From Non-Commutative Optimal Transport to Limitations of Quantum Simulations

This lecture presents Peixue Wu's research on "From non-commutative optimal transport to limitations of quantum simulations" delivered at IPAM's Dynamics of Density Operators Workshop. Recorded on May 1, 2025, the 44-minute talk introduces a framework for quantifying minimal resources required for quantum simulations based on the Lipschitz dual picture of non-commutative Wasserstein metric. Explore how this approach establishes rigorous lower bounds on circuit depth and volume necessary to implement quantum operations and prepare quantum states. Discover findings showing that simulating a quantum channel with Lipschitz constant scaling linearly with system size requires circuit depth lower bounded by Ω(logn), and learn why Lindbladian-based algorithms for Gibbs or ground state preparation require circuit volume scaling at least linearly with system size, even in systems engineered for rapid mixing.