Related papers: Classical and Quantum Query Complexity of Boolean …
Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces `spooky' hidden mechanisms. Whether one can…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
It has been hypothesized that quantum computers may lend themselves well to applications in machine learning. In the present work, we analyze function classes defined via quantum kernels. Quantum computers offer the possibility to…
Classification is a well-studied machine learning task which concerns the assignment of instances to a set of outcomes. Classification models support the optimization of managerial decision-making across a variety of operational business…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
It has long been recognized that certain quantum correlations are incompatible with particular assumption about classical causal structure. Given a causal structure of unknown classicality, the presence of such correlations certifies the…
Causal discovery methods seek to identify causal relations between random variables from purely observational data, as opposed to actively collected experimental data where an experimenter intervenes on a subset of correlates. One of the…
In this paper, we propose causality as a unified framework to explain query answers and non-answers, thus generalizing and extending several previously proposed approaches of provenance and missing query result explanations. We develop our…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
Requiring that the causal structure between different parties is well-defined imposes constraints on the correlations they can establish, which define so-called causal correlations. Some of these are known to have a "dynamical" causal order…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…
Early in 1992, Deutsch-Jozsa algorithm computed a symmetric partial Boolean function with a single quantum query, and thus achieved the best separation between classical deterministic and exact quantum query complexity. Until recent years,…
Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
We prove the following conjecture, raised by Aaronson and Ambainis in 2008: Let $f:\{-1,1\}^n \rightarrow [-1,1]$ be a multilinear polynomial of degree $d$. Then there exists a variable $x_i$ whose influence on $f$ is at least…
Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…