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

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 1 arXiv:2105.09488v1 [physics.chem-ph] 20 May 2021 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.

Implementation of Quantum Machine Learning for Electronic Structure Calculations of Periodic Systems on Quantum Computing Devices

“…The current quantum machine learning method could calculate only on the ground state energy of the periodic systems, i.e., the valence band, an extension needed to treat systems with multiple valence bands or to procure higher order energy bands. This can be done by sampling the orthogonal subspace of the previously computed valence band . Also, to calculate the transition matrix elements, the valence and conduction Bloch wavevectors should be obtained.…”

Variational Quantum Circuits to Prepare Low Energy Symmetry States

“…Hybrid variational quantum algorithms have been extensively studied in the context of solving unconstrained [14][15][16][17] and even constrained optimization problems [11,18,19]. The primary workhorse of such methods revolve around iteratively minimizing a cost function through a usual gradient-based optimization scheme to tweak the parameters of the quantum circuit subsequently.…”

Variational quantum support vector machine based on $$\Gamma $$ matrix expansion and variational universal-quantum-state generator

“…In addition, an ansatz based on the restricted Boltzmann machine requires quantum gates, while a unitary-coupled cluster ansatz requires quantum gates 16 , 34 .…”