Related papers: The Amplified Quantum Fourier Transform: solving t…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
This letter presents a novel \textit{quantum algorithm} for signal denoising, which performs a thresholding in the frequency domain through amplitude amplification and using an adaptive threshold determined by local mean values. The…
The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for…
Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing…
The approximate quantum Fourier transform (AQFT) on $n$ qubits can be implemented in logarithmic depth using $8n$ qubits with all-to-all connectivity, as shown in [Hales, PhD Thesis Berkeley, 2002]. However, realizing the required…
The aim of the paper is to propose a bounded-error quantum polynomial time (BQP) algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a…
Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…
High-precision nonlocal temporal correlation identification in the entangled photon pairs is critical to measure the time offset between remote independent time scales for many quantum information applications. The first nonlocal…
Attaining a quantum speedup in solving practically useful optimization problems has been one of the holy grails in the field of quantum computing. While prior approaches have demonstrated speedups for certain structured problem classes,…
In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…
Multisite local orbitals, which are formed from linear combinations of pseudo-atomic orbitals from a target atom and its neighbor atoms, have been introduced in the large-scale density functional theory calculation code CONQUEST. Multisite…
We present a local Fourier slice equation that enables local and sparse projection of a signal. Our result exploits that a slice in frequency space is an iso-parameter set in spherical coordinates. Therefore, the projection of suitable…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…
The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…
We present a polynomial-time algorithm that discovers all maximal patterns in a point set, $D\subset\mathbb{R}^k$, that are related by transformations in a user-specified class, $F$, of bijections over $\mathbb{R}^k$. We also present a…
We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…