Related papers: Deutsch-Jozsa Algorithm Revisited in the Domain of…
In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f^2 = I. We describe several generalisations of well-known results in the theory of boolean functions, including…
Finding Boolean functions suitable for cryptographic primitives is a complex combinatorial optimization problem, since they must satisfy several properties to resist cryptanalytic attacks, and the space is very large, which grows super…
It remains an open question whether the apparent additional power of quantum computation derives inherently from quantum mechanics, or merely from the flexibility obtained by "lifting" Boolean functions to linear operators and evaluating…
Differentially 4-uniform permutations on $\gf_{2^{2k}}$ with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred…
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box.…
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
Deutsch's algorithm for two qubits (one control qubit plus one auxiliary qubit) is extended to two $d$-dimensional quantum systems or qudits for the case in which $d$ is equal to $2^n$, $n=1,2,...$ . This allows one to classify a certain…
The work offers a new approach to the formation of functions which are used in cryptography and cryptanalysis. It will use alternative forms of representation of Boolean functions, that is, those which are different from the classical form,…
Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…
In this paper we present a generic construction to obtain an optimal T depth quantum circuit for any arbitrary $n$-input $m$-output Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}^m$ having algebraic degree $k\leq n$, and it achieves an…
A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…
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…
Our problem is to evaluate a multi-valued Boolean function $F$ through oracle calls. If $F$ is one-to-one and the size of its domain and range is the same, then our problem can be formulated as follows: Given an oracle $f(a,x):…
We propose a physical scheme for implementing the Deutsch-Jozsa algorithm using atomic ensembles and optical devices. The scheme has inherent fault tolerance to the realistic noise and efficient scaling with the number of ensembles for some…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve…
Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…
The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…