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This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a…
We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to…
In this work we address two questions concerning Grover's algorithm. In the first we give an answer to the question how to employ Grover's algorithm for actual search over database. We introduce a quantum model of an unordered phone book…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Different mathematical models of recognition processes are known. In the present paper we consider a pattern recognition algorithm as an oracle computation on a Turing machine. Such point of view seems to be useful in pattern recognition as…
An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores…
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…
Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…
Grover's algorithm has achieved great success. But quantum search algorithms still are not complete algorithms because of Grover's Oracle. We concerned on this problem and present a new quantum search algorithm in adiabatic model without…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough.…
Quantum algorithms allow to outperform their classical counterparts in various tasks, most prominent example being Shor's algorithm for efficient prime factorization on a quantum computer. It is clear that one of the reasons for the speedup…
We consider the problem of inserting one item into a list of N-1 ordered items. We previously showed that no quantum algorithm could solve this problem in fewer than log N/(2 log log N) queries, for N large. We transform the problem into a…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
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…