SFB TRR 352

Talk by Shi Jin
2025-05-08 12:15 (Europe/Berlin) | Room 03.06.011, Boltzmannstr. 3, Garching Forschungszentrum, 85748, Germany
On Thursday, May 08, 2025, at 12:15 pm, Prof. Dr. Shi Jin (Shanghai Jiao Tong University) will give a talk on “Quantum Computation of partial differential equations and related problems” at TUM, Boltzmannstr. 3, 85748 Garching Forschungszentrum, room 03.06.011.
Abstract: Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counterparts, and can lead to technology revolution in the 21st century. Since quantum computers are designed based on quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. The most efficient quantum PDE solver is quantum simulation based on solving the Schrodinger equation. It will be interesting to explore what other problems in scientific computing, such as ODEs, PDEs, and linear algebra that arise in both classical and quantum systems, can be handled by quantum simulation.
We will present a systematic way to develop quantum simulation algorithms for general differential equations. Our basic framework is dimension lifting, that transfers non-autonomous ODEs/PDEs systems to autonomous ones, nonlinear PDEs to linear ones, and linear ones to Schrodinger type PDEs—coined “Schrodingerization”—with uniform evolutions. Our formulation allows both qubit and qumode (continuous-variable) formulations, and their hybridizations, and provides the foundation for analog quantum computing which are easier to realize in the near term.

High-performance local automaton decoders for defect matching in 1D
2025-05-26 14:00 | Room 5608.02.020 (Seminarraum (M11)), Boltzmannstr. 3, Garching b. München, 85748, Germany

Condensing zero range process
2025-05-28 14:00 | University of Augsburg, Room 2004 (L1), Universitätsstraße 14, Augsburg, 86159
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is described by a piecewise linear trajectory in the simplex indexed by the sites. The linear coefficients are determined by the trace process of the underlying random walk on the subset of non-empty sites, and the trajectory reaches an absorbing configuration in finite time. We identify the set of absorbing configurations and characterize the absorbing boundaries.
Joint work with Johel Beltrán, Daniela Cuesta and Milton Jara.

Wasserstein spaces and error control in approximations by neural networks
2025-05-28 14:00 | University of Augsburg, Room 2004 (L1), Universitätsstraße 14, Augsburg, 86159
We explore a connection between a weak topology on spaces of probability measures, a classical combinatorial problem in matching, and numerical schemes for the solution of PDEs by neural networks.
