82 research outputs found
Visitor Notes: Jacob Biamonte − Categorical Models of Quantum Information in the Simulation of Many−Body Systems
No full textCQT attracts both long and short term visitors from all over the world. Jacob Biamonte, a Research Fellow at the University of Oxford and Lecturer in Physics at St Peter's College, explains the results of his two collaborative visits with several members of CQT staff, including Stephen Clark. Their work involved using higher mathematics to create a new theory of tensor network states and has numerous practical applications in the simulation of physical systems
Categorical Tensor Network States
No full textWe examine the use of the mathematics of category theory in the description of quantum states by tensor networks. This approach enables the development of a categorical framework allowing a solution to the quantum decomposition problem. Specifically, given an n-body quantum state ψ, we present a general method to factor ψ into a tensor network. Moreover, this decomposition of ψ uses building blocks defined mathematically in terms of purely diagrammatic laws. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states. Blogs about this paper: (i) http://golem.ph.utexas.edu/category/2010/09/bimonoids_from_biproducts.html (ii) http://johncarlosbaez.wordpress.com/2010/09/29/jacob-biamonte-on-tensor-networks/ Talks about this paper: (i) http://new.iqc.ca/news-events/calendar/generated/jacob-biamonte-2010-12-2 (IQC, Institute for Quantum Computing University of Waterloo, Canada) Link to arXiv version: * http://arxiv.org/abs/1012.053
Spectral Entropies as Information-Theoretic Tools for Complex Network Comparison
No full textAny physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Rényi q entropy, generalized Kullback-Leibler and Jensen-Shannon divergences, the latter allowing us to define a natural distance measure between complex networks. First, we show that by minimizing the Kullback-Leibler divergence between an observed network and a parametric network model, inference of model parameter(s) by means of maximum-likelihood estimation can be achieved and model selection can be performed with appropriate information criteria. Second, we show that the information-theoretic metric quantifies the distance between pairs of networks and we can use it, for instance, to cluster the layers of a multilayer system. By applying this framework to networks corresponding to sites of the human microbiome, we perform hierarchical cluster analysis and recover with high accuracy existing community-based associations. Our results imply that spectral-based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory
Ground State Spin Calculus
No full textWe present an intuitive compositional theory from which one is able to predict and also to control the ground state manifold (and higher energy excitations) of interacting spin systems governed by variants of tunable Ising models, hence giving precise control over the apriori additive structure of Hamiltonian composition. This compositional theory is given in terms of string diagrams: these results were made possible by mapping a variant of the Boolean F2-calculus onto spins and synthesizing modern ideas appearing in Category Theory, Coalgebras, Classical Network Theory and Graphical Calculus. Specifically, we present an algebraic method which allows one to explicitly engineer several energy levels including the low-energy subspace of interacting spin systems. We call this new framework: Ground State Spin Calculus, and in the first instance, the theory requires interactions of up to third order (3- body). By introducing ancillary qubits, we present a novel approach allowing k-body interactions to be captured exactly using only two-body Hamiltonians [Biamonte, Phys. Rev. A 77(5), 052331 (2008)]. Our reduction method has no dependence on perturbation theory or the associated large spectral gap and allows for problem instance solutions to be embedded into the ground energy state of Ising spin systems. This could have important applications for future technology as adiabatic quantum evolution might be used to place such a computational system into it’s ground state
Ground State Spin Calculus
No full textWe present an intuitive compositional theory from which one is able to predict and also to control the ground state manifold (and higher energy excitations) of interacting spin systems governed by variants of tunable Ising models, hence giving precise control over the apriori additive structure of Hamiltonian composition. This compositional theory is given in terms of string diagrams: these results were made possible by mapping a variant of the Boolean F2-calculus onto spins and synthesizing modern ideas appearing in Category Theory, Coalgebras, Classical Network Theory and Graphical Calculus. Specifically, we present an algebraic method which allows one to explicitly engineer several energy levels including the low-energy subspace of interacting spin systems. We call this new framework: Ground State Spin Calculus, and in the first instance, the theory requires interactions of up to third order (3- body). By introducing ancillary qubits, we present a novel approach allowing k-body interactions to be captured exactly using only two-body Hamiltonians [Biamonte, Phys. Rev. A 77(5), 052331 (2008)]. Our reduction method has no dependence on perturbation theory or the associated large spectral gap and allows for problem instance solutions to be embedded into the ground energy state of Ising spin systems. This could have important applications for future technology as adiabatic quantum evolution might be used to place such a computational system into it’s ground state
Complex systems in the spotlight: next steps after the 2021 Nobel Prize in Physics
No full textThe 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems.The authors acknowledge their funding sources, including: Royal Society (IEC\NSFC\191147 (G Bianconi); NSF Grants CCF-1839232, PHY-1806372, DGE-2125899, PHY-2210566 (L.C.); NRF, Grant No. NRF-2014R1A3A2069005 and the KENTECH Research Grant (KRG2021-01-007) (B Kahng); EU H2020 ICT48 project ‘Humane AI Net’ under Contract #952026 and EU Horizon 2020—ERC Synergy Grant 810115 ‘Dynasnet’ (J Kertesz); ICREA Academia Award, Catalan Institution for Research and Advanced Studies (C Masoller); National Science Foundation Award No. DMS-1647351 (A E Motter); Slovenian Research Agency (Grant Nos. P1-0403 and J1-2457) (M Perc); PID2019-106811GB-C31 from MCIN/AEI/10.13039/501100011033 (M Sales Pardo); PACSS (RTI2018-093732-B-C21) and MDM-2017-0711 from MCIN/AEI/10.13039/501100011033, Spain (M San Miguel). FR acknowledges support by the Army Research Office (W911NF-21-1-0194) and by the Air Force Office of Scientific Research (FA9550-21-1-0446).Peer ReviewedArticle signat per 19 autors/es : Ginestra Bianconi, Alex Arenas, Jacob Biamonte, Lincoln D Carr, Byungnam Kahng, Janos Kertesz, Jürgen Kurths, Linyuan Lu, Cristina Masoller, Adilson E Motter Matjaz Perc, Filippo Radicchi, Ramakrishna Ramaswamy, Francisco A Rodrigues, Marta Sales-Pardo, Maxi San Miguel, Stefan Thurner and Taha Yasseri.Postprint (published version
Racing a quantum computer through Minkowski spacetime
No full textThe Lorentzian length of a timelike curve connecting both endpoints of a computation in Minkowski spacetime is smaller than the Lorentzian length of the corresponding geodesic. In this talk, I will point out some properties of spacetime that allow an inertial classical computer to outperform a quantum one, at the completion of a long journey. We will focus on a comparison between the optimal quadratic Grover speed up from quantum computing and an n=2 speedup using classical computers and relativistic effects. These results are not practical as a new model of computation, but allow us to probe the ultimate limits physics places on computers
On Commutative Penalty Functions in Parent-Hamiltonian Constructions
No full textThere are several known techniques to construct a Hamiltonian with an
expected value that is minimized uniquely by a given quantum state. Common
approaches include the parent Hamiltonian construction from matrix product
states, building approximate ground state projectors, and, in a common case,
developing penalty functions from the generalized Ising model. Here we consider
the framework that enables one to engineer exact parent Hamiltonians from
commuting polynomials. We derive elementary classification results of quadratic
Ising parent Hamiltonians and to generally derive a non-injective parent
Hamiltonian construction. We also consider that any -qubit stabilizer state
has a commutative parent Hamiltonian with terms and we develop an
approach that allows the derivation of parent Hamiltonians by composition of
network elements that embed the truth tables of discrete functions into a
kernel space. This work presents a unifying framework that captures components
of what is known about exact parent Hamiltonians and bridges a few techniques
across the domains that are concerned with such constructions.Comment: 23 page
Positive Neutrality: Nasser’s Most Consequential Policy
No full textGamal Nasser was the President of Egypt from 1954 until his death in 1970 at age 52. He remains a hero in Egypt for gaining full independence after centuries of colonial rule, implementing sweeping social programs, modernizing its economy, and transforming Egypt into a regional political and military power. Extensive research involving a number of peer-reviewed articles and primary sources shows that Nasser required a vast amount of financial and military foreign aid to accomplish his goals. During the height of the Cold War, Egypt received substantial aid from numerous sources including the USSR and the United States. An examination of the main events before and during Nasser’s reign reveals that he never wavered from his strict policy of positive neutrality, which involved cooperating, but never participating in formal allegiances with any foreign powers. This essay demonstrates that Nasser’s positive neutrality policy was the central reason for his success
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