A quantum machine learning classifier to search for new physics

TL;DR

This work introduces quantum searching neighbor (QSN) and variational QSN (VQSN) as quantum classifiers to hunt for new physics signals in high-dimensional collider data, leveraging quantum state overlaps as a distance measure and amplitude-encoded feature spaces. Demonstrations span muon colliders and the LHC, with applications to gluon quartic gauge couplings and anomalies quartic gauge couplings within SMEFT frameworks, and include both simulated results and hardware tests showing noise resilience. Compared to classical k-nearest neighbors, VQSN achieves comparable discriminative power with significantly reduced circuit depth and gate counts, highlighting potential advantages for handling the growing data volumes anticipated at future colliders. The work provides concrete NP sensitivity projections, demonstrates versatility across processes, and discusses the trade-offs between global weight-based quantum classifications and nearest-neighbor approaches for high-luminosity experiments.

Abstract

Due to the success of the Standard Model~(SM), it is reasonable to anticipate that the signal of new physics~(NP) beyond the SM is small. Consequently, future searches for NP and precision tests of the SM will require high luminosity collider experiments. Moreover, as precision tests advance, rare processes with many final-state particles require consideration which demand the analysis of a vast number of observables. The high luminosity produces a large amount of experimental data spanning a large observable space, posing a significant data-processing challenge. In recent years, quantum machine learning has emerged as a promising approach for processing large amounts of complex data on a quantum computer. In this study, we propose quantum searching neighbor~(QSN) and variational QSN~(VQSN) algorithms to search for NP. The QSN is a classification algorithm. The VQSN introduces variation to the QSN to process classical data. As applications, we apply the (V)QSN in the phenomenological study of the NP at the Large Hadron Collider and muon colliders. Examples are implemented on a real quantum hardware, which confirms reliable performance under noisy conditions. The results indicate that the VQSN demonstrates superior efficiency in the sense of computational complexity to a classical counterpart k-nearest neighbor algorithm, even when dealing with classical data.

Figures (18)

• Figure 1: The problem addressed by (V)QSN. Given known classifications of some points in a feature space (e.g., $32$ colored points in a $2$-dimensional space as shown in the figure), how to classify an unknown point (marked as '$\times$' in the figure). (V)QSN classifies '$\times$' based on its distance to the known points, assigning it to the class belonging to the known points closer to it (its neighbors).
• Figure 2: The circuit to construct the state $\langle\phi | \psi _n\rangle|n\rangle$. $U_{|\psi _j\rangle _{a}|j\rangle _{b}}$ and $U_{|\phi\rangle}$ are the circuits to encode the training set points $U_{|\psi _j\rangle _{a}|j\rangle _{b}}|0\rangle_a|0\rangle_b=|\psi _j\rangle _{a}|j\rangle _{b}$ and test point $U_{|\phi\rangle}|0\rangle=|\phi\rangle$, respectively. If the measurement on $a$ register yields the $|0\ldots 0\rangle _a$ state, the result is $|0\ldots 0\rangle _a \langle \phi |\psi _j\rangle |j\rangle _b$.
• Figure 3: The circuit to fit the ansatz. $U_A$ denotes the ansatz circuit with trainable parameters $\alpha _i$. The goal is to adjust $\alpha _i$ to maximize the probability where $|0\ldots 0\rangle$ is measured. An example of $U_A$ with the 'SCA' layer is shown.
• Figure 4: The circuit to find the classification assignment of $|\phi\rangle$. If the measurement on the $a$ register yields $|0\ldots 0\rangle$, then $b_1$ is measured. If the quantum states corresponding to the points classified as $k$ in the training set have larger overlaps with $|\phi\rangle$, the measurement on $b_1$ yields outcome $|k\rangle _{b_1}$ with higher probability.
• Figure 5: The circuit running on tianyan176-2 to classify a test point. The $X2M$ is $R_x(-\pi/2)$ gate, $X2P$ is $R_x(\pi/2)$ gate. The parameters of the gates depicted using dashed edged boxes are different for different test points. The parameters of the gates depicted using solid edged boxes are the same because they are used to build the ansatz. The $Q43$ is $a$ register, $Q44$ and $Q49$ make up the $b_1$ register, and the others make up the $b_2$ register.