Permanents in linear optical networks
By S. Scheel. 2004
149 citations recorded by the source corpus.
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to the computation of permanents. An implication of this remarkable fact is that all calculations that are based on evaluating matrix elements are generically computationally hard. Moreover, quantum mechanics provides simpler derivations of certain matrix analysis results which we exemplify by showing that the permanent of any unitary matrix takes its values across the unit disk in the complex plane.
Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/6fbd9411c100c18297699fa51095b67e17722ec1
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In Atomic and Molecular Physics, and Optics
In Electrical and Electronic Engineering
Citations in the corpus
- Sampling of partially distinguishable bosons and the relation to the multidimensional permanent (2014, background): “An outstanding example for a fruitful interface between physics and computer science is Boson-Sampling [2], the simulation of many indistinguishable bosons that scatter through a randomly chosen linear network with many more modes than particles: As a physical problem [3], it is implemented straight”
- The computational complexity of linear optics (2010, background): “Building on earlier work [14, 15, 22, 27, 36], we define and study a formal model of quantum computation with noninteracting bosons.”
- Boson Sampling on a Photonic Chip (2012, background): “1 in the main text [34].”