Related papers: Prime factorization using quantum annealing and co…
Recent advancements in quantum annealing hardware and numerous studies in this area suggests that quantum annealers have the potential to be effective in solving unconstrained binary quadratic programming problems. Naturally, one may desire…
In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…
In this paper we present a new efficient variant to compute strong Gr\"obner basis over quotients of principal ideal domains. We show an easy lifting process which allows us to reduce one computation over the quotient $R/nR$ to two…
Advancements in quantum computing are fuelling emerging applications across disciplines, including finance, where quantum and quantum-inspired algorithms can now make market predictions, detect fraud, and optimize portfolios. Expanding this…
Determining the prime factors of a given number N is a problem, which requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by P. Shor for quantum computers. However, the realization of…
In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579] proposed the algorithm for factorization of unitary operators in the finite M dimensional Hilbert space according to a coprime decomposition of M. Using a special…
Recent advances in the development of commercial quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary programs. However, the relatively small number of…
We construct an analog computer based on light interference to encode the hyperbolic function f({\zeta}) = 1/{\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=\C\Z_2\cdot\C\Z_2$. We also further extend the coalgebra…
In this paper it has been described how to use the unitary dynamics of quantum mechanics to solve the prime factorization problem on a spin ensemble without any quantum entanglement. The ensemble quantum computation for the prime…
An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally…
This paper proposes a geometric solution to the problem of prime decomposability of concurrent processes first explored by R. Milner and F. Moller in [MM93]. Concurrent programs are given a geometric semantics using cubical areas, for which…
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…
Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…