Related papers: Shallow Depth Factoring Based on Quantum Feasibili…
Partitioning a polygonal mesh into meaningful parts can be challenging. Many applications require decomposing such structures for further processing in computer graphics. In the last decade, several methods were proposed to tackle this…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
Many fundamental problems in data mining can be reduced to one or more NP-hard combinatorial optimization problems. Recent advances in novel technologies such as quantum and quantum-inspired hardware promise a substantial speedup for…
In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric non-negative matrices simultaneously. This can be considered as a generalization of the…
Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative matrix as the inner product of two positive semidefinite (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is…
There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is…
Due to the rapid development of quantum computing, the compact representation of quantum operations based on decision diagrams has been received more and more attraction. Since variable orders have a significant impact on the size of the…
Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for combinatorial problems. The simulation of…
We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
Numerous problems in signal processing and imaging, statistical learning and data mining, or computer vision can be formulated as optimization problems which consist in minimizing a sum of convex functions, not necessarily differentiable,…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
Binary quantization approaches, which replace weight matrices with binary matrices and substitute costly multiplications with cheaper additions, offer a computationally efficient approach to address the increasing computational and storage…
We report a quantum-classical hybrid scheme for factorization of bi-prime numbers (which are odd and square-free) using IBM's quantum processors. The hybrid scheme proposed here involves both classical optimization techniques and adiabatic…
It is NP-complete to find non-negative factors $W$ and $H$ with fixed rank $r$ from a non-negative matrix $X$ by minimizing $\|X-WH^\top\|_F^2$. Although the separability assumption (all data points are in the conical hull of the extreme…
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…