Abstract:
Simulating the dynamics of many-body quantum systems is one of the foremost challenges in modern-day physics. In this talk I will demonstrate how structured tensor networks can be used to meet this challenge. I will begin by introducing a graphical approach to working with tensor networks and show how it allows the seamless implementation of message-passing-based contraction schemes for their efficient contraction and subsequent optimization.
I will then focus on several recent quantum simulation experiments and show how a tensor-network ansatz which reflects the underlying lattice geometry can be used to efficiently model these systems at scale – despite claims to the contrary. The most recent of these involves the quantum annealing of two and three-dimensional lattices of spins [1]. For finite-time quenches, we can perform accurate simulations which scale only linearly in the number of qubits and capture the universal physics present via extraction of the corresponding Kibble-Zurek exponent [2]. I will conclude by discussing the future prospects of a structured tensor-network based approach to quantum simulation.
[1] A. D. King et al, Beyond-classical computation in quantum simulation, Science, 10.1126/science.ado6285 (2025)
[2] J. Tindall et al, Dynamics of disordered quantum systems with two- and three-dimensional tensor networks arXiv:2503.0569 (2025)