Coarse-grained spectral projection (CGSP): A scalable and parallelizable deep learning-based approach to quantum unitary dynamics

We propose the coarse-grained spectral projection method (CGSP), a deep learning approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show CGSP can extract spectral components of many-body quantum states systematically with highly entangled neural network quantum ansatz. CGSP exploits fully the linear unitary nature of the quantum dynamics, and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Practical aspects such as naturally parallelized implementations on modern deep learning infrastructures are also discussed. Preliminary numerical experiments are carried out to guide future development of CGSP.