Related papers: Quantum Fourier Transform in Computational Basis
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits…
We study a quantum computer with fixed and permanent interaction of diagonal type between qubits. It is controlled only by one-qubit quick transformations. It is shown how to implement Quantum Fourier Transform and to solve Shroedinger…
We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
Shor's factoring algorithm provides a super-polynomial speed-up over all known classical factoring algorithms. Here, we address the question of which quantum properties fuel this advantage. We investigate a sequential variant of Shor's…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
The Quantum Fourier Transform is a famous example in quantum computing for being the first demonstration of a useful algorithm in which a quantum computer is exponentially faster than a classical computer. However when giving an explanation…
Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the…