Information Technology Convergence and Services最新文献_第4页

A Subpolynomial-Time Algorithm for the Free Energy of One-Dimensional Quantum Systems in the Thermodynamic Limit 一维量子系统在热力学极限下自由能的次多项式时间算法

Information Technology Convergence and Services Pub Date : 2022-09-29 DOI: 10.22331/q-2023-05-22-1011

Hamza Fawzi, Omar Fawzi, Samuel O. Scalet

{"title":"A Subpolynomial-Time Algorithm for the Free Energy of One-Dimensional Quantum Systems in the Thermodynamic Limit","authors":"Hamza Fawzi, Omar Fawzi, Samuel O. Scalet","doi":"10.22331/q-2023-05-22-1011","DOIUrl":"https://doi.org/10.22331/q-2023-05-22-1011","url":null,"abstract":"We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T=0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed temperature T>0 in subpolynomial time, i.e., in time O((1ε)c) for any constant c>0 where ε is the additive approximation error. Previously, the best known algorithm had a runtime that is polynomial in 1ε. Our algorithm is also particularly simple as it reduces to the computation of the spectral radius of a linear map. This linear map has an interpretation as a noncommutative transfer matrix and has been studied previously to prove results on the analyticity of the free energy and the decay of correlations. We also show that the corresponding eigenvector of this map gives an approximation of the marginal of the Gibbs state and thereby allows for the computation of various thermodynamic properties of the quantum system.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"os-8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128082721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Opponent Indifference in Rating Systems: A Theoretical Case for Sonas 评级系统中的对手冷漠:一个Sonas的理论案例

Information Technology Convergence and Services Pub Date : 2022-09-08 DOI: 10.48550/arXiv.2209.03950

Gregory Bodwin, Forest Zhang

{"title":"Opponent Indifference in Rating Systems: A Theoretical Case for Sonas","authors":"Gregory Bodwin, Forest Zhang","doi":"10.48550/arXiv.2209.03950","DOIUrl":"https://doi.org/10.48550/arXiv.2209.03950","url":null,"abstract":"In competitive games, it is common to assign each player a real number rating signifying their skill level. A rating system is a procedure by which player ratings are adjusted upwards each time they win, or downwards each time they lose. Many matchmaking systems give players some control over their opponent's rating; for example, a player might be able to selectively initiate matches against opponents whose ratings are publicly visible, or abort a match without penalty before it begins but after glimpsing their opponent's rating. It is natural to ask whether one can design a rating system that does not incentivize a rating-maximizing player to act strategically, seeking matches against opponents of one rating over another. We show the following: - The full version of this\"opponent indifference\"property is unfortunately too strong to be feasible. Although it is satisfied by some rating systems, these systems lack certain desirable expressiveness properties, suggesting that they are not suitable to capture most games of interest. - However, there is a natural relaxation, roughly requiring indifference between any two opponents who are ``reasonably evenly matched'' with the choosing player. We prove that this relaxed variant of opponent indifference, which we call $P$ opponent indifference, is viable. In fact, a certain strong version of $P$ opponent indifference precisely characterizes the rating system Sonas, which was originally proposed for its empirical predictive accuracy on the outcomes of high-level chess matches.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132224996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations 量子态的浓度界和多项式近似对QAOA的限制

Information Technology Convergence and Services Pub Date : 2022-09-06 DOI: 10.22331/q-2023-05-11-999

Anurag Anshu, Tony Metger

{"title":"Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations","authors":"Anurag Anshu, Tony Metger","doi":"10.22331/q-2023-05-11-999","DOIUrl":"https://doi.org/10.22331/q-2023-05-11-999","url":null,"abstract":"We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from cite{DMRF22}; (ii) injective matrix product states; (iii) output states of dense Hamiltonian evolution, i.e. states of the form eιH(p)⋯eιH(1)|ψ0⟩ for any n-qubit product state |ψ0⟩, where each H(i) can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits. Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates.An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level p=o(log⁡log⁡n), assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level, improving upon the recent result [BGMZ22].","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"157 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133682371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Necessary Conditions in Multi-Server Differential Privacy 多服务器差分隐私的必要条件

Information Technology Convergence and Services Pub Date : 2022-08-17 DOI: 10.48550/arXiv.2208.08540

Albert Cheu, Chao Yan

引用次数: 3

False Consensus, Information Theory, and Prediction Markets 错误共识，信息理论和预测市场

Information Technology Convergence and Services Pub Date : 2022-06-07 DOI: 10.48550/arXiv.2206.02993

Yuqing Kong, G. Schoenebeck

{"title":"False Consensus, Information Theory, and Prediction Markets","authors":"Yuqing Kong, G. Schoenebeck","doi":"10.48550/arXiv.2206.02993","DOIUrl":"https://doi.org/10.48550/arXiv.2206.02993","url":null,"abstract":"We study a setting where Bayesian agents with a common prior have private information related to an event's outcome and sequentially make public announcements relating to their information. Our main result shows that when agents' private information is independent conditioning on the event's outcome whenever agents have similar beliefs about the outcome, their information is aggregated. That is, there is no false consensus. Our main result has a short proof based on a natural information theoretic framework. A key ingredient of the framework is the equivalence between the sign of the ``interaction information'' and a super/sub-additive property of the value of people's information. This provides an intuitive interpretation and an interesting application of the interaction information, which measures the amount of information shared by three random variables. We illustrate the power of this information theoretic framework by reproving two additional results within it: 1) that agents quickly agree when announcing (summaries of) beliefs in round robin fashion [Aaronson 2005]; and 2) results from [Chen et al 2010] on when prediction market agents should release information to maximize their payment. We also interpret the information theoretic framework and the above results in prediction markets by proving that the expected reward of revealing information is the conditional mutual information of the information revealed.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133870935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions 可信的，防策略的，最优的，有限的预期轮单项目拍卖的所有分布

Information Technology Convergence and Services Pub Date : 2022-05-29 DOI: 10.4230/LIPIcs.ITCS.2022.66

Meryem Essaidi, Matheus V. X. Ferreira, S. Weinberg

引用次数: 7

The Complexity of Infinite-Horizon General-Sum Stochastic Games 无限视界一般和随机对策的复杂性

Information Technology Convergence and Services Pub Date : 2022-04-08 DOI: 10.48550/arXiv.2204.04186

Yujia Jin, Vidya Muthukumar, Aaron Sidford

引用次数: 15

Matrix multiplication via matrix groups 通过矩阵群进行矩阵乘法

Information Technology Convergence and Services Pub Date : 2022-04-08 DOI: 10.48550/arXiv.2204.03826

J. Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, C. Umans

{"title":"Matrix multiplication via matrix groups","authors":"J. Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, C. Umans","doi":"10.48550/arXiv.2204.03826","DOIUrl":"https://doi.org/10.48550/arXiv.2204.03826","url":null,"abstract":"In 2003, Cohn and Umans proposed a group-theoretic approach to bounding the exponent of matrix multiplication. Previous work within this approach ruled out certain families of groups as a route to obtaining $omega = 2$, while other families of groups remain potentially viable. In this paper we turn our attention to matrix groups, whose usefulness within this framework was relatively unexplored. We first show that groups of Lie type cannot prove $omega=2$ within the group-theoretic approach. This is based on a representation-theoretic argument that identifies the second-smallest dimension of an irreducible representation of a group as a key parameter that determines its viability in this framework. Our proof builds on Gowers' result concerning product-free sets in quasirandom groups. We then give another barrier that rules out certain natural matrix group constructions that make use of subgroups that are far from being self-normalizing. Our barrier results leave open several natural paths to obtain $omega = 2$ via matrix groups. To explore these routes we propose working in the continuous setting of Lie groups, in which we develop an analogous theory. Obtaining the analogue of $omega=2$ in this potentially easier setting is a key challenge that represents an intermediate goal short of actually proving $omega = 2$. We give two constructions in the continuous setting, each of which evades one of our two barriers.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129559392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Decision-Making under Miscalibration 误差校准下的决策

Information Technology Convergence and Services Pub Date : 2022-03-18 DOI: 10.48550/arXiv.2203.09852

G. Rothblum, G. Yona

{"title":"Decision-Making under Miscalibration","authors":"G. Rothblum, G. Yona","doi":"10.48550/arXiv.2203.09852","DOIUrl":"https://doi.org/10.48550/arXiv.2203.09852","url":null,"abstract":"ML-based predictions are used to inform consequential decisions about individuals. How should we use predictions (e.g., risk of heart attack) to inform downstream binary classification decisions (e.g., undergoing a medical procedure)? When the risk estimates are perfectly calibrated, the answer is well understood: a classification problem's cost structure induces an optimal treatment threshold $j^{star}$. In practice, however, some amount of miscalibration is unavoidable, raising a fundamental question: how should one use potentially miscalibrated predictions to inform binary decisions? We formalize a natural (distribution-free) solution concept: given anticipated miscalibration of $alpha$, we propose using the threshold $j$ that minimizes the worst-case regret over all $alpha$-miscalibrated predictors, where the regret is the difference in clinical utility between using the threshold in question and using the optimal threshold in hindsight. We provide closed form expressions for $j$ when miscalibration is measured using both expected and maximum calibration error, which reveal that it indeed differs from $j^{star}$ (the optimal threshold under perfect calibration). We validate our theoretical findings on real data, demonstrating that there are natural cases in which making decisions using $j$ improves the clinical utility.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130955767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

On Flipping the Fréchet Distance 关于改变交换距离

Information Technology Convergence and Services Pub Date : 2022-03-09 DOI: 10.4230/LIPIcs.ITCS.2023.51

O. Filtser, Mayank Goswami, Joseph S. B. Mitchell, V. Polishchuk

{"title":"On Flipping the Fréchet Distance","authors":"O. Filtser, Mayank Goswami, Joseph S. B. Mitchell, V. Polishchuk","doi":"10.4230/LIPIcs.ITCS.2023.51","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2023.51","url":null,"abstract":"The classical and extensively-studied Fr'echet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a\"flipped\"Fr'echet measure defined by a sup min -- the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of\"social distance\"between two curves (or general domains), where agents traverse curves while trying to stay as far apart as possible. We first study the flipped Fr'echet measure between two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms. We then consider this measure on polygons, where it denotes the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon. We investigate several variants of the problem in this setting, for some of which we provide linear time algorithms. Finally, we consider this measure on graphs. We draw connections between our proposed flipped Fr'echet measure and existing related work in computational geometry, hoping that our new measure may spawn investigations akin to those performed for the Fr'echet distance, and into further interesting problems that arise.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128675627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1