Related papers: Quantum arithmetic operations based on quantum Fou…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly.…
After quantum computers come out, governments and rich companies will have the abilities to buy these useful quantum computers, meanwhile they are familiar with these technologies proficiently. If a client wants to perform quantum computing…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
Quantum addition circuits are considered being of two types: 1) Toffolli-adder circuits which use only classical reversible gates (CNOT and Toffoli), and 2) QFT-adder circuits based on the quantum Fourier transformation. We present the…
We present a general method for the implementation of quantum algorithms that optimizes both gate count and circuit depth. Our approach introduces connectivity-adapted CNOT-based building blocks called Parity Twine chains. It outperforms…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
A system of unitary transformations providing two optimal copies of an arbitrary input cubit is obtained. An algorithm based on classical Boolean algebra and allowing one to find any unitary transformation realized by the quantum CNOT…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer…
The scalability of quantum computing is currently limited by physical, technological, and architectural constraints that hinder the integration of a large number of qubits within a single quantum processor. Distributed quantum computing…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…