Non-Hermitian quantum circuits with renormalization after fixed non-unitary gates are equivalent to PostBQP, which equals PP, in the uniform circuit model.
In fact, many have outputs that can be reproduced by algorithms in BPP or even P
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Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
Non-Hermitian quantum circuits with renormalization after fixed non-unitary gates are equivalent to PostBQP, which equals PP, in the uniform circuit model.