The Series Product and Its Application to Quantum Feedforward and Feedback Networks

By John Edward Gough, Matthew R. James. IEEE Transactions on Automatic Control, 2007

412 citations recorded by the source corpus.

The purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks. These methods build on and generalize existing methods for series (or cascade) connections by allowing for more general interfaces, and by introducing an efficient algebraic tool, the series product. We also introduce another product, which we call the concatenation product, that is useful for assembling and representing systems without necessarily having connections. We show how the concatenation and series products can be used to describe feedforward and feedback networks. A selection of examples from the quantum control literature are analyzed to illustrate the utility of our network modeling methodology.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/86e5a3dd13c41ecf520878f53659f40b5ac76611

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Citations in the corpus

Quantum feedback: theory, experiments, and applications (2014, methodology): “its G 1 = (S 1;L 1;H 1) and G 2 = (S 2;L 2;H 2), the unit that describes both these units with no connections between them is G 1 G 2 = S 1 0 0 S 2 ! ; L 1 L 2 ! ;H 1 + H 2 ! : (3.15) Gough and James [85] refer to this rule as the concatenation product. The second rule for combing circuit elements t”
Squeezing Components in Linear Quantum Feedback Networks (2009, methodology): “In what follows we generalize this type of representation to our class of LQFNs (see also [9], [15]).”
Concepts of quantum non-Markovianity: A hierarchy (2017, methodology): “Indeed, we even allow Hamiltonians that only exist as a singular limit of regular models [26], as required to describe ‘quantum white noise’ [27, 28].”
Quantum control theory and applications: A survey (2009, neutral): “ystems with non-Markovian dynamics [156], [157], [173]? What is the capability of feedback to deal with uncertainties in quantum systems? How do we synthesize complex quantum feedback network systems [174]? (3) Robust control of quantum systems. It is inevitable that quantum systems are subject to m”