Graphical calculus for Gaussian pure states
By Nicolas C. Menicucci, Steven T. Flammia, Peter van Loock. 2010
160 citations recorded by the source corpus.
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CVmore » one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.« less
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/de5bd05c1ad029a48c26cb340b0662db3ef21263
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. (2013, background): “…when considering magic-state distillation, as discussed in Appendix B.) Since Gaussian unitary evolution corresponds to linear—and specifically, symplectic—evolution on phase space in the Heisenberg picture [20], we can model this as where S is a symplectic matrix representing the evolution.”