Distributed Quantum Dynamics Algorithms with Tensor Networks on Hybrid Classical - Quantum Hardware

Quantum nuclear dynamics plays a critical role in understanding chemical, biological, materials, and atmospheric processes such as hydrogen-transfer reactions in biological systems, spectroscopy of water clusters, and reactions of atmospheric species in water. These problems require the simultaneous study of electronic structure and nuclear dynamics. Accurate simulation of such processes is complicated by the need to propagate nuclear wavepackets on multidimensional electronic potentials, where computational cost grows exponentially with the number of nuclear degrees of freedom, making these systems classically intractable.

Quantum computers, which can encode and process quantum states, offer a promising pathway to overcome these limitations. However, in the current NISQ era, deep quantum circuits introduce significant noise and errors. To address this challenge, we develop a distributed hybrid quantum–classical framework that uses tensor networks to reduce circuit depth. By expressing both the time-evolution operator and the nuclear wavepacket in tensor network form, we derive reduced-dimensional effective Hamiltonians that can be simulated in parallel on classical or quantum processors. As a proof of concept, we simulate shared-proton dynamics in a short, strongly hydrogen-bonded system on IonQ’s 11-qubit Harmony quantum processor.