Related papers: Very narrow quantum OBDDs and width hierarchies fo…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…
This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are…
Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Classical dimensional analysis has two limitations: (i) the computed dimensionless groups are not unique, and (ii) the analysis does not measure relative importance of the dimensionless groups. We propose two algorithms for estimating…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…
We report on an experimental test of classical and quantum dimension. We have used a dimension witness which can distinguish between quantum and classical systems of dimension 2,3 and 4 and performed the experiment for all five cases. The…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
It is proved that the width of a function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is demonstrated for…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
In the context of knowledge compilation (KC), we study the effect of augmenting Ordered Binary Decision Diagrams (OBDD) with two kinds of decomposition nodes, i.e., AND-vertices and OR-vertices which denote conjunctive and disjunctive…
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.…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs…