English
Related papers

Related papers: Query-to-Communication Lifting for BPP

200 papers

By considering quantum computation as a communication process, we relate its efficiency to a communication capacity. This formalism allows us to rederive lower bounds on the complexity of search algorithms. It also enables us to link the…

Quantum Physics · Physics 2009-11-06 S. Bose , L. Rallan , V. Vedral

The log-rank conjecture is one of the fundamental open problems in communication complexity. It speculates that the deterministic communication complexity of any two-party function is equal to the log of the rank of its associated matrix,…

Computational Complexity · Computer Science 2014-04-01 Shachar Lovett

In a variant of communication complexity tasks, two or more separated parties cooperate to compute a function of their local data, using a limited amount of communication. It is known that communication of quantum systems and shared…

Quantum Physics · Physics 2015-12-21 Adrien Feix , Mateus Araújo , Časlav Brukner

We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…

Quantum Physics · Physics 2022-03-29 Dmytro Gavinsky

In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…

Quantum Physics · Physics 2007-05-23 Wim van Dam , Patrick Hayden

Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…

Computational Complexity · Computer Science 2010-06-29 Nadia Creignou , Johannes Schmidt , Michael Thomas

The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans)…

Computational Complexity · Computer Science 2024-01-24 Clément L. Canonne , Venkatesan Guruswami , Raghu Meka , Madhu Sudan

We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs…

Computational Complexity · Computer Science 2021-07-06 Cyrus Rashtchian , David P. Woodruff , Peng Ye , Hanlin Zhu

We introduce the lifted Generalized Belief Propagation (GBP) message passing algorithm, for the computation of sum-product queries in Probabilistic Relational Models (e.g. Markov logic network). The algorithm forms a compact region graph…

Artificial Intelligence · Computer Science 2016-10-06 Udi Apsel

We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…

Discrete Mathematics · Computer Science 2024-08-14 Matthias Walter

Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…

Quantum Physics · Physics 2020-03-04 Salman Beigi , Leila Taghavi

Compositionality is an important explanatory target in emergent communication and language evolution. The vast majority of computational models of communication account for the emergence of only a very basic form of compositionality:…

Neural and Evolutionary Computing · Computer Science 2020-10-30 Tomasz Korbak , Julian Zubek , Joanna Rączaszek-Leonardi

In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…

Computational Complexity · Computer Science 2015-12-02 Alexander Kozachinskiy

We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory.…

Quantum Physics · Physics 2009-11-10 Aram W. Harrow

Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of…

Quantum Physics · Physics 2020-11-09 Sutapa Saha , Some Sankar Bhattacharya , Tamal Guha , Saronath Halder , Manik Banik

We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…

Data Analysis, Statistics and Probability · Physics 2016-03-11 Marco Gherardi , Pietro Rotondo

Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…

Quantum Physics · Physics 2017-12-19 Andris Ambainis

Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks such as parallel computation and circuit optimisation. Crucially, the communication overhead introduced by the allotment process should be…

Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone $C$ and its dual $C^*$. We show that whether some one-way communication complexity problems can be…

Quantum Physics · Physics 2014-07-01 Samuel Fiorini , Serge Massar , Manas K. Patra , Hans Raj Tiwary

We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…

Computational Complexity · Computer Science 2008-12-15 Russell Impagliazzo