Information Technology Convergence and Services最新文献_第5页

A Lower Bound on the Space Overhead of Fault-Tolerant Quantum Computation 容错量子计算空间开销的下界

Information Technology Convergence and Services Pub Date : 2022-01-31 DOI: 10.4230/LIPIcs.ITCS.2022.68

Omar Fawzi, Alexander Müller-Hermes, Ala Shayeghi

{"title":"A Lower Bound on the Space Overhead of Fault-Tolerant Quantum Computation","authors":"Omar Fawzi, Alexander Müller-Hermes, Ala Shayeghi","doi":"10.4230/LIPIcs.ITCS.2022.68","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.68","url":null,"abstract":"The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a constant level. A recent work by Fawzi, Grospellier and Leverrier (FOCS 2018) building on a result by Gottesman (QIC 2013) has shown that the space overhead can be asymptotically reduced to a constant independent of the circuit provided we only consider circuits with a length bounded by a polynomial in the width. In this work, using a minimal model for quantum fault tolerance, we establish a general lower bound on the space overhead required to achieve fault tolerance. For any non-unitary qubit channel $mathcal{N}$ and any quantum fault tolerance schemes against $mathrm{i.i.d.}$ noise modeled by $mathcal{N}$, we prove a lower bound of $maxleft{mathrm{Q}(mathcal{N})^{-1}n,alpha_mathcal{N} log Tright}$ on the number of physical qubits, for circuits of length $T$ and width $n$. Here, $mathrm{Q}(mathcal{N})$ denotes the quantum capacity of $mathcal{N}$ and $alpha_mathcal{N}>0$ is a constant only depending on the channel $mathcal{N}$. In our model, we allow for qubits to be replaced by fresh ones during the execution of the circuit and we allow classical computation to be free and perfect. This improves upon results that assumed classical computations to be also affected by noise, and that sometimes did not allow for fresh qubits to be added. Along the way, we prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude damping noise resolving a conjecture by Ben-Or, Gottesman, and Hassidim (2013).","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114585578","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: 6

A Complete Linear Programming Hierarchy for Linear Codes 线性码的完全线性规划层次

Information Technology Convergence and Services Pub Date : 2021-12-16 DOI: 10.4230/LIPIcs.ITCS.2022.51

L. N. Coregliano, F. G. Jeronimo, C. Jones

{"title":"A Complete Linear Programming Hierarchy for Linear Codes","authors":"L. N. Coregliano, F. G. Jeronimo, C. Jones","doi":"10.4230/LIPIcs.ITCS.2022.51","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.51","url":null,"abstract":"A longstanding open problem in coding theory is to determine the best (asymptotic) rate R2(δ) of binary codes with minimum constant (relative) distance δ. An existential lower bound was given by Gilbert and Varshamov in the 1950s. On the impossibility side, in the 1970s McEliece, Rodemich, Rumsey and Welch (MRRW) proved an upper bound by analyzing Delsarte’s linear programs. To date these results remain the best known lower and upper bounds on R2(δ) with no improvement even for the important class of linear codes. Asymptotically, these bounds differ by an exponential factor in the blocklength. In this work, we introduce a new hierarchy of linear programs (LPs) that converges to the true size ALin 2 (n, d) of an optimum linear binary code (in fact, over any finite field) of a given blocklength n and distance d. This hierarchy has several notable features: 1. It is a natural generalization of the Delsarte LPs used in the first MRRW bound. 2. It is a hierarchy of linear programs rather than semi-definite programs potentially making it more amenable to theoretical analysis. 3. It is complete in the sense that the optimum code size can be retrieved from level O(n2). 4. It provides an answer in the form of a hierarchy (in larger dimensional spaces) to the question of how to cut Delsarte’s LP polytopes to approximate the true size of linear codes. We obtain our hierarchy by generalizing the Krawtchouk polynomials and MacWilliams inequalities to a suitable “higher-order” version taking into account interactions of l words. Our method also generalizes to translation schemes under mild assumptions. 2012 ACM Subject Classification Theory of computation","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125804451","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

Multiscale entropic regularization for MTS on general metric spaces 广义度量空间上MTS的多尺度熵正则化

Information Technology Convergence and Services Pub Date : 2021-11-21 DOI: 10.4230/LIPIcs.ITCS.2022.60

Farzam Ebrahimnejad, James R. Lee

引用次数: 3

Uniform Brackets, Containers, and Combinatorial Macbeath Regions 统一括号、容器和组合麦克白区域

Information Technology Convergence and Services Pub Date : 2021-11-19 DOI: 10.4230/LIPIcs.ITCS.2022.59

Kunal Dutta, Arijit Ghosh, S. Moran

引用次数: 2

Multi-Channel Bayesian Persuasion 多通道贝叶斯说服

Information Technology Convergence and Services Pub Date : 2021-11-18 DOI: 10.4230/LIPIcs.ITCS.2022.11

Y. Babichenko, Inbal Talgam-Cohen, Haifeng Xu, Konstantin Zabarnyi

{"title":"Multi-Channel Bayesian Persuasion","authors":"Y. Babichenko, Inbal Talgam-Cohen, Haifeng Xu, Konstantin Zabarnyi","doi":"10.4230/LIPIcs.ITCS.2022.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.11","url":null,"abstract":"The celebrated Bayesian persuasion model considers strategic communication between an informed agent (the sender) and uninformed decision makers (the receivers). The current rapidly-growing literature mostly assumes a dichotomy: either the sender is powerful enough to communicate separately with each receiver (a.k.a. private persuasion), or she cannot communicate separately at all (a.k.a. public persuasion). We study a model that smoothly interpolates between the two, by considering a natural multi-channel communication structure in which each receiver observes a subset of the sender's communication channels. This captures, e.g., receivers on a network, where information spillover is almost inevitable. We completely characterize when one communication structure is better for the sender than another, in the sense of yielding higher optimal expected utility universally over all prior distributions and utility functions. The characterization is based on a simple pairwise relation among receivers - one receiver information-dominates another if he observes at least the same channels. We prove that a communication structure $M_1$ is (weakly) better than $M_2$ if and only if every information-dominating pair of receivers in $M_1$ is also such in $M_2$. We also provide an additive FPTAS for the optimal sender's signaling scheme when the number of states is constant and the graph of information-dominating pairs is a directed forest. Finally, we prove that finding an optimal signaling scheme under multi-channel persuasion is, generally, computationally harder than under both public and private persuasion.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"1623 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129240882","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

Larger Corner-Free Sets from Combinatorial Degenerations 组合退化中的更大无角集

Information Technology Convergence and Services Pub Date : 2021-11-16 DOI: 10.4230/LIPIcs.ITCS.2022.48

M. Christandl, Omar Fawzi, Hoang Ta, Jeroen Zuiddam

{"title":"Larger Corner-Free Sets from Combinatorial Degenerations","authors":"M. Christandl, Omar Fawzi, Hoang Ta, Jeroen Zuiddam","doi":"10.4230/LIPIcs.ITCS.2022.48","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.48","url":null,"abstract":"There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets in powers of a fixed small (directed or undirected) hypergraph, also called the Shannon capacity. An important instance of this is the corner problem studied in the context of multiparty communication complexity in the Number On the Forehead (NOF) model. Versions of this problem and the NOF connection have seen much interest (and progress) in recent works of Linial, Pitassi and Shraibman (ITCS 2019) and Linial and Shraibman (CCC 2021). We introduce and study a general algebraic method for lower bounding the Shannon capacity of directed hypergraphs via combinatorial degenerations, a combinatorial kind of\"approximation\"of subgraphs that originates from the study of matrix multiplication in algebraic complexity theory (and which play an important role there) but which we use in a novel way. Using the combinatorial degeneration method, we make progress on the corner problem by explicitly constructing a corner-free subset in $F_2^n times F_2^n$ of size $Omega(3.39^n/poly(n))$, which improves the previous lower bound $Omega(2.82^n)$ of Linial, Pitassi and Shraibman (ITCS 2019) and which gets us closer to the best upper bound $4^{n - o(n)}$. Our new construction of corner-free sets implies an improved NOF protocol for the Eval problem. In the Eval problem over a group $G$, three players need to determine whether their inputs $x_1, x_2, x_3 in G$ sum to zero. We find that the NOF communication complexity of the Eval problem over $F_2^n$ is at most $0.24n + O(log n)$, which improves the previous upper bound $0.5n + O(log n)$.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122402467","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: 4

Rigidity for Monogamy-Of-Entanglement Games 一夫一妻纠缠博弈的刚性

Information Technology Convergence and Services Pub Date : 2021-11-15 DOI: 10.4230/LiPIcs.ITCS.2023.28

A. Broadbent, Eric Culf

{"title":"Rigidity for Monogamy-Of-Entanglement Games","authors":"A. Broadbent, Eric Culf","doi":"10.4230/LiPIcs.ITCS.2023.28","DOIUrl":"https://doi.org/10.4230/LiPIcs.ITCS.2023.28","url":null,"abstract":"In a monogamy-of-entanglement (MoE) game, two players who do not communicate try to simultaneously guess a referee's measurement outcome on a shared quantum state they prepared. We study the prototypical example of a game where the referee measures in either the computational or Hadamard basis and informs the players of her choice. We show that this game satisfies a rigidity property similar to what is known for some nonlocal games. That is, in order to win optimally, the players' strategy must be of a specific form, namely a convex combination of four unentangled optimal strategies generated by the Breidbart state. We extend this to show that strategies that win near-optimally must also be near an optimal state of this form. We also show rigidity for multiple copies of the game played in parallel. We give three applications: (1) We construct for the first time a weak string erasure (WSE) scheme where the security does not rely on limitations on the parties' hardware. Instead, we add a prover, which enables security via the rigidity of this MoE game. (2) We show that the WSE scheme can be used to achieve bit commitment in a model where it is impossible classically. (3) We achieve everlasting-secure randomness expansion in the model of trusted but leaky measurement and untrusted preparation and measurements by two isolated devices, while relying only on the temporary assumption of pseudorandom functions. This achieves randomness expansion without the need for shared entanglement.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131556690","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: 4

Prefix Discrepancy, Smoothed Analysis, and Combinatorial Vector Balancing 前缀差异，平滑分析和组合向量平衡

Information Technology Convergence and Services Pub Date : 2021-11-13 DOI: 10.4230/LIPIcs.ITCS.2022.13

N. Bansal, Haotian Jiang, R. Meka, Sahil Singla, Makrand Sinha

{"title":"Prefix Discrepancy, Smoothed Analysis, and Combinatorial Vector Balancing","authors":"N. Bansal, Haotian Jiang, R. Meka, Sahil Singla, Makrand Sinha","doi":"10.4230/LIPIcs.ITCS.2022.13","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.13","url":null,"abstract":"A well-known result of Banaszczyk in discrepancy theory concerns the prefix discrepancy problem (also known as the signed series problem): given a sequence of $T$ unit vectors in $mathbb{R}^d$, find $pm$ signs for each of them such that the signed sum vector along any prefix has a small $ell_infty$-norm? This problem is central to proving upper bounds for the Steinitz problem, and the popular Koml'os problem is a special case where one is only concerned with the final signed sum vector instead of all prefixes. Banaszczyk gave an $O(sqrt{log d+ log T})$ bound for the prefix discrepancy problem. We investigate the tightness of Banaszczyk's bound and consider natural generalizations of prefix discrepancy: We first consider a smoothed analysis setting, where a small amount of additive noise perturbs the input vectors. We show an exponential improvement in $T$ compared to Banaszczyk's bound. Using a primal-dual approach and a careful chaining argument, we show that one can achieve a bound of $O(sqrt{log d+ log!log T})$ with high probability in the smoothed setting. Moreover, this smoothed analysis bound is the best possible without further improvement on Banaszczyk's bound in the worst case. We also introduce a generalization of the prefix discrepancy problem where the discrepancy constraints correspond to paths on a DAG on $T$ vertices. We show that an analog of Banaszczyk's $O(sqrt{log d+ log T})$ bound continues to hold in this setting for adversarially given unit vectors and that the $sqrt{log T}$ factor is unavoidable for DAGs. We also show that the dependence on $T$ cannot be improved significantly in the smoothed case for DAGs. We conclude by exploring a more general notion of vector balancing, which we call combinatorial vector balancing. We obtain near-optimal bounds in this setting, up to poly-logarithmic factors.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116290633","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

Geometric Bounds on the Fastest Mixing Markov Chain 最快混合马尔可夫链的几何边界

Information Technology Convergence and Services Pub Date : 2021-11-10 DOI: 10.4230/LIPIcs.ITCS.2022.109

Sam Olesker-Taylor, Luca Zanetti

{"title":"Geometric Bounds on the Fastest Mixing Markov Chain","authors":"Sam Olesker-Taylor, Luca Zanetti","doi":"10.4230/LIPIcs.ITCS.2022.109","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.109","url":null,"abstract":"In the Fastest Mixing Markov Chain problem, we are given a graph $G = (V, E)$ and desire the discrete-time Markov chain with smallest mixing time $tau$ subject to having equilibrium distribution uniform on $V$ and non-zero transition probabilities only across edges of the graph. It is well-known that the mixing time $tau_textsf{RW}$ of the lazy random walk on $G$ is characterised by the edge conductance $Phi$ of $G$ via Cheeger's inequality: $Phi^{-1} lesssim tau_textsf{RW} lesssim Phi^{-2} log |V|$. Analogously, we characterise the fastest mixing time $tau^star$ via a Cheeger-type inequality but for a different geometric quantity, namely the vertex conductance $Psi$ of $G$: $Psi^{-1} lesssim tau^star lesssim Psi^{-2} (log |V|)^2$. This characterisation forbids fast mixing for graphs with small vertex conductance. To bypass this fundamental barrier, we consider Markov chains on $G$ with equilibrium distribution which need not be uniform, but rather only $varepsilon$-close to uniform in total variation. We show that it is always possible to construct such a chain with mixing time $tau lesssim varepsilon^{-1} (operatorname{diam} G)^2 log |V|$. Finally, we discuss analogous questions for continuous-time and time-inhomogeneous chains.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115768248","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: 6

A Unifying Framework for Characterizing and Computing Width Measures 描述和计算宽度度量的统一框架

Information Technology Convergence and Services Pub Date : 2021-09-28 DOI: 10.4230/LIPIcs.ITCS.2022.63

E. Eiben, R. Ganian, Thekla Hamm, L. Jaffke, O-joung Kwon

引用次数: 9