Quantum Elastic Network Models and their Application to Graphene

TL;DR

This paper introduces Quantum Elastic Network Models (QENMs) that leverage quantum algorithms to efficiently simulate large-scale materials like graphene, overcoming classical computational limitations and enabling practical atomistic simulations.

Contribution

The paper presents a novel quantum algorithm-based approach for simulating elastic network models, specifically applying it to graphene to achieve exponential efficiency improvements.

Findings

Quantum algorithms enable efficient simulation of large-scale graphene sheets.

Simulation complexity is significantly reduced, requiring only around 160 logical qubits.

Potential to simulate centimeter-scale materials with classical resources would be infeasible.

Abstract

Molecular dynamics simulations are a central computational methodology in materials design for relating atomic composition to mechanical properties. However, simulating materials with atomic-level resolution on a macroscopic scale is infeasible on current classical hardware, even when using the simplest elastic network models (ENMs) that represent molecular vibrations as a network of coupled oscillators. To address this issue, we introduce Quantum Elastic Network Models (QENMs) and utilize the quantum algorithm of Babbush et al. (PRX, 2023), which offers an exponential advantage when simulating systems of coupled oscillators under some specific conditions and assumptions. Here, we demonstrate how our method enables the efficient simulation of planar materials. As an example, we apply our algorithm to the task of simulating a 2D graphene sheet. We analyze the exact complexity for initial-state preparation, Hamiltonian simulation, and measurement of this material, and provide two real-world applications: heat transfer and the out-of-plane rippling effect. We estimate that an atomistic simulation of a graphene sheet on the centimeter scale, classically requiring hundreds of petabytes of memory and prohibitive runtimes, could be encoded and simulated with as few as $\sim 160$ logical qubits.