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The reduction of the volume and footprint requirements of membrane bioreactors (MBR)s is constrained by the maximum amount of biomass that can be accommodated in the aerobic basin. However, the biomass concentration is mainly limited by the extremely low oxygen transfer efficiency (OTE) experienced by conventional aeration bubble diffuser systems at mixed liquor total suspended solids (MLSS) concentrations higher than 20 g L-1. Another potential limitation for the operation of MBRs at such high MLSS concentrations is the reduction on the membrane permeability due to excessive fouling..., BT/Environmental Biotechnology

Simulating general quantum processes that describe realistic interactions of quantum systems following a non-unitary evolution is challenging for conventional quantum computers that directly implement unitary gates. We analyze complexities for promising methods such as the Sz.-Nagy dilation and linear combination of unitaries that can simulate open systems by the probabilistic realization of non-unitary operators, requiring multiple calls to both the encoding and state preparation oracles. We propose a quantum two-unitary decomposition (TUD) algorithm to decompose a d-dimensional operator A with non-zero singular values as A = (U1 + U2)/2 using the quantum singular value transformation algorithm, avoiding classically expensive singular value decomposition (SVD) with an O(d3) overhead in time. The two unitaries can be deterministically implemented, thus requiring only a single call to the state preparation oracle for each. The calls to the encoding oracle can also be reduced significantly at the expense of an acceptable error in measurements. Since the TUD method can be used to implement non-unitary operators as only two unitaries, it also has potential applications in linear algebra and quantum machine learning., BT/Environmental Biotechnology