Permanents, Bosons and Linear Optics

Particular complexity of linear quantum optical networks is deserved recently certain attention due to possible implications for theory of quantum computation. Two relevant models of bosons are discussed in presented work. Symmetric product of Hilbert spaces produces rather abstract model. The second one is obtained by quantization of harmonic oscillator. In contrast to considered bosonic processes, so-called "fermionic linear optics" is effectively simulated on classical computer. The comparison of bosonic and fermionic case clarifies the controversy and the more elaborated oscillator model provides a deeper analogy.