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Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. We compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM's quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y-rotations on all qubits., Comment: final version, to appear in Quantum Science and Technology (2021); 10 pages (main paper) + 6 pages (appendices), 8 figures (main paper) + 6 figures (appendices)

With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. Recent works found promise in recasting the problem of quantum state reconstruction to learning the probability distribution of quantum state measurement vectors using generative neural network models. Here we propose the "Attention-based Quantum Tomography" (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. The AQT is based on the model proposed in "Attention is all you need" by Vishwani et al (2017) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for natural language processing captures the correlations among words in a sentence.

There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. ``Interpretability'' remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? ``Interpretable'' machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting non-linear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, $\mathbb{Z}_2$ topological insulator, and $\mathbb{Z}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a ``domain knowledge''-guided approach to feature selection, facilitates the construction of faithful phase diagrams and semi-quantitative interpretation of the criteria in certain cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems., Comment: 9 pages, 11 figures

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify pivotal components to which coarse-grained, or aggregate, properties are sensitive. As an example, we introduce our approach on a reduced toy model with a median voter who always votes in the majority. The sensitivity of majority-minority divisions to changing voter behaviour pinpoints the unique role of the median. More generally, the sensitivity identifies pivotal components that precisely determine collective outcomes generated by a complex network of interactions. Using perturbations to target pivotal components in the models, we analyse datasets from political voting, finance and Twitter. Across these systems, we find remarkable variety, from systems dominated by a median-like component to those whose components behave more equally. In the context of political institutions such as courts or legislatures, our methodology can help describe how changes in voters map to new collective voting outcomes. For economic indices, differing system response reflects varying fiscal conditions across time. Thus, our information-geometric approach provides a principled, quantitative framework that may help assess the robustness of collective outcomes to targeted perturbation and compare social institutions, or even biological networks, with one another and across time.

Neural networks have been shown to have a remarkable ability to uncover low dimensional structure in data: the space of possible reconstructed images form a reduced model manifold in image space. We explore this idea directly by analyzing the manifold learned by Deep Belief Networks and Stacked Denoising Autoencoders using Monte Carlo sampling. The model manifold forms an only slightly elongated hyperball with actual reconstructed data appearing predominantly on the boundaries of the manifold. In connection with the results we present, we discuss problems of sampling high-dimensional manifolds as well as recent work [M. Transtrum, G. Hart, and P. Qiu, Submitted (2014)] discussing the relation between high dimensional geometry and model reduction.

A classification of companies into sectors of the economy is important for macroeconomic analysis and for investments into the sector-specific financial indices and exchange traded funds (ETFs). Major industrial classification systems and financial indices have historically been based on expert opinion and developed manually. Here we show how unsupervised machine learning can provide a more objective and comprehensive broad-level sector decomposition of stocks. An emergent low-dimensional structure in the space of historical stock price returns automatically identifies "canonical sectors" in the market, and assigns every stock a participation weight into these sectors. Furthermore, by analyzing data from different periods, we show how these weights for listed firms have evolved over time., Comment: Some new figures; minor textual changes

We explore the use of semantic word embeddings in text segmentation algorithms, including the C99 segmentation algorithm and new algorithms inspired by the distributed word vector representation. By developing a general framework for discussing a class of segmentation objectives, we study the effectiveness of greedy versus exact optimization approaches and suggest a new iterative refinement technique for improving the performance of greedy strategies. We compare our results to known benchmarks, using known metrics. We demonstrate state-of-the-art performance for an untrained method with our Content Vector Segmentation (CVS) on the Choi test set. Finally, we apply the segmentation procedure to an in-the-wild dataset consisting of text extracted from scholarly articles in the arXiv.org database., Comment: 10 pages, 4 figures. KDD2015 submission

We consider the incidence of text "reuse" by researchers, via a systematic pairwise comparison of the text content of all articles deposited to arXiv.org from 1991--2012. We measure the global frequencies of three classes of text reuse, and measure how chronic text reuse is distributed among authors in the dataset. We infer a baseline for accepted practice, perhaps surprisingly permissive compared with other societal contexts, and a clearly delineated set of aberrant authors. We find a negative correlation between the amount of reused text in an article and its influence, as measured by subsequent citations. Finally, we consider the distribution of countries of origin of articles containing large amounts of reused text., Comment: 6 pages, plus 10 pages of supplementary material. To appear in PNAS (online 8 Dec 2014)

This is the transcript of the after-dinner talk I gave at the close of the 16 Nov 2013 symposium "Celebrating the Science of Kenneth Geddes Wilson" [1] at Cornell University (see Fig. 1 for the poster). The video of my talk is on-line [2], and this transcript is more or less verbatim, with the slides used included as figures. I've also annotated it with a few clarifying footnotes, and provided references to the source materials where available. The talk itself pulls together anecdotes from various points in his career, discusses my own graduate student experiences with him, and finishes with some video excerpts from an interview he did in 2010., Comment: v2: changed "tux" to "white tie and tails" and other similarly crucial corrections, plus some additional footnotes. v3: corrected only multiple mistranscriptions of "Gell-Mann", as pointed out by M.E.Fisher. Contributed to special issue of the Journal of Statistical Physics in memory of Kenneth G. Wilson

We report on a numerical experiment in which we use time-dependent potentials to braid non-abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where $\nu$, the ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for $\nu$ near $1$ and $3/2$, with Berry matrices respectively consistent with Ising and Fibonacci anyons. Near $\nu=1/2$, the braids commute., Comment: 5 pages, 1 figure

To mark the 20th anniversary of the (14 Aug 1991) commencement of hep-th@xxx.lanl.gov (now arXiv.org), I've adapted this article from one that first appeared in Physics World (2008), was later reprinted (with permission) in Learned Publishing (2009), but never appeared in arXiv. I trace some historical context and early development of the resource, its later trajectory, and close with some thoughts about the future. This version is closer to my original draft, with some updates for this occasion, plus an astounding $2^5$ added footnotes., Comment: 9 pages. v2: additional edifying comments interspersed throughout

We continue investigation of the effect of position in announcements of newly received articles, a single day artifact, with citations received over the course of ensuing years. Earlier work [arXiv:0907.4740, arXiv:0805.0307] focused on the "visibility" effect for positions near the beginnings of announcements, and on the "self-promotion" effect associated to authors intentionally aiming for these positions, with both found correlated to a later enhanced citation rate. Here we consider a "reverse-visibility" effect for positions near the ends of announcements, and on a "procrastination" effect associated to submissions made within the 20 minute period just before the daily deadline. For two large subcommunities of theoretical high energy physics, we find a clear "reverse-visibility" effect, in which articles near the ends of the lists receive a boost in both short-term readership and long-term citations, almost comparable in size to the "visibility" effect documented earlier. For one of those subcommunities, we find an additional "procrastination" effect, in which last position articles submitted shortly before the deadline have an even higher citation rate than those that land more accidentally in that position. We consider and eliminate geographic effects as responsible for the above, and speculate on other possible causes, including "oblivious" and "nightowl" effects., Comment: 13p, appeared JASIST on-line first (12 Oct 2010)

arXiv.org mediates contact with the literature for entire scholarly communities, both through provision of archival access and through daily email and web announcements of new materials, potentially many screenlengths long. We confirm and extend a surprising correlation between article position in these initial announcements, ordered by submission time, and later citation impact, due primarily to intentional "self-promotion" on the part of authors. A pure "visibility" effect was also present: the subset of articles accidentally in early positions fared measurably better in the long-term citation record than those lower down. Astrophysics articles announced in position 1, for example, overall received a median number of citations 83\% higher, while those there accidentally had a 44\% visibility boost. For two large subcommunities of theoretical high energy physics, hep-th and hep-ph articles announced in position 1 had median numbers of citations 50\% and 100\% larger than for positions 5--15, and the subsets there accidentally had visibility boosts of 38\% and 71\%. We also consider the positional effects on early readership. The median numbers of early full text downloads for astro-ph, hep-th, and hep-ph articles announced in position 1 were 82\%, 61\%, and 58\% higher than for lower positions, respectively, and those there accidentally had medians visibility-boosted by 53\%, 44\%, and 46\%. Finally, we correlate a variety of readership features with long-term citations, using machine learning methods, thereby extending previous results on the predictive power of early readership in a broader context. We conclude with some observations on impact metrics and dangers of recommender mechanisms., Comment: 28 pages, to appear in JASIST

We describe a large-scale application of methods for finding plagiarism in research document collections. The methods are applied to a collection of 284,834 documents collected by arXiv.org over a 14 year period, covering a few different research disciplines. The methodology efficiently detects a variety of problematic author behaviors, and heuristics are developed to reduce the number of false positives. The methods are also efficient enough to implement as a real-time submission screen for a collection many times larger., Comment: Sixth International Conference on Data Mining (ICDM'06), Dec 2006

Are the e-prints (electronic preprints) from the arXiv repository being used instead of the journal articles? In this paper we show that the e-prints have not undermined the usage of journal papers in the astrophysics community. As soon as the journal article is published, the astronomical community prefers to read the journal article and the use of e-prints through the NASA Astrophysics Data System drops to zero. This suggests that the majority of astronomers have access to institutional subscriptions and that they choose to read the journal article when given the choice. Within the NASA Astrophysics Data System they are given this choice, because the e-print and the journal article are treated equally, since both are just one click away. In other words, the e-prints have not undermined journal use in the astrophysics community and thus currently do not pose a financial threat to the publishers. We present readership data for the arXiv category "astro-ph" and the 4 core journals in astronomy (Astrophysical Journal, Astronomical Journal, Monthly Notices of the Royal Astronomical Society and Astronomy & Astrophysics). Furthermore, we show that the half-life (the point where the use of an article drops to half the use of a newly published article) for an e-print is shorter than for a journal paper. The ADS is funded by NASA Grant NNG06GG68G. arXiv receives funding from NSF award #0404553, Comment: 8 pages, 4 figures, submitted to Learned Publishing

Stephen Hawking's recent concession that black holes do not irretrievably eradicate information after all has garnered much attention. It is refreshing to see the public focused, if just for a moment, on an important conundrum that has fascinated theoretical physicists for three decades, and prompted much conceptual progress. The scientific issues, however, remain much less settled than Dr. Hawking's celebrated wager on the question.

We illustrate the use of machine learning techniques to analyze, structure, maintain, and evolve a large online corpus of academic literature. An emerging field of research can be identified as part of an existing corpus, permitting the implementation of a more coherent community structure for its practitioners., Comment: 10 pages, 4 figures, presented at Arthur M. Sackler Colloquium on "Mapping Knowledge Domains", 9--11 May 2003, Beckman Center, Irvine, CA, proceedings to appear in PNAS

We present a general discussion of strings propagating on noncompact coset spaces $G/H$ in terms of gauged WZW models, emphasizing the role played by isometries in the existence of target space duality. Fixed points of the gauged transformations induce metric singularities and, in the case of abelian subgroups $H$, become horizons in a dual geometry. We also give a classification of models with a single timelike coordinate together with an explicit list for dimensions $D\leq 10$. We study in detail the class of models described by the cosets $SL(2,\IR)\otimes SO(1,1)^{D-2}/SO(1,1)$. For $D\geq 2$ each coset represents two different spacetime geometries: (2D black hole)$\otimes \IR^{D-2}$ and (3D black string)$\otimes \IR^{D-3}$ with nonvanishing torsion. They are shown to be dual in such a way that the singularity of the former geometry (which is not due to a fixed point) is mapped to a regular surface (i.e.\ not even a horizon) in the latter . These cosets also lead to the conformal field theory description of known and new cosmological string models., Comment: 30 pages

These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in 2 dimensions 3. The central charge and the Virasoro algebra 4. Kac determinant and unitarity 5. Identication of m = 3 with the critical Ising model 6. Free bosons and fermions 7. Free fermions on a torus 8. Free bosons on a torus 9. Affine Kac-Moody algebras and coset constructions 10. Advanced applications, Comment: Lectures given at Les Houches summer session, Jun 28 -- Aug 5, 1988

We provide a detailed analysis of the problems and prospects of superstring theory c. 1986, anticipating much of the progress of the decades to follow., Comment: originally appeared as a Reference Frame in Physics Today, May 1986