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Cayley graphs and analysis of quantum cost for reversible circuit synthesis [article]

A. C. Ribeiro, C. M. H. de Figueiredo, F. L. Marquezino, L. A. B. Kowada
2012 arXiv   pre-print
We propose the theory of Cayley graphs as a framework to analyse gate counts and quantum costs resulting from reversible circuit synthesis.  ...  Those two Cayley graphs have degree n2^n-1 and order 2^n!. Maslov, Dueck and Miller proposed a reversible circuit synthesis that we model by the Cayley graph I_n.  ...  ACKNOWLEDGEMENTS The authors thank Luís Cunha and Roberto Sampaio for helpful discussions.  ... 
arXiv:1209.3275v1 fatcat:teej2elejbghtdabdfjkgykdiq

Shorter quantum circuits [article]

Vadym Kliuchnikov, Kristin Lauter, Romy Minko, Adam Paetznick, Christophe Petit
2022 arXiv   pre-print
We provide a number of further applications of the magnitude approximation problems, as well as improved algorithms for exact synthesis, in the Appendices.  ...  two in approximation costs.  ...  In [CLG09] , Charles, Goren and Lauter (CGL) proposed a Cayley hash function based on LPS graphs. LPS graphs were introduced by Lubotsky, Phillips and Sarnak in [LPS88] .  ... 
arXiv:2203.10064v1 fatcat:awisa2gi2jcqzfnymvlixrr37q

Space-efficient Quantization Method for Reversible Markov Chains [article]

Chen-Fu Chiang, Anirban Chowdhury, Pawel Wocjan
2022 arXiv   pre-print
In a seminal paper, Szegedy showed how to construct a quantum walk W(P) for any reversible Markov chain P such that its eigenvector with eigenphase 0 is a quantum sample of the limiting distribution of  ...  We show that it is possible to avoid this doubling of state space for certain Markov chains that employ a symmetric proposal probability and a subsequent accept/reject probability to sample from the Gibbs  ...  For instance, this is the case if we consider random walks on Cayley graphs with generating sets that are closed under taking inverses (this condition is necessary for the graph to be undirected).  ... 
arXiv:2206.06886v1 fatcat:2jkizc5myrdr5lp22mnoxveuta

Reference list of indexed articles

2000 Discrete Applied Mathematics  
Mezey, Embedding and characterization of quantum chemical reaction graphs on twodimensional orientable surfaces 19 (1988) 205-214 5 12. E.C. Hass and P.J.  ...  Finkelstein, New methods for using Cayley graphs in interconnection networks 37/38 (1992) 95-l 18 908. S.K. Das, J. Ghosh and N.  ... 
doi:10.1016/s0166-218x(00)00209-2 fatcat:l53yxlj45ffdrdecl3uah2gj3y

Cascading Network Failure in Power Grid Blackouts [chapter]

Dr.Ian Dobson
2014 Encyclopedia of Systems and Control  
The emerging risk analysis, simulation, and modeling of cascading blackouts are briefly surveyed, and key references are suggested.  ...  Cascading failure consists of complicated sequences of dependent failures and can cause large blackouts.  ...  System analysis and synthesis are concerned with the investigation of properties of the underlying synthesis model and in the determination of a control system which fulfills basic requirements for the  ... 
doi:10.1007/978-1-4471-5102-9_264-1 fatcat:slhzrvsilfephprfzlkkccbyma

Cooperative Manipulators [chapter]

Fabrizio Caccavale
2015 Encyclopedia of Systems and Control  
The emerging risk analysis, simulation, and modeling of cascading blackouts are briefly surveyed, and key references are suggested.  ...  Cascading failure consists of complicated sequences of dependent failures and can cause large blackouts.  ...  System analysis and synthesis are concerned with the investigation of properties of the underlying synthesis model and in the determination of a control system which fulfills basic requirements for the  ... 
doi:10.1007/978-1-4471-5058-9_175 fatcat:gzo7xen4ynezhesyrpsldzj5bi

Quantum homeopathy works: Efficient unitary designs with a system-size independent number of non-Clifford gates [article]

Jonas Haferkamp, Felipe Montealegre-Mora, Markus Heinrich, Jens Eisert, David Gross, Ingo Roth
2020 arXiv   pre-print
Many quantum information protocols require the implementation of random unitaries.  ...  Our proofs exploit a recently developed variant of Schur-Weyl duality for the Clifford group, as well as bounds on restricted spectral gaps of averaging operators.  ...  Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy -Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 -390534769  ... 
arXiv:2002.09524v2 fatcat:egqbxjtxszb77fgseqzusv3sny

Subject Index to Volumes 1–75

2001 Information Processing Letters  
computation, 1655 size of a drawing, 3666 description, 663 domains, 1080, 1235 linear circuits, 4088 logic circuits, 751 projections, 762 resolution proofs, 1925 size of the description of a  ...  , 2198 natural language, 1059 syntax of atoms and terms, 847 natural languages, 3162 programming languages, 1331, 1988 set expressions, 3827 syntax rules, 1331 tree, 1311, 1318, 2519 synthesis  ...  , 1221 , 1288 , 1822 , 3661 planar graphs, 2058 , 3612 simple graph, 668 tree, 3158 unequal costs, 3327 unfailing completion procedure, 2202 unfair, 1158 P and V operations, 1158 unfairness, 575 unfold  ... 
doi:10.1016/s0020-0190(01)00175-2 fatcat:5y67tfm6yfbblakrus5nnhs73e

Cellular Automata: Reversibility, Semi-reversibility and Randomness [article]

Kamalika Bhattacharjee
2019 arXiv   pre-print
To decide reversibility of a finite CA, we need to know both the rule and the CA size. However, for infinite CAs, reversibility is decided based on the local rule only.  ...  To do so, reversibility of CAs is redefined and the notion of semi-reversible CAs is introduced.  ...  There are many interesting results regarding reversibility of 1-dimensional CAs, over a given local map R, for the first three cases: Theorem 4.1 : The following statements hold for 1-dimensional infinite  ... 
arXiv:1911.03609v1 fatcat:522xu4usonfdbguuckurl4eeqi

The golden rule of complementary feedback

Jeffrey M. Dambacher, Philippe A. Rossignol
2001 ACM SIGSAM Bulletin  
This work demonstrates the occurrence of the Fibonacci sequence in the qualitative analysis of Lotka-Volterra dynamical systems.  ...  The largest eigenvalue of this matrix equals Φ exactly, and is the exponentiated growth rate (r) of the  ...  It is our hope that the general observations presented in the above examples may lead to a more formal analysis by matrix and graph theoreticians.  ... 
doi:10.1145/509520.509522 fatcat:yruhmy5wpfejblcqzn6fkbcsty

This Week's Finds in Mathematical Physics (1-50) [article]

John C. Baez
2022 arXiv   pre-print
These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of n-categories to these subjects.  ...  These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993 to March 12, 1995.  ...  The gauge-invariant operators and hamiltonian are realized in a Hilbert space of open path and loop functionals.  ... 
arXiv:2101.04168v3 fatcat:kh5eurusrjevbkttpuq24p3s4q

Distance geometry and data science

Leo Liberti
2020 TOP - An Official Journal of the Spanish Society of Statistics and Operations Research  
In this survey, we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming.  ...  We discuss applications, solution methods, dimensional reduction techniques, and some of their limits.  ...  Salazar, the Editor-in-Chief of TOP, for inviting me to write this survey.  ... 
doi:10.1007/s11750-020-00563-0 fatcat:xh3xjiir6nbdpnspyipehcayu4

Multiscale Structure in Eco-Evolutionary Dynamics [article]

Blake C. Stacey
2015 arXiv   pre-print
For complex systems, "more is different," and I address this from several perspectives.  ...  I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or  ...  The logic we used to findf (0) ,f (1) andf (2) in terms of expectation values works just as well on the k = 3 Cayley tree graph.  ... 
arXiv:1509.02958v1 fatcat:pr2t7t3fxbej7asibkvjgareja

SO(8) supergravity and the magic of machine learning

Iulia M. Comsa, Moritz Firsching, Thomas Fischbacher
2019 Journal of High Energy Physics  
embedding into SO(8) and minimal polynomials for the cosmological constant.  ...  with SO(3) residual symmetry, one new potentially stabilizable non-supersymmetric solution, and examples for "Galois conjugate pairs" of solutions, i.e. solution-pairs that share the same gauge group  ...  T.F. would like to thank Hermann Nicolai and the Albert Einstein Institute in Potsdam for hospitality and useful discussions during the final phase of this project, and also Krzysztof Pilch, Nikolay Bobev  ... 
doi:10.1007/jhep08(2019)057 fatcat:zybuw7pwkzcp5gubgicld3zazq

Distance Geometry and Data Science [article]

Leo Liberti
2019 arXiv   pre-print
In this survey we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming.  ...  We discuss applications, solution methods, dimensional reduction techniques and some of their limits.  ...  Salazar, the Editor-in-Chief of TOP, for inviting me to write this survey.  ... 
arXiv:1909.08544v1 fatcat:5m6n4lozsra6fbo27gqymi2fte
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