48 research outputs found
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
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
Categorical Models of Quantum Circuits
No full textIt is shown that equations that hold in appropriate monoidal categories have an explicit representation in terms of quantum circuits. Hence, we adjust and map the graphical calculus of Abramsky and Coecke's categorical axiomatization of quantum theory onto quantum circuits, making a suitable extension applicable to problems stated in the language of quantum information science. Viewed in this new way, circuit diagrams themselves now become arrows in a Category, making quantum circuits a special case of a much more general mathematical framework. By building a precise connection between the quantum circuit language and the categorical model, we were able to use this new framework to produce results new to both areas. This should lead to more cross communication between the field of Categorical Quantum Theory, and Quantum Information Science
Automated Test Pattern Generation for Quantum Circuits
No full textThis work extends a general method used to test classical circuits to quantum circuits. Gate internal errors are address using a discrete fault model. Fault models to represent unwanted nearest neighbor entanglement as well as unwanted qubit rotation are presented. When witnessed, the faults we model are probabilistic, but there is a set of tests with the highest probability of detecting a discrete repetitive fault. A method of probabilistic set covering to identify the minimal set of tests is introduced. A large part of our work consisted of writing a software package that allows us to compare various fault models and test strategies for quantum networks.
Faculty Mentor: Marek A. Perkowsk
Fault Testing Quantum Switching Circuits
No full textTest pattern generation is an electronic design automation tool that attempts to find an input (or test) sequence that, when applied to a digital circuit, enables one to distinguish between the correct circuit behavior and the faulty behavior caused by particular faults. The effectiveness of this classical method is measured by the fault coverage achieved for the fault model and the number of generated vectors, which should be directly proportional to test application time. This work address the quantum process validation problem by considering the quantum mechanical adaptation of test pattern generation methods used to test classical circuits. We found that quantum mechanics allows one to execute multiple test vectors concurrently, making each gate realized in the process act on a complete set of characteristic states in space/time complexity that breaks classical testability lower bounds
