Permanents, Bosons and Linear Optics

TL;DR

This paper explores the complexity of linear quantum optical networks, comparing bosonic and fermionic models to clarify their computational implications and deepen understanding of quantum versus classical simulation capabilities.

Contribution

It introduces two models of bosons in linear optics and compares them to fermionic systems, providing insights into their computational complexity and simulation.

Findings

Bosonic models are complex and relevant for quantum computation.

Fermionic linear optics can be efficiently simulated classically.

Oscillator model offers a deeper analogy for bosonic processes.

Abstract

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.