IA Scholar Query: Explicit Ramsey graphs and orthonormal labelings.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 20 Jul 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Suppressing quantum errors by scaling a surface code logical qubit
https://scholar.archive.org/work/5himghrjlvfifnja7ltkjxrysq
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle (2.914%± 0.016% compared to 3.028%± 0.023%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7×10^-6 logical error per round floor set by a single high-energy event (1.6×10^-7 when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.Rajeev Acharya, Igor Aleiner, Richard Allen, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Ben Chiaro, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Dripto M. Debroy, Alexander Del Toro Barba, Sean Demura, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Lara Faoro, Edward Farhi, Reza Fatemi, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Michael C. Hamilton, Matthew P. Harrigan, Sean D. Harrington, Oscar Higgott, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Pavol Juhas, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, Paul V. Klimov, Andrey R. Klots, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Lily Laws, Joonho Lee, Kenny Lee, Brian J. Lester, Alexander Lill, Wayne Liu, Aditya Locharla, Erik Lucero, Fionn D. Malone, Jeffrey Marshall, Orion Martin, Jarrod R. McClean, Trevor Mccourt, Matt McEwen, Anthony Megrant, Bernardo Meurer Costa, Xiao Mi, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Alexis Morvan, Emily Mount, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Ani Nersisyan, Hartmut Neven, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Murphy Yuezhen Niu, Thomas E. O'Brien, Alex Opremcak, John Platt, Andre Petukhov, Rebecca Potter, Leonid P. Pryadko, Chris Quintana, Pedram Roushan, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Vladimir Shvarts, Jindra Skruzny, Vadim Smelyanskiy, W. Clarke Smith, George Sterling, Doug Strain, Marco Szalay, Alfredo Torres, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Theodore White, Cheng Xing, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhuwork_5himghrjlvfifnja7ltkjxrysqWed, 20 Jul 2022 00:00:00 GMTThe Variational Quantum Eigensolver: a review of methods and best practices
https://scholar.archive.org/work/zlqmzjpmjngy3bc4pboozn46yq
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, Jonathan Tennysonwork_zlqmzjpmjngy3bc4pboozn46yqSun, 12 Jun 2022 00:00:00 GMTModel selection in the space of Gaussian models invariant by symmetry
https://scholar.archive.org/work/bsponsira5a6tlolgowaxj7pyq
We consider multivariate centered Gaussian models for the random variable Z=(Z_1,..., Z_p), invariant under the action of a subgroup of the group of permutations on {1,..., p}. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter Σ and also the analytic expression of the normalizing constant of the Diaconis-Ylvisaker conjugate prior for the precision parameter K=Σ^-1. We can thus perform Bayesian model selection in the class of complete Gaussian models invariant by the action of a subgroup of the symmetric group, which we could also call complete RCOP models. We illustrate our results with a toy example of dimension 4 and several examples for selection within cyclic groups, including a high dimensional example with p=100.Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek, Hélène Massamwork_bsponsira5a6tlolgowaxj7pyqMon, 16 May 2022 00:00:00 GMTTerm structure modeling, forecasting and implications for monetary policy
https://scholar.archive.org/work/wl6r4536nrhsnkkucsey3gxhea
This thesis examines the macro-finance-fiscal term structure model to incorporate fiscal instability variables and the term spread to understand the impact of the sovereign debt crisis on the evolution of the yield curve. My findings reveal financial instability increases the term spread associated with the expectation of higher sovereign default risk and consequently signals economic agents to reduce their spending, and thus worsens economic activity. Secondly, I also investigate whether the dynamic factor model with nonparametric factor loadings is more accurate relative to other term structure models by employing the dynamic semi-parametric factor model (DSFM). The empirical results indicate that a better in-sample fit is provided by the dynamic semiparametric factor model. However, the overall forecasting results are not encouraging. The dynamic semiparametric factor model provides accurate results in forecasting a persistent trend while the dynamic Nelson-Siegel model is more suitable to fit more volatile series. Thirdly,I use a Sheen-Trueck-Wang business conditions index for term structure modeling and forecasting. I find the cross-sectional yield provides guidance to anchor the yield in the next period. The prediction performance of the model is enhancedby using the index since it includes information on frequently released or more recent available data. The index is significantly related to the slope factor, which suggests the forward-looking information from the index inuences the adjustmentthe in the yield slope. Lastly, I examine the effectiveness of the US quantitative easing (QE) policy with a Bayesian structural vector auto regressive (B-SVAR)model with sign restrictions. I find the transmission mechanism of the Federal Reserve asset purchase effectively expands output and avert deflation through a compression in the yield spread.Chamadanai Marknualwork_wl6r4536nrhsnkkucsey3gxheaMon, 28 Mar 2022 00:00:00 GMTSome Fundamental Theorems in Mathematics
https://scholar.archive.org/work/6lqit72adje3zlo54s5zpgviem
An expository hitchhikers guide to some theorems in mathematics.Oliver Knillwork_6lqit72adje3zlo54s5zpgviemFri, 04 Feb 2022 00:00:00 GMTExtending the capabilities of Multi-Configurational short-range Density Functional Theory based methods
https://scholar.archive.org/work/j2kxeodzbbc7hnkid46zoorara
Triplet excitation energies from multiconfigurational short-range density-functional theory response calculations" The Journal of chemical physics 151 (12), 124113 Paper II Erik Rosendahl Kjellgren and Hans Jørgen Aagaard Jensen, "Multi-configurational short-range density functional theory can describe spin-spin coupling constants of transition metal complexes" J. Chem. Phys. 155, 084102 (2021)Erik Kjellgrenwork_j2kxeodzbbc7hnkid46zooraraNon-asymptotic quantum metrology
https://scholar.archive.org/work/jdzewzl4pfacdpuyh24ww6h6vq
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a methodology that departs from asymptotic approximations and restricted parameter locations, while practical convenience requires that it is also flexible and easy to use in applications with limited data. We submit that this methodology can and should be built on a Bayesian framework, and in this thesis we propose, construct, explore and exploit a new non-asymptotic quantum metrology. First we show the consistency of taking those solutions that are optimal in the asymptotic regime of many trials as a guide to calculate a Bayesian measure of uncertainty. This provides an approximate but useful way of studying the non-asymptotic regime whenever an exact optimisation is intractable, and it avoids the non-physical results that can arise when only the asymptotic theory is used. Secondly, we construct a new non-asymptotic Bayesian bound without relying on the previous approximation by first selecting a single-shot optimal quantum strategy, and then simulating a sequence of repetitions of this scheme. These methods are then applied to a single-parameter Mach-Zehnder interferometer, and to multi-parameter qubit and optical sensing networks. Our results provide a detailed characterisation of how the interplay between prior information, correlations and a limited amount of data affects the performance of quantum metrology protocols, which opens the door to a vast set of unexplored possibilities to enhance non-asymptotic schemes. Finally, we provide practical researchers with a numerical toolbox for Bayesian metrology, while theoretical workers will benefit from the broader and more fundamental perspective that arises from the unified character of our methodology.Jesús Rubiowork_jdzewzl4pfacdpuyh24ww6h6vqWed, 01 Dec 2021 00:00:00 GMTAsymptotic Frame Theory for Analog Coding
https://scholar.archive.org/work/s5lwflrvj5apjlryxccjxm652i
Over-complete systems of vectors, or in short, frames, play the role of analog codes in many areas of communication and signal processing. To name a few, spreading sequences for code-division multiple access (CDMA), over-complete representations for multiple-description (MD) source coding, space-time codes, sensing matrices for compressed sensing (CS), and more recently, codes for unreliable distributed computation. In this survey paper we observe an information-theoretic random-like behavior of frame subsets. Such sub-frames arise in setups involving erasures (communication), random user activity (multiple access), or sparsity (signal processing), in addition to channel or quantization noise. The goodness of a frame as an analog code is a function of the eigenvalues of a sub-frame, averaged over all sub-frames. Within the highly symmetric class of Equiangular Tight Frames (ETF), as well as other "near ETF" families, we show a universal behavior of the empirical eigenvalue distribution (ESD) of a randomly-selected sub-frame: (i) the ESD is asymptotically indistinguishable from Wachter's MANOVA distribution; and (ii) it exhibits a convergence rate to this limit that is indistinguishable from that of a matrix sequence drawn from MANOVA (Jacobi) ensembles of corresponding dimensions. Some of these results follow from careful statistical analysis of empirical evidence, and some are proved analytically using random matrix theory arguments of independent interest. The goodness measures of the MANOVA limit distribution are better, in a concrete formal sense, than those of the Marchenko-Pastur distribution at the same aspect ratio, implying that deterministic analog codes are better than random (i.i.d.) analog codes. We further give evidence that the ETF (and near ETF) family is in fact superior to any other frame family in terms of its typical sub-frame goodness.Marina Haikin, Matan Gavish, Dustin G. Mixon, Ram Zamirwork_s5lwflrvj5apjlryxccjxm652iSun, 14 Nov 2021 00:00:00 GMTMethods for simulating string-net states and anyons on a digital quantum computer
https://scholar.archive.org/work/geybknmeijenlhc4eoreee5usu
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to realize a large class of topologically ordered states and simulate their quasiparticle excitations on a digital quantum computer. To achieve this we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with quantum circuits to simulate the creation and braiding of abelian and non-abelian anyons. Our scheme allows us to directly probe characteristic topological properties, including topological entanglement entropy, braiding statistics, and fusion channels of anyons. Moreover, this set of efficiently prepared topologically ordered states has potential applications in the development of fault-tolerant quantum computers.Yu-Jie Liu, Kirill Shtengel, Adam Smith, Frank Pollmannwork_geybknmeijenlhc4eoreee5usuTue, 05 Oct 2021 00:00:00 GMT