Non-Hermitian quantum circuits with renormalization after fixed non-unitary gates are equivalent to PostBQP, which equals PP, in the uniform circuit model.
Papadimitriou, Computational Complexity (Addison Wesley Longman, Reading, Massachusetts, 1995)
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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.