Related papers: Quantum Fourier Transform in Computational Basis
The Fourier transform proves indispensable in the processing of classical information as well as in the quantum domain, where it finds many applications ranging from state reconstruction to prime factoring. An implementation scheme of the…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
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…
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
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…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…
Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal…
In this work, we aim to confirm the impact of the Fourier series on the quantum machine learning model. We will propose models, tests, and demonstrations to achieve this objective. We designed a quantum machine learning leveraged on the…