El grupo de Termodinámica y Computación Cuántica les invita al siguiente seminario Fecha: Viernes 27/9/2024 Hora: 11:00 am Lugar: Laboratorio de Fïsica Computacional, Dept de Electromagnetismo y Física de al Materia, Planta Baja, Facultad de Ciencias (junto al péndulo gigante) Ponente: Paula García-Molina (Instituto de Física Fundamental - CSIC) Titulo: Pseudospectral method for solving PDEs using Matrix Product States (arXiv:2409.02916) Resumen: This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schrödinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating Functionals (HDAF) to MPS, a highly accurate pseudospectral method for approximating functions of derivatives. Integrating HDAF into an MPS finite precision algebra, we test four types of quantum-inspired algorithms for time evolution: explicit Runge-Kutta methods, Crank-Nicolson method, explicitly restarted Arnoli iteration and split-step. The benchmark problem is the expansion of a particle in a quantum quench, characterized by a rapid increase in space requirements, where HDAF surpasses traditional finite difference methods in accuracy with a comparable cost. Moreover, the efficient HDAF approximation to the free propagator avoids the need for Fourier transforms in split-step methods, significantly enhancing their performance with an improved balance in cost and accuracy. Both approaches exhibit similar error scaling and run times compared to FFT vector methods; however, MPS offer an exponential advantage in memory, overcoming vector limitations to enable larger discretizations and expansions. Finally, the MPS HDAF split-step method successfully reproduces the physical behavior of a particle expansion in a double-well potential, demonstrating viability for actual research scenarios. El seminario es accesible para los estudiantes de grado, a los que recomendamos encarecidamente que asistan. Para aquellos que no puedan asistir, también hemos configurado una reunión de Google donde el seminario se transmitirá en vivo. https://meet.google.com/csb-snng-bmu También os recordamos a todos la página web del Seminario de Grupos, https://ic1.ugr.es/eventos/wp/qjc/ donde se publicarán anuncios pasados, presentes y futuros. Nos vemos a todos allí DJM ________________________________________________________________________________ Dear all The Quantum Thermodynamics and Computation group cordially invites you to the following seminar Date: Friday 27/9/2024 Time: 11:00 am Location: Computational Physics Laboratory, Department of Electromagnetism and Condensed Mater, Ground Floor, Faculty of Science (next to the giant pendulum) Speaker: Paula García-Molina (Instituto de Física Fundamental - CSIC) Title: Pseudospectral method for solving PDEs using Matrix Product States (arXiv:2409.02916) Abstract: This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schrödinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating Functionals (HDAF) to MPS, a highly accurate pseudospectral method for approximating functions of derivatives. Integrating HDAF into an MPS finite precision algebra, we test four types of quantum-inspired algorithms for time evolution: explicit Runge-Kutta methods, Crank-Nicolson method, explicitly restarted Arnoli iteration and split-step. The benchmark problem is the expansion of a particle in a quantum quench, characterized by a rapid increase in space requirements, where HDAF surpasses traditional finite difference methods in accuracy with a comparable cost. Moreover, the efficient HDAF approximation to the free propagator avoids the need for Fourier transforms in split-step methods, significantly enhancing their performance with an improved balance in cost and accuracy. Both approaches exhibit similar error scaling and run times compared to FFT vector methods; however, MPS offer an exponential advantage in memory, overcoming vector limitations to enable larger discretizations and expansions. Finally, the MPS HDAF split-step method successfully reproduces the physical behavior of a particle expansion in a double-well potential, demonstrating viability for actual research scenarios. The seminar is accessible to undergraduate students, whom we strongly encourage to attend. For those of you unable to attend the seminar, we have set-up the following google meet link for the upcoming seminar. https://meet.google.com/csb-snng-bmu We would also like to bring to your attention the groups seminar page https://ic1.ugr.es/eventos/wp/qjc/ where you can find relevant material and information about past, present, and future seminars. See you all there DJM. --------------------------------------------------------------------------------- Daniel Manzano Quantum Thermodynamics and Quantum Computation Group University of Granada Facultad de Ciencias, Av. Fuentenueva s/n Granada 18071, Spain Phone: +34 958241000 Ext: 20569 https://ic1.ugr.es/members/dmanzano/