Related papers: Computational speed-up in a single qudit NMR quant…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits…
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary…
Quantum computers (QCs) are maturing. When QCs are powerful enough, they may be able to handle problems in chemistry, physics, and finance that are not classically solvable. However, the applicability of quantum algorithms to speed up…
Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…