Speaker
Description
This work applies a tensor-network space–time framework based on the Quantized Tensor Train (QTT) representation to the Gross–Pitaevskii equation (GPE), following the matrix-product-state space–time formulation introduced in Ref. [1]. The wavefunction is encoded as a Matrix Product State, while spatial differential operators, trapping potentials, temporal couplings, and nonlinear interaction terms are represented as Matrix Product Operators. By quantizing the spatial and temporal grids into binary tensor dimensions, the approach aims to reduce the storage and computational cost associated with large discretized wavefunctions.
The GPE is formulated as a space–time all-at-once system, in which the complete solution over the spatial and temporal domain is obtained simultaneously rather than through conventional sequential time stepping. The resulting tensor-network systems are solved using DMRG-based alternating optimization, while the nonlinear interaction is treated through self-consistent Picard iterations and relaxation. The implementation is progressively validated using harmonic-oscillator and GPE benchmark problems in one and two spatial dimensions. The framework is then applied to Bose–Einstein-condensate dynamics, including breathing-mode evolution motivated by previous QTT studies of the GPE [2]. These results provide a basis for investigating nonlinear quantum dynamics using compressed space–time tensor-network representations.
References
[1] R. D. Peddinti, S. Pisoni, N. Rapaka, M. K. Riahi, E. Tiunov, and L. Aolita, Quantum-inspired space-time PDE solver and dynamic mode decomposition, arXiv:2510.21767 (2025).
[2] Q.-C. Chen, I.-K. Liu, J.-W. Li, and C.-M. Chung, Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics, arXiv:2507.04279 (2026).