QFlux: Quantum Circuit Implementations of Molecular Dynamics. Part II - Closed Quantum Systems

Quantum computers offer a powerful platform for simulating real-time molecular and materials dynamics, where coherence, entanglement, and many-body correlations govern processes such as charge transport, tunneling, and spin exchange. Building on the foundations introduced in Part I, this tutorial presents practical algorithms for quantum dynamical simulation on qubit-based hardware using the open-source QFlux framework. We formulate molecular and spin Hamiltonians in the Pauli basis and map their propagators to quantum circuits using parity-based phase constructions and local basis rotations. Expectation values and state overlaps are obtained with the Hadamard test, or by direct measurement of Pauli strings, providing a unified protocol for extracting complex observables and variational quantities. We introduce the Quantum Split-Operator Fourier Transform ( Q-SOFT ), the quantum analog of the classical SOFT method for quantum dynamics simulations, which applies kinetic and potential phase operators in conjugate bases connected by the Quantum Fourier Transform to implement second-order Trotterized evolution. A simulation of proton transfer in an asymmetric double-well potential modeling a DNA base pair reproduces benchmark simulations. We also present a variational time-evolution scheme based on the McLachlan principle, implemented in QFlux’s VarQRTE driver. Applied to a two-spin Heisenberg model, it captures coherent spin exchange with shallow, noise-resilient circuits. Together, these methods establish a reproducible workflow—from Hamiltonian encoding to circuit execution and measurement—bridging classical and quantum simulation and providing a practical toolkit for real-time quantum dynamics on near-term hardware.