Related papers: Quantum Computing and Shor`s Factoring Algorithm
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
A refinement of Shor's Algorithm for determining order is introduced, which determines a divisor of the order after any one run of a quantum computer with almost absolute certainty. The information garnered from each run is accumulated to…
We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring…
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…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
This is an introductory review on the basic principles of quantum computation. Various important quantum logic gates and algorithms based on them are introduced. Quantum teleportation and decoherence are discussed briefly. Some problems,…
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…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance…
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…