Distributed Quantum Computing Algorithms for Quantum Dynamics using Tensor Networks

Quantum nuclear dynamics plays a vital role in biological, materials, and atmospheric systems. For example, the rate-limiting step in fatty acid oxidation by soybean lipoxygenase-1 involves hydrogen transfer influenced by quantum tunneling. Similarly, hydrogen transfer governs key processes in nitrogen fixation and artificial photosynthesis. However, simulating such dynamics is computationally demanding, as the cost grows exponentially with the number of nuclear degrees of freedom. This challenge, often called the curse of dimensionality, is compounded by the need to compute accurate potential energy surfaces through electronic structure calculations over many nuclear configurations.

Quantum computers offer a way forward by naturally encoding quantum states in exponentially large Hilbert spaces. Yet current NISQ devices are limited by noise, shallow qubit counts, and gate errors. To overcome this, hybrid quantum–classical strategies are essential.

In this work, we present a tensor-network-based framework that decomposes multidimensional wavefunctions and unitary operators into parallel one-dimensional components. Each reduced system is simulated independently on quantum hardware. As a proof of concept, we implement shared-proton dynamics on a two-dimensional potential surface using IonQ’s trapped-ion processor.