Dear colleagues,
We are pleased to announce the next online seminar on QOART (Quantum optics and related topics)!
Title of the talk: Solving quantum dynamics in continuous variables: tensor-train encoding of wavefunctions and the Schrödinger equation as a PDE
Speaker: E.S. Tiunov
Abstract:
Many quantum systems, such as light modes described by quadrature coordinates, have wavefunctions on a continuous domain. Simulating them requires a fine grid, and the number of grid points grows exponentially with the number of modes. We encode these wavefunctions as tensor trains (TTs), in which each grid index is written in binary and the resulting chain of small arrays stores smooth functions compactly. The position and derivative operators in the Hamiltonian are represented as matrix product operators (MPOs), which act directly on the same chain. With both the state and the operator in TT form, the time-dependent Schrödinger equation becomes a PDE solved entirely in compressed form. Time is advanced with implicit Euler, where each step is a linear system solved by local sweeps in TT format. We study how accuracy and cost depend on grid resolution, time step, and maximum bond dimension, and we benchmark against exact diagonalization where it is feasible. As an application, we explore degenerate spontaneous parametric down-conversion in the quadrature representation, where one pump photon converts into two signal photons. Fock-basis simulation becomes infeasible at high pump amplitude, and the TT approach addresses that regime.
Date and Time: 23 October 2026, 14:30 PM (Moscow Time)
Duration: 90–120 minutes
Language: The presentation will be delivered in English.
Link to join the seminar: https://mian.ktalk.ru/cyi5u831v1cs?pinCode=6468
QOART Seminar: https://sites.google.com/view/qoart/seminar
Best regards,
Ranjit
+7 909 680 67 87
https://www.mathnet.ru/eng/person86793
QOART Telegram Channel: https://t.me/+i6rnhM_Wp1YwY2Ji
Optical ‘Cat-like’ State: https://www.mathnet.ru/eng/present47506
QOART 2026 Conference: https://sites.google.com/view/qoart/2026
QOART Seminar: https://sites.google.com/view/qoart/seminar
