Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

TL;DR

This paper introduces a quantum algorithm for filtering any energy eigenstate in two-dimensional materials, leveraging quantum neural networks and demonstrating its effectiveness on real quantum hardware and simulators.

Contribution

It presents a novel quantum eigenstate filtering algorithm that works beyond ground states, using a shallow neural network and quantum sampling, applicable to complex 2D materials.

Findings

Successfully implemented on IBM-Q devices with good agreement to classical methods.

Resource requirements are strictly quadratic, making it efficient.

Applied to transition metal dichalcogenides, revealing new insights into their electronic structure.

Abstract

Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However the discussion in all these recipes focus specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or on a predefined choice of the user. The work horse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs- Boltzmann distribution using a quantum circuit and the phase information obtained classically from the non-linear activation of a separate set of neurons. We show that the resource requirements of our algorithm is strictly quadratic. To demonstrate its efficacy, we use state-filtration in monolayer transition metal-dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring band-structures of exquisite materials to usual electronic structure methods or machine learning techniques which are implementable solely on a classical computer