Related papers: Quantum Algorithm based on Quantum Fourier Transfo…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
There are important algorithms built upon a mixture of basic techniques described; for example, the Fast Fourier Transform (FFT) employs both Divide-and-Conquer and Transform-and-Conquer techniques. In this article, the evolution of a…
An implementation of a universal solid-state quantum register based on electron space states in field-defined double quantum dots (DQD possesses one electron in two adjacent tunnel bound dots) in an ultrathin semiconductor nanowire is…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Finding the minimum value in an unordered database is a common and fundamental task in computer science. However, the optimal classical deterministic algorithm can find the minimum value with a time complexity that grows linearly with the…
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…
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Quantum amplitude amplification and quantum phase estimation are two fundamental quantum algorithms. All known quantum algorithms are derived from these two algorithms. Even the adiabatic quantum algorithms can also be efficiently simulated…
Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as $|i_1 i_2 ... i_n\ket$ with $i_j$ being either 0 or 1, but is a…
We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For…
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as in other disciplines. In 1971, Sch{\"o}nhage and Strassen designed an algorithm that improved the multiplication time for…
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…