Efficient Simulation of Pre-Born-Oppenheimer Dynamics on a Quantum Computer

TL;DR

This paper introduces a highly efficient quantum algorithm for simulating electron-nuclear dynamics from first principles, significantly reducing computational costs for complex chemical reactions on quantum computers.

Contribution

The work presents a novel quantum algorithm with improved efficiency for simulating pre-Born-Oppenheimer molecular Hamiltonians using real-space grids and optimized arithmetic routines.

Findings

Achieved over an order-of-magnitude cost reduction for the NH3+BF3 reaction.

Demonstrated a Toffoli cost of 8.7×10^9 per femtosecond with 1362 qubits.

Provided foundational quantum primitives for broader quantum simulation applications.

Abstract

In this work, we present a quantum algorithm for direct first-principles simulation of electron-nuclear dynamics on a first-quantized real-space grid. Our algorithm achieves best-in-class efficiency for block-encoding the pre-Born-Oppenheimer molecular Hamiltonian by harnessing the linear scaling of swap networks for implementing the quadratic number of particle interactions, while using a novel alternating sign implementation of the Coulomb interaction that exploits highly optimized arithmetic routines. We benchmark our approach for a series of scientifically and industrially relevant chemical reactions. We demonstrate over an order-of-magnitude reduction in costs compared to previous state-of-the-art for the $\rm NH_3+BF_3$ reaction, achieving a Toffoli cost of $8.7\times10^{9}$ per femtosecond using $1362$ logical qubits (system + ancillas). Our results significantly lower the resources required for fault-tolerant simulations of photochemical reactions, while providing a suite of algorithmic primitives that are expected to serve as foundational building blocks for a broader class of quantum algorithms.