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Entanglement dynamics in nonunitary quantum systems have been found to exhibit novel nonequilibrium quantum phase transitions and have attracted tremendous attention with connections to various aspects of quantum information theory. This work establishes, for systems of noninteracting fermions, an exact three-way correspondence between (i) nonunitary (as well as unitary) quantum circuits dynamics in d spatial dimensions; (ii) (d+1) -dimensional Gaussian tensor networks, and (iii) fermion systems in (d+1) spatial dimensions subject to unitary evolution with static Hamiltonians. Through this correspondence, d-dimensional random quantum circuits are connected with the classic subject area of Anderson localization in (d+1) spatial dimensions and consequently follow the ``tenfold way'' Altland-Zirnbauer classification. Selected examples of quantum circuits exhibiting entanglement phases and criticalities are used to illustrate these general principles.
Jian et al. (Fri,) studied this question.