Quantum kernels for classifying dynamical singularities in a multiqubit system

TL;DR

This paper introduces a quantum support vector machine approach utilizing quantum kernels to classify dynamical singularities in multiqubit systems, demonstrating efficiency and adaptability in complex quantum dynamical scenarios.

Contribution

It presents a novel QSVM method with physically inspired quantum kernels for classifying dynamical singularities in multiqubit quantum systems.

Findings

Quantum kernels effectively classify dynamical singularities.

The approach adapts to time-dependent fields and larger qubit systems.

Quantum kernels outperform classical methods in this task.

Abstract

Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine (QSVM) algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using $N$ long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.