Quantum Elastic Network Models and their Application to Graphene

TL;DR

The paper addresses the challenge of atomistic molecular dynamics at macroscopic scales by introducing Quantum Elastic Network Models (QENMs), which map harmonic ENMs onto a quantum evolution framework inspired by a recent exponential-speedup algorithm for coupled oscillators. It provides concrete encodings to load Maxwell–Boltzmann samples, constructs a graphene-specific connectivity oracle, and details how to prepare initial states, simulate the Hamiltonian, and measure observables. The authors demonstrate two practical graphene applications—heat transfer and out-of-plane rippling—and estimate that centimeter-scale graphene could be encoded with roughly 160 logical qubits, highlighting promising space savings and polynomial-time advantages under certain conditions. They also discuss roadblocks to realism, such as anharmonic forces and coupling to baths, and outline future work needed to bridge toward practical quantum MD simulations with defects and dopants.

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.

Figures (11)

• Figure 1: Illustration of a molecule and its corresponding ENM representation Panel (a) shows an illustration of a molecule, while panel (b) highlights the simplification in which atoms or groups of atoms are replaced by nodes connected (up to a desired cutoff distance) via springs.
• Figure 2:
• Figure 3: Illustration of sampling from Boltzmann distribution by sampling from $D=2$ independent Gaussians
• Figure 4: Two-point approximation of the Maxwell-Boltzmann distribution. The probability mass is partitioned exactly at the median velocity to ensure equiprobable buckets ($P_0=P_1=0.5$). The representative velocities $\tilde{v}_0$ and $\tilde{v}_1$ are chosen symmetrically around the mean ($\mu \pm \sigma$) to strictly conserve the system's kinetic energy and momentum moments.
• Figure 5: Circuit for randomized bucket assigment: Given a randomly sampled $\theta=(s,r) \in \{0,1\}^{n+1}$, and an $n$ qubit quantum register $\ket{j}$, the above construction computes $(j\cdot s) \oplus r$, where the dot product is in $\mathbb{F}_2$

Theorems & Definitions (3)

• Lemma 3.1
• proof
• Corollary 3.2