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arXiv 2020年

作者： van Lancker, Kelly Vandebosch, An Vansteelandt, Stijn Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium Janssen R&D Division of Janssen Pharmaceutica NV Beerse Belgium Department of Medical Statistics London School of Hygiene and Tropical Medicine London United Kingdom

Motivated by a clinical trial conducted by Janssen Pharmaceuticals in which a flexible dosing regimen is compared to placebo, we evaluate how switchers in the treatment arm (i.e., patients who were switched to the higher dose) would have fared had they been kept on the low dose. This in order to understand whether flexible dosing is potentially beneficial for them. Simply comparing these patients’ responses with those of patients who stayed on the low dose is unsatisfactory because the latter patients are usually in a better health condition. Because the available information in the considered trial is too scarce to enable a reliable adjustment, we will instead transport data from a fixed dosing trial that has been conducted concurrently on the same target, albeit not in an identical patient population. In particular, we will propose an estimator which relies on an outcome model and a propensity score model for the association between study and patient characteristics. The proposed estimator is asymptotically unbiased if at least one of both models is correctly specified, and efficient (under the model defined by the restrictions on the propensity score) when both models are correctly specified. We show that the proposed method for using results from an external study is generically applicable in studies where a classical confounding adjustment is not possible due to positivity violation (e.g., studies where switching takes place in a deterministic manner). Monte Carlo simulations and application to the motivating study demonstrate adequate performance. Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Generative ensemble regression: Learning particle dynamics from observations of ensembles with physics-informed deep generative models

arXiv

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arXiv 2020年

作者： Yang, Liu Daskalakis, Constantinos Karniadakis, George Em Division of Applied Mathematics Brown University ProvidenceRI02912 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Pacific Northwest National Laboratory RichlandWA99354 United States

We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates "fake" sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks (GANs). We refer to this method as generative "ensemble-regression" (GER), in analogy to the classic "point-regression", where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Lévy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support. Copyright © 2020, The Authors. All rights reserved.

关键词： Regression analysis

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Clustering with Semidefinite programming and Fixed Point Iteration

arXiv

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arXiv 2020年

作者： Felzenszwalb, Pedro Klivans, Caroline Paul, Alice School of Engineering Department of Computer Science Brown University ProvidenceRI02912 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Department of Biostatistics Brown University ProvidenceRI02912 United States

We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear optimization. We show the vertices of the Max k-Cut relaxation correspond to partitions of the data into at most k sets. We also show the vertices are attractive fixed points of iterated linear optimization. Each step of this iterative process solves a relaxation of the closest vertex problem and leads to a new clustering problem where the underlying clusters are more clearly defined. Our experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation leads to significantly better results when compared to randomized rounding. © 2020, CC BY.

关键词： Linear programming

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Analysis of variance of graph-clique mining for scalable proof of work 14th

Analysis of variance of graph-clique mining for scalable pro...

引用

14th International Conference on Information Security and Cryptology, Inscrypt 2018

作者： Anada, Hiroaki Matsushima, Tomohiro Su, Chunhua Meng, Weizhi Kawamoto, Junpei Bag, Samiran Sakurai, Kouichi Department of Information Security University of Nagasaki Nagasaki Japan Department of Informatics Graduate School and Faculty of Information Science and Electrical Engineering Kyushu University Fukuoka Japan Division of Computer Science University of Aizu Aizuwakamatsu Japan Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark School of Computing Science Newcastle University Newcastle upon Tyne United Kingdom

ISBN: (纸本)9783030142339

Recently, Bitcoin is becoming one of the most popular decentralized cryptographic currency technologies, and Bitcoin mining is a process of adding transaction records to Bitcoin’s public ledger of past transactions or blockchain. To obtain a bitcoin, the mining process involves compiling recent transactions into blocks and trying to solve a computationally difficult puzzle, e.g., proof of work puzzle. A proof of work allows miners the ability to quantify how much work a given proof contains. Basically, the required time for mining is decided in advance, but problems will occur if the value is large for dispersion. In this paper, we first accept that the required time between consecutive blocks follows the exponential distribution. That is, the variance is stable as long as the expected time is fixed. Then, we focus on the graph clique mining technique proposed by the literature, like Tromp (BITCOIN 2015) and Bag-Ruj-Sakurai (Inscrypt 2015), which is based on a computational difficulty problem of searching cliques of undirected graphs, where a clique is a subset of vertices. In particular, when the clique size is two, graph clique mining can be used to gain Bitcoins. The previous work also claimed that if the clique size is parameterized and increased, even if the expected time is fixed, the variance would not be stable. However, no qualitative or quantitative results were given to support their claim. Motivated by this issue, in this work, we propose a simple search algorithm for graph cliques mining, and perform a small scale evaluation on Bitcoin and Graph cliques’s solo mining to investigate the variance issue. © 2019, Springer Nature Switzerland AG.

关键词： Blockchain

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Traceable random numbers from a nonlocal quantum advantage

arXiv

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arXiv 2024年

作者： Kavuri, Gautam A. Palfree, Jasper Reddy, Dileep V. Zhang, Yanbao Bienfang, Joshua C. Mazurek, Michael D. Alhejji, Mohammad A. Siddiqui, Aliza U. Cavanagh, Joseph M. Dalal, Aagam Abellán, Carlos Amaya, Waldimar Mitchell, Morgan W. Stange, Katherine E. Beale, Paul D. Brandão, Luís T.A.N. Booth, Harold Peralta, René Nam, Sae Woo Mirin, Richard P. Stevens, Martin J. Knill, Emanuel Shalm, Lynden K. Department of Physics University of Colorado BoulderCO80309 United States The National Institute of Standards and Technology BoulderCO80305 United States Quantum Information Science Section Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Joint Quantum Institute National Institute of Standards and Technology University of Maryland 100 Bureau Drive GaithersburgMD20899 United States Center for Quantum Information and Control University of New Mexico AlbuquerqueNM87131 United States Department of Electrical Computer and Energy Engineering University of Colorado BoulderCO80309 United States Physical Measurement Laboratory National Institute of Standards and Technology GaithersburgMD20899 United States Quside Technologies S.L. Castelldefels Barcelona Spain ICFO-Institut de Ciencies Fotoniques The Barcelona Institute of Science and Technology Castelldefels Barcelona08860 Spain ICREA - Institució Catalana de Recerca i Estudis Avançats Barcelona08010 Spain Department of Mathematics University of Colorado BoulderCO80309 United States GaithersburgMD20899 United States Information Technology Laboratory National Institute of Standards and Technology GaithersburgMD20899 United States Physical Measurement Laboratory National Institute of Standards and Technology BoulderCO80305 United States Center for Theory of Quantum Matter University of Colorado BoulderCO80305 United States Applied and Computational Mathematics Division National Institute of Standards and Technology BoulderCO80305 United States Quantum Engineering Initiative Department of Electrical Computer and Energy Engineering University of Colorado BoulderCO80309 United States

The unpredictability of random numbers is fundamental to both digital security [1, 2] and applications that fairly distribute resources [3, 4]. However, existing random number generators have limitations—the generation processes cannot be fully traced, audited, and certified to be unpredictable. The algorithmic steps used in pseudorandom number generators [5] are auditable, but they cannot guarantee that their outputs were a priori unpredictable given knowledge of the initial seed. Device-independent quantum random number generators [6–9] can ensure that the source of randomness was unknown beforehand, but the steps used to extract the randomness are vulnerable to tampering. Here, for the first time, we demonstrate a fully traceable random number generation protocol based on device-independent techniques. Our protocol extracts randomness from unpredictable non-local quantum correlations, and uses distributed intertwined hash chains to cryptographically trace and verify the extraction process. This protocol is at the heart of a public traceable and certifiable quantum randomness beacon that we have launched [10]. Over the first 40 days of operation, we completed the protocol 7434 out of 7454 attempts—a success rate of 99.7%. Each time the protocol succeeded, the beacon emitted a pulse of 512 bits of traceable randomness. The bits are certified to be uniform with error times actual success probability bounded by 2−64. The generation of certifiable and traceable randomness represents one of the first public services that operates with an entanglement-derived advantage over comparable classical approaches. Copyright © 2024, The Authors. All rights reserved.

关键词： Random number generation

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Randomized Compiling for Scalable Quantum Computing on a Noisy Superconducting Quantum Processor

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Physical Review X 2021年第4期11卷 041039-041039页

作者： Akel Hashim Ravi K. Naik Alexis Morvan Jean-Loup Ville Bradley Mitchell John Mark Kreikebaum Marc Davis Ethan Smith Costin Iancu Kevin P. O’Brien Ian Hincks Joel J. Wallman Joseph Emerson Irfan Siddiqi Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Graduate Group in Applied Science and Technology University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02142 USA Quantum Benchmark Inc. Kitchener Ontario N2H 5G5 Canada Keysight Technologies Canada Kanata Ontario K2K 2W5 Canada Institute for Quantum Computing and Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error that has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.

关键词： Quantum algorithms Quantum benchmarking Quantum control Quantum information with solid state qubits

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Lower Bounds on Quantum Annealing Times

arXiv

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arXiv 2022年

作者： García-Pintos, Luis Pedro Brady, Lucas T. Bringewatt, Jacob Liu, Yi-Kai Joint Center for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States Joint Quantum Institute University of Maryland College ParkMD20742 United States Los Alamos National Laboratory Los AlamosNM87545 United States Quantum Artificial Intelligence Laboratory NASA Ames Research Center Moffett FieldCA94035 United States KBR 601 Jefferson St. HoustonTX77002 United States Applied and Computational Mathematics Division National Institute of Standards and Technology GaithersburgMD20899 United States

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p−spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource. © 2022, CC BY-NC-ND.

关键词： Ground state

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Experimental implementation of an efficient test of quantumness

arXiv

引用

arXiv 2022年

作者： Lewis, Laura Zhu, Daiwei Gheorghiu, Alexandru Noel, Crystal Katz, Or Harraz, Bahaa Wang, Qingfeng Risinger, Andrew Feng, Lei Biswas, Debopriyo Egan, Laird Vidick, Thomas Cetina, Marko Monroe, Christopher Institute for Quantum Information and Matter Department of Computing and Mathematical Sciences California Institute of Technology CA91125 United States Division of Physics Mathematics and Astronomy California Institute of Technology CA91125 United States Joint Quantum Institute Departments of Physics and Electrical and Computer Engineering University of Maryland College ParkMD20742 United States Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States IonQ Inc. College ParkMD20740 United States Departments of Electrical and Computer Engineering University of Maryland College ParkMD20742 United States Institute for Theoretical Studies ETH Zürich CH 8001 Switzerland Duke Quantum Center Department of Physics Duke University DurhamNC27708 United States Department of Electrical and Computer Engineering Duke University DurhamNC27708 United States Chemical Physics Program Institute for Physical Science and Technology University of Maryland College ParkMD20742 United States

A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current quantum computers rely on either interactive challenges with efficient verification, or non-interactive challenges with inefficient (exponential time) verification. In this paper, we execute an efficient non-interactive test of quantumness on an ion-trap quantum computer. Our results significantly exceed the bound for a classical device’s success. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

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Generating function for projected entangled-pair states

arXiv

引用

arXiv 2023年

作者： Tu, Wei-Lin Vanderstraeten, Laurens Schuch, Norbert Lee, Hyun-Yong Kawashima, Naoki Chen, Ji-Yao Faculty of Science and Technology Keio University 3-14-1 Hiyoshi Kohoku-ku Yokohama223-8522 Japan Center for Nonlinear Phenomena and Complex Systems Université Libre de Bruxelles Belgium University of Vienna Faculty of Physics Boltzmanngasse 5 Wien1090 Austria University of Vienna Faculty of Mathematics Oskar-Morgenstern-Platz 1 Wien1090 Austria Division of Display and Semiconductor Physics Korea University Sejong30019 Korea Republic of Department of Applied Physics Graduate School Korea University Sejong30019 Korea Republic of Interdisciplinary Program in E·ICT-Culture-Sports Convergence Korea University Sejong30019 Korea Republic of Institute for Solid State Physics The University of Tokyo Chiba Kashiwa277-8581 Japan Trans-scale Quantum Science Institute The University of Tokyo Bunkyo Tokyo113-0033 Japan Center for Neutron Science and Technology Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices School of Physics Sun Yat-sen University Guangzhou510275 China

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating function approach for tensor network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-1/2 transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-1/2 J1-J2 model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multi-particle excitations. © 2023, CC BY.

关键词： Excited states

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Random pulse sequences for qubit noise spectroscopy

引用

Physical Review applied 2025年第5期23卷 054090-054090页

作者： Kaixin Huang Demitry Farfurnik Alireza Seif Mohammad Hafezi Yi-Kai Liu Joint Quantum Institute (JQI) NIST/University of Maryland College Park Maryland 20742 USA Joint Center for Quantum Information and Computer Science (QuICS) NIST/University of Maryland College Park Maryland 20742 USA Department of Electrical and Computer Engineering and Department of Physics North Carolina State University Raleigh North Carolina 27695 USA Pritzker School of Molecular Engineering University of Chicago Chicago Illinois 60637 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg Maryland 20899 USA

Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. Here we describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.

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