Related papers: A Quantum Algorithm for the Classification of Patt…
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
In this paper, we consider the problem of finding perfectly balanced Boolean functions with high non-linearity values. Such functions have extensive applications in domains such as cryptography and error-correcting coding theory. We provide…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the…
We consider collocated wireless sensor networks, where each node has a Boolean measurement and the goal is to compute a given Boolean function of these measurements. We first consider the worst case setting and study optimal block…
We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
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,…
In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities…
A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…
The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order…
It is known that the order of correlation immunity of a nonconstant unbalanced Boolean function in $n$ variables cannot exceed $2n/3-1$; moreover, it is $2n/3-1$ if and only if the function corresponds to an equitable $2$-partition of the…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Boolean functions with few-valued spectra have wide applications in cryptography, coding theory, sequence designs, etc. In this paper, we further study the parametric construction approach to obtain balanced Boolean functions using…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
Homogenous Boolean function is an essential part of any cryptographic system. The ability to construct an optimized reversible circuits for homogeneous Boolean functions might arise the possibility of building cryptographic system on novel…