相关论文: Generic Quantum Fourier Transforms

In this research paper, our primary focus revolves around the domain-specific hardware mapping strategy tailored for Quantum Fourier Transformation (QFT) circuits. While previous approaches have heavily relied on SAT solvers or heuristic…

Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…

For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…

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…

We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum…

We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…

When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are…

Quantum normalizer circuits were recently introduced as generalizations of Clifford circuits [arXiv:1201.4867]: a normalizer circuit over a finite Abelian group $G$ is composed of the quantum Fourier transform (QFT) over G, together with…

Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…

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),…

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…

Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…

In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…

What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…

Quantum field theory (QFT) for interacting many-electron systems is fundamental to condensed matter physics, yet achieving accurate solutions confronts computational challenges in managing the combinatorial complexity of Feynman diagrams,…

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…

The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…

We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…

We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…