Related papers: Classical and Quantum Query Complexity of Boolean …

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…

Finding a causal model for a set of classical variables is now a well-established task---but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for…

Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme.…

Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum…

Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…

This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We show that a certain tensor norm, the completely bounded norm, can be expressed by a semidefinite program. This tensor norm recently attracted attention in the field of quantum computing, where it was used by Arunachalam, Bri\"{e}t and…

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…

In this paper, we consider first-order logic over unary functions and study the complexity of the evaluation problem for conjunctive queries described by such kind of formulas. A natural notion of query acyclicity for this language is…

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…

Though the topic of causal inference is typically considered in the context of classical statistical models, recent years have seen great interest in extending causal inference techniques to quantum and generalized theories. Causal…

In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix…

We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…

Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple sub-fields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation…

Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…

An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…

Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…

Causal models capture cause-effect relations both qualitatively - via the graphical causal structure - and quantitatively - via the model parameters. They offer a powerful framework for analyzing and constructing processes. Here, we…