  A new paradigm of quantum computing, namely, soft quantum computing, is
proposed for nonclassical computation using real world quantum systems with
naturally occurring environment-induced decoherence and dissipation. As a
specific example of soft quantum computing, we suggest a quantum neural
network, where the neurons connect pairwise via the "controlled Kraus
operations", hoping to pave an easier and more realistic way to quantum
artificial intelligence and even to better understanding certain functioning of
the human brain. Our quantum neuron model mimics as much as possible the
realistic neurons and meanwhile, uses quantum laws for processing information.
The quantum features of the noisy neural network are uncovered by the presence
of quantum discord and by non-commutability of quantum operations. We believe
that our model puts quantum computing into a wider context and inspires the
hope to build a soft quantum computer much earlier than the standard one.
