical models. This signals the possible advantage of applying quantum kernel machine learning to autonomous materials discovery. In this work, we compare quantum and classical kernels for their utility in sequential phase space navigation for autonomous materials science. Specifically, we compute a quantum kernel and several classical kernels for x-ray diffraction patterns taken from an Fe-Ga-Pd ternary composition spread library. We conduct our study on both IonQ's Aria trapped ion quantum computer hardware and the corresponding classical noisy simulator. We experimentally verify that a quantum kernel model can outperform some classical kernel models. The results highlight the potential of quantum kernel machine learning methods for accelerating materials discovery and suggest complex x-ray diffraction data is a candidate for robust quantum kernel model advantage.

Figures (6)

• Figure 1: A schematic of a typical iterative autonomous phase mapping workflow. Asterisks (*) indicate which steps use kernel methods. (a) A new x-ray diffraction measurement is performed at a specific composition (shown in units of atomic fraction). Sample indices 1 -- 20 were chosen manually here for illustration and do not reflect a typical measurement order. (b) All of the measured compositions are clustered into groups and assigned a corresponding label (color and symbol to the left) using an x-ray diffraction kernel function. (c) The labels of the unmeasured compositions are then extrapolated using a composition kernel function. (d) To minimize the total uncertainty in the extrapolated labels, the composition with the maximum uncertainty (entropy) in its predicted label is chosen as the next composition to measure, indicated by the star. Note that the clustering and extrapolation methods are both kernel methods but use different kernel functions which compare different types of data (x-ray diffraction patterns and compositions).
• Figure 2: The quantum circuit used to compare two XRD patterns, $x_1$ and $x_2$. (a) The kernel circuit is composed of a forward and a reverse copy of the feature map circuit, $U$, which takes the intensities of an XRD pattern as parameters. The initial state of each qubit is $\ket{0}$ and the kernel value is the probability that the final state of every qubit is $\ket{0}$. (b) The feature map circuit, $U$, is composed of 1- and 2-qubit operations, or "gates". Each horizontal line represents a qubit, and the circuit computation proceeds from left to right. The gray, 1-qubit gate is a Hadamard gate, the gray 2-qubit gate is a $\sqrt{i\text{SWAP}}$ gate, and the triplets of white gates are rotation gates about the $z$, $y$, and $z$ axes respectively. The numbers indicate the order in which XRD intensities parameterize the rotation gates. (c) A schematic illustrating how the XRD intensities determine the angle of rotation in the rotation gates, a $z$ axis rotation on the left and a $y$ axis rotation on the right.
• Figure 3: Comparison of the quantum and classical kernel matrices. The axis values are sample indices from Figure \ref{['fig:active_learning']}a. Quantum kernel matrices are shown with a logarithmic colormap to show the fine details not picked up by the classical kernels, while the classical kernels are shown with a linear colormap. See SI for all kernels in both logarithmic and linear scales.
• Figure 4: The relative performance of the quantum and classical kernels on the supervised learning task. Both plots show the accuracy of the Gaussian process classifier using the quantum kernel (simulated and measured) relative to one of the classical kernels. The left plot is relative to the radial basis function kernel and the right plot is relative to the cosine similarity kernel. The shaded regions indicate 95 % confidence intervals.
• Figure 5: The relative performance of the quantum and classical kernels on the engineered labels. The ternary plot on the left shows the engineered labels of the XRD patterns as a function of their composition. Like Figure \ref{['fig:kernel_performance']}, the plot on the right shows the accuracy of the Gaussian process classifier using the quantum kernel relative to the performance the cosine similarity. Again, shaded regions indicate 95 % confidence intervals.