  Non-Markovianity, the intricate dependence of an open quantum system on its
temporal evolution history, holds tremendous implications across various
scientific disciplines. However, accurately characterizing the complex
non-Markovian effects has posed a formidable challenge for numerical
simulations. Despite the promising potential of emerging quantum computing
technologies, the pursuit of a universal theory enabling practical
implementation of quantum computation algorithms remains ongoing. In this
paper, we present a major advancement in bridging this critical gap: the
development of dissipaton-embedded quantum master equation in second
quantization (DQME-SQ). The DQME-SQ is an exact and compact theory, and its
unique capabilities are demonstrated through digital quantum simulations of
non-Markovian dissipative dynamics in both bosonic and fermionic environments.
Our new theoretical developments pave the way for efficient exploration of
complex open quantum systems.
