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Small hitting-sets for tiny arithmetic circuits or: How to turn bad designs into good

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arXiv 2017年

作者： Agrawal, Manindra Forbes, Michael Ghosh, Sumanta Saxena, Nitin Department of Computer Science and Engineering Iit Kanpur India Simons Institute for the Theory of Computing University of California Berkeley United States Cse Iitk

Research in the last decade has shown that to prove lower bounds or to derandomize polynomial identity testing (PIT) for general arithmetic circuits it suffices to solve these questions for restricted circuits. In this work, we study the smallest possibly restricted class of circuits, in particular depth-4 circuits, which would yield such results for general circuits (that is, the complexity class VP). We show that if we can design poly(s)-time hitting-sets for Σ a ΣO(log s)circuits of size s, where a = ω(1) is arbitrarily small and the number of variables, or arity n, is O(log s), then we can derandomize blackbox PIT for general circuits in quasipolynomial time. Further, this establishes that either E6⊆#P/poly or that VP6=VNP. We call the former model tiny diagonal depth-4. Note that these are merely polynomials with arity O(log s) and degree ω(log s). In fact, we show that one only needs a poly(s)-time hitting-set against individual-degree a′ = ω(1) polynomials that are computable by a size-s arity-(log s) ΣπΣ circuit (note: Π fanin may be s). Alternatively, we claim that, to understand VP one only needs to find hitting-sets, for depth-3, that have a small parameterized complexity. Another tiny family of interest is when we restrict the arity n = ω(1) to be arbitrarily small. In parameterized complexity terms: We show that if we can design poly(s, μ(n))-time hitting-sets for size-s arity-n ΣΠ circuits (resp. Σ a ΣΠ), where function μ is arbitrary, then we can solve PIT for VP in quasipoly-time, and prove the corresponding lower bounds. Our methods are strong enough to prove a surprising arity reduction for PIT- to solve the general problem completely it suffices to find a blackbox PIT with time-complexity sd2O(n). This suggests that, in algebraic-geometry terms, PIT is inherently an 'extremely low'-dimensional (or 'extremely low' individual-degree) problem. One expects that with this severe restriction on n, a and the semantic individual-degree, it should be at le

关键词： Timing circuits

Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement

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Physical Review A 2017年第2期96卷 020303(R)-020303(R)页

作者： Xi-Han Li Shohini Ghose Department of Physics Chongqing University Chongqing China Department of Physics and Computer Science Wilfrid Laurier University Waterloo Canada Institute for Quantum Computing University of Waterloo Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada

We present a technique for hyperentangled Bell-state analysis that only relies on linear optics and is assisted by auxiliary entangled states. This technique can be used to implement hyperdense coding with an experimentally realizable two-photon state hyperentangled in polarization and two longitudinal-momentum degrees of freedom. The 16 hyperentangled states in the first two degrees of freedom are classified into 12 groups with the help of the third degree of freedom. This allows the transmission of 3.58 bits/photon via our hyperdense coding scheme. We also generalize our technique to n-qubit hyperentangled Bell-state analysis assisted by additional auxiliary entangled states. We show that given n degrees of freedom, the 4n hyperentangled Bell states can be separated via linear optics into xk=2n+k+1−22k groups with the help of k(k≤n) ancillary entangled states. When k=n, all 4n hyperentangled states can be distinguished. Our results are useful for quantum information processing based on hyperentanglement.

关键词： Entanglement detection Optical quantum information processing quantum measurements quantum states of light

Standardized Assessment of Automatic Segmentation of White Matter Hyperintensities and Results of the WMH Segmentation Challenge

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arXiv 2019年

作者： Kuijf, Hugo J. Biesbroek, J. Matthijs Bresser, Jeroen de Heinen, Rutger Andermatt, Simon Bento, Mariana Berseth, Matt Belyaev, Mikhail Cardoso, M. Jorge Casamitjana, Adrià Collins, D. Louis Dadar, Mahsa Georgiou, Achilleas Ghafoorian, Mohsen Jin, Dakai Khademi, April Knight, Jesse Li, Hongwei Lladó, Xavier Luna, Miguel Mahmood, Qaiser McKinley, Richard Mehrtash, Alireza Ourselin, Sébastien Park, Bo-yong Park, Hyunjin Park, Sang Hyun Pezold, Simon Puybareau, Elodie Rittner, Leticia Sudre, Carole H. Valverde, Sergi Vilaplana, Verónica Wiest, Roland Xu, Yongchao Xu, Ziyue Zeng, Guodong Zhang, Jianguo Zheng, Guoyan Chen, Christopher Flier, Wiesje van der Barkhof, Frederik Viergever, Max A. Biessels, Geert Jan Image Sciences Institute UMC Utrecht Utrecht University Netherlands Brain Center Rudolf Magnus UMC Utrecht Utrecht University Netherlands Department of Radiology UMC Utrecht Department of Radiology LUMC Leiden Netherlands Department of Biomedical Engineering University of Basel Allschwil Switzerland Radiology and Clinical Neuroscience Hotchkiss Brain Institute University of Calgary AB Canada NLP Logix Skolkovo Institute of Science and Technology School of Biomedical Engineering and Imaging Sciences King’s College London Centre for Medical Image Computing University College London Signal Theory and Communications Department Universitat Politècnica de Catalunya BarcelonaTech Barcelona Spain McGill University Canada Computational Statistics and Machine Learning MSc University College London TomTom Amsterdam Netherlands Department of Radiology and Imaging Science National Institutes of Health United States Ryerson University Canada University of Guelph Canada Sun Yat-sen University University of Dundee Technical University of Munich Research institute of Computer Vision and Robotics University of Girona Spain Department of Robotics Engineering Daegu Gyeongbuk Institute of Science and Technology Daegu Korea Republic of Pakistan Institute of Nuclear Science and Technology Support Center for Advanced Neuroimaging Institute for Diagnostic and Interventional Neuroradiology Inselspital University of Bern Switzerland Electrical and Computer Engineering Department University of British Columbia Vancouver Department of Radiology Brigham and Women’s Hospital Harvard Medical School Boston School of Biomedical Engineering and Imaging Sciences King’s College London Suwon Korea Republic of School of Electronic and Electrical Engineering Sungkyunkwan University Suwon Korea Republic of France School of Electrical and Computer Engineering University of Campinas SP Brazil School of Biomedical Engineering and Imaging Sciences King’s College London Centre for Medical I

Quantification of cerebral white matter hyperintensities (WMH) of presumed vascular origin is of key importance in many neurological research studies. Currently, measurements are often still obtained from manual segmentations on brain MR images, which is a laborious procedure. Automatic WMH segmentation methods exist, but a standardized comparison of the performance of such methods is lacking. We organized a scientific challenge, in which developers could evaluate their method on a standardized multi-center/-scanner image dataset, giving an objective comparison: the WMH Segmentation Challenge (https://***/).Sixty T1+FLAIR images from three MR scanners were released with manual WMH segmentations for training. A test set of 110 images from five MR scanners was used for evaluation. Segmentation methods had to be containerized and submitted to the challenge organizers. Five evaluation metrics were used to rank the methods: (1) Dice similarity coefficient, (2) modified Hausdorff distance (95th percentile), (3) absolute log-transformed volume difference, (4) sensitivity for detecting individual lesions, and (5) F1-score for individual lesions. Additionally, methods were ranked on their inter-scanner *** participants submitted their method for evaluation. This paper provides a detailed analysis of the results. In brief, there is a cluster of four methods that rank significantly better than the other methods, with one clear winner. The inter-scanner robustness ranking shows that not all methods generalize to unseen *** challenge remains open for future submissions and provides a public platform for method evaluation. Copyright © 2019, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

Towards the manipulation of topological states of matter: A perspective from electron transport

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arXiv 2018年

作者： Zhang, Cheng Lu, Hai-Zhou Shen, Shun-Qing Chen, Yong P. Xiu, Faxian State Key Laboratory of Surface Physics and Department of Physics Fudan University Shanghai200433 China Collaborative Innovation Center of Advanced Microstructures Nanjing210093 China Institute for Quantum Science and Engineering Department of Physics South University of Science and Technology of China Shenzhen518055 China Shenzhen Key Laboratory of Quantum Science and Engineering Shenzhen518055 China Department of Physics University of Hong Kong Pokfulam Road Hong Kong Department of Physics and Astronomy Purdue University West LafayetteIN47907 United States Birck Nanotechnology Center Purdue University West LafayetteIN47907 United States School of Electrical and Computer Engineering Purdue University West LafayetteIN47907 United States Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai200433 China

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications. Copyright © 2018, The Authors. All rights reserved.

关键词： Electron transport properties

Estimating the Cost of Generic quantum Pre-image Attacks on SHA-2 and SHA-3 1

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23rd International Conference on Selected Areas in Cryptography, SAC 2016

作者： Amy, Matthew Di Matteo, Olivia Gheorghiu, Vlad Mosca, Michele Parent, Alex Schanck, John David R. Cheriton School of Computer Science University of Waterloo Waterloo Canada Department of Physics and Astronomy University of Waterloo Waterloo Canada Department of Combinatorics and Optimization University of Waterloo Waterloo Canada Institute for Quantum Computing University of Waterloo Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada Canadian Institute for Advanced Research Toronto Canada

ISBN: (数字)9783319694535

ISBN: (纸本)9783319694528

We investigate the cost of Grover’s quantum search algorithm when used in the context of pre-image attacks on the SHA-2 and SHA-3 families of hash functions. Our cost model assumes that the attack is run on a surface code based fault-tolerant quantum computer. Our estimates rely on a time-area metric that costs the number of logical qubits times the depth of the circuit in units of surface code cycles. As a surface code cycle involves a significant classical processing stage, our cost estimates allow for crude, but direct, comparisons of classical and quantum algorithms. We exhibit a circuit for a pre-image attack on SHA-256 that is approximately 2153.8 surface code cycles deep and requires approximately 2.12.6 logical qubits. This yields an overall cost of 2.166.4 logical-qubit-cycles. Likewise we exhibit a SHA3-256 circuit that is approximately 2.146.5 surface code cycles deep and requires approximately 2.20 logical qubits for a total cost of, again, 2.166.5logical-qubit-cycles. Both attacks require on the order of 2128 queries in a quantum black-box model, hence our results suggest that executing these attacks may be as much as 275 billion times more expensive than one would expect from the simple query analysis. © 2017, Springer International Publishing AG.

关键词： Hash functions

Comment on "Inherent security of phase coding quantum key distribution systems against detector blinding attacks" [Laser Phys. Lett. 15, 095203 (2018)]

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arXiv 2018年

作者： Fedorov, Aleksey Gerhardt, Ilja Huang, Anqi Jogenfors, Jonathan Kurochkin, Yury Lamas-Linares, Antía Larsson, Jan-Åke Leuchs, Gerd Lydersen, Lars Makarov, Vadim Skaar, Johannes Russian Quantum Center Skolkovo Moscow143025 Russia QRate Skolkovo Moscow143025 Russia QApp Skolkovo Moscow143025 Russia Institute of Physics University of Stuttgart Institute for Quantum Science and Technology Pfaffenwaldring 57 StuttgartD-70569 Germany Max Planck Institute for Solid State Research Heisenbergstraße 1 StuttgartD-70569 Germany Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer National University of Defense Technology Changsha410073 China Department of Electrical Engineering Linköping University LinköpingSE-58183 Sweden Texas Advanced Computing Center University of Texas at Austin AustinTX United States Max Planck Institute for the Science of Light University of Erlangen-Nürnberg ErlangenD-91058 Germany Kringsjåvegen 3E TrondheimNO-7032 Norway National University of Science and Technology MISIS Moscow119049 Russia Department of Technology Systems University of Oslo Box 70 KjellerNO-2027 Norway

quantum error correction and one-way locc state distinguishability

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arXiv 2018年

作者： Kribs, David W. Mintah, Comfort Nathanson, Michael Pereira, Rajesh Department of Mathematics & Statistics University of Guelph GuelphONN1G 2W1 Canada Institute for Quantum Computing and Department of Physics & Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Department of Mathematics and Computer Science Saint Mary's College of California MoragaCA94556 United States

We explore the intersection of studies in quantum error correction and quantum local operations and classical communication (LOCC). We consider one-way LOCC measurement protocols as quantum channels and investigate their error correction properties, emphasizing an operator theory approach to the subject, and we obtain new applications to one-way LOCC state distinguishability as well as new derivations of some established results. We also derive conditions on when states that arise through the stabilizer formalism for quantum error correction are distinguishable under one-way LOCC.47L90, 47L05, 81P15, 81P45, 81R15 Copyright © 2018, The Authors. All rights reserved.

关键词： Error correction

Two-kind boson mixture honeycomb Hamiltonian of Bloch exciton-polaritons

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Physical Review B 2019年第4期99卷 045302-045302页

作者： Haining Pan K. Winkler Mats Powlowski Ming Xie A. Schade M. Emmerling M. Kamp S. Klembt C. Schneider Tim Byrnes S. Höfling Na Young Kim Institute for Quantum Computing University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1 Condensed Matter Theory Center and Joint Quantum Institute Department of Physics University of Maryland College Park Maryland 20742 USA Technische Physik Physikalisches Institut Universität Würzbug D-97074 Würzburg Germany Department of Electrical and Computer Engineering University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1 Department of Physics The University of Texas at Austin Austin Texas 78712 USA State Key Laboratory of Precision Spectroscopy School of Physical and Material Sciences East China Normal University Shanghai 200062 China New York University Shanghai 1555 Century Ave. Pudong Shanghai 200122 China NYU-ECNU Institute of Physics at NYU Shanghai 366 Zhongshan Road North Shanghai 200062 China Department of Physics New York University New York New York 10003 USA School of Physics and Astronomy University of St. Andrews St. Andrews KY16 9SS United Kingdom Department of Physics and Astronomy University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1 Department of Chemistry University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1

The electronic band structure of a solid is a collection of allowed bands separated by forbidden bands, revealing the geometric symmetry of the crystal structures. Comprehensive knowledge of the band structure with band parameters explains intrinsic physical, chemical, and mechanical properties of the solid. Here we report the artificial polaritonic band structures of two-dimensional honeycomb lattices for microcavity exciton-polaritons using GaAs semiconductors in the wide-range detuning values, from cavity photonlike (red-detuned) to excitonlike (blue-detuned) regimes. In order to understand the experimental band structures and their band parameters, such as gap energies, bandwidths, hopping integrals, and density of states, we originally establish a polariton band theory within an augmented plane wave method with two-kind bosons, cavity photons trapped at the lattice sites, and freely moving excitons. In particular, this two-kind band theory is absolutely essential to elucidate the exciton effect in the band structures of blue-detuned exciton-polaritons, where the flattened excitonlike dispersion appears at larger in-plane momentum values captured in our experimental access window. We reach an excellent agreement between theory and experiments in all detuning values.

关键词： Band gap Electronic structure Polaritons quantum wells

Extended coulomb liquid of paired hardcore boson model on a pyrochlore lattice

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arXiv 2018年

作者： Huang, Chun-Jiong Liu, Changle Meng, Ziyang Yu, Yue Deng, Youjin Chen, Gang Shanghai Branch National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Shanghai201315 China CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics University of Science and Technology of China Hefei Anhui230026 China CAS-Alibaba Quantum Computing Laboratory Shanghai201315 China State Key Laboratory of Surface Physics and Department of Physics Fudan University Shanghai200433 China Beijing National Laboratory for Condensed Matter Physics Institute of Physics CAS Beijing100190 China Center for Field Theory and Particle Physics Fudan University Shanghai200433 China Collaborative Innovation Center of Advanced Microstructures Nanjing University Nanjing210093 China

There is a growing interest in the U(1) Coulomb liquid in both quantum materials in pyrochlore ice and cluster Mott insulators and cold atom systems. We explore a paired hardcore boson model on a pyrochlore lattice. This model is equivalent to the XYZ spin model that was proposed for rare-earth pyrochlores with "dipole-octupole" doublets. Since this model has no sign problem for quantum Monte Carlo (QMC) simulations in a large parameter regime, we carry out both analytical and QMC calculations. We find that the U(1) Coulomb liquid is quite stable and spans a rather large portion of the phase diagram with boson pairing. Moreover, we numerically find thermodynamic evidence that the boson pairing could induce a possible Z2 liquid in the vicinity of the phase boundary between Coulomb liquid and Z2 symmetry-broken phase. Besides the materials' relevance with quantum spin ice, we point to quantum simulation with cold atoms on optical lattices. Copyright © 2018, The Authors. All rights reserved.

关键词： Rare earths