Quantum Algorithms for Cosmological Simulations

Numerical simulations are a cornerstone of modern cosmology, providing a direct bridge between theoretical models and astronomical observations. They trace the evolution of dark matter (DM) and baryonic structures from the early Universe to the complex large-scale structures observed today. Achieving sufficient resolution while generating the large ensembles necessary to explore parameter space presents substantial computational challenges. Quantum computing offers a promising avenue to address these demands. Building on a correspondence between the Schrödinger-Poisson (SP) equation and the Vlasov-Poisson (VP) equation, which governs DM evolution, we first verified that SP can reproduce VP dynamics for cold DM when an appropriate coarse-graining is applied. To this end, we developed four classical numerical solvers—two direct VP integrations, one particle-mesh (PM) solver, and one spectral SP solver—and tested them in representative one- and two-dimensional scenarios. The results confirmed that coarse-grained SP captures the essential features of VP evolution, establishing a solid foundation for subsequent quantum simulations. Leveraging this result, we then developed variational quantum algorithms for real-time SP evolution on near-term devices. Resource requirements, circuit depth, and accuracy were analyzed, and alternative linearization strategies, including Carleman embedding, were explored. These studies highlighted intrinsic limitations of direct quantum simulations, particularly due to nonlinearities and scaling constraints. As a complementary approach, we introduced QFRANS, a quantum algorithm for the Fixed-Radius Neighbor Search (FRANS), a key bottleneck in classical N-body and hydrodynamical simulations. Although current hardware limits practical deployment, this algorithm illustrates how quantum acceleration can strategically target computationally intensive tasks, offering a viable route for near-term applications. Overall, this work establishes a framework for integrating quantum computing into cosmological simulations. While fully quantum simulations remain challenging, hybrid strategies that focus on critical computational bottlenecks represent the most practical path forward, opening new opportunities for high-precision, large-scale modeling of the Universe.