Related papers: Scaling and better approximating quantum Fourier t…
Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that…
The quaternion Fourier transform (QFT), a generalization of the classical 2D Fourier transform, plays an increasingly active role in particular signal and colour image processing. There tends to be an inordinate degree of interest placed on…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
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…
One of the outstanding challenges in contemporary science and technology is building a quantum computer that is useful in applications. By starting from an estimate of the algorithm success rate, we can explicitly connect gate fidelity to…
The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
The discrete Fourier transform (DFT) is widely employed for multi-beam digital beamforming. The DFT can be efficiently implemented through the use of fast Fourier transform (FFT) algorithms, thus reducing chip area, power consumption,…
A simple and flexible scheme for high-dimensional linear quantum operations on optical transverse spatial modes is demonstrated. The quantum Fourier transformation (QFT) and quantum state tomography (QST) via symmetric informationally…
Thinning antenna arrays through quantum Fourier transform (QFT) is proposed. Given the lattice of the candidate locations for the array elements, the problem of selecting which antenna location has to be either occupied or not by an array…
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set $\{\U(2), \textrm{CNOT}\}$, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1,…
Quantum state tomography is a central technique for the characterization and verification of quantum systems. Standard tomography is widely used for low-dimensional systems, but for larger systems, it becomes impractical due to the…
We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…
In this study, we propose an efficient quantum multiplication approach based on a QFT-assisted parallelized addition scheme. The multiplication stage is implemented using a structure composed entirely of Toffoli gates, which generate…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
Most quantum processors requires pulse sequences for controlling quantum states. Here, we present an alternative algorithm for computing an optimal pulse sequence in order to perform a specific task, being an implementation of a quantum…
Near-term hardware is constrained by high error rates, small qubit counts, and relatively low output fidelity, making the execution of large, high performance quantum circuits difficult. Circuit partitioning (or circuit cutting) has emerged…
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure…