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The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly…
The remarkable achievements of machine learning techniques in analyzing discrete structures have drawn significant attention towards their integration into combinatorial optimization algorithms. Typically, these methodologies improve…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
According to the theoretical results, the quantum searching algorithm can be generalized by replacing the Walsh-Hadamard(W-H) transform by almost any quantum mechanical operation. We have implemented the generalized algorithm using nuclear…
In this paper I present a 3SAT algorithm based on the randomized algorithm of Papadimitriou from 1991, and Schoning from 1991. We also present strong arguments that this algorithm finds a solution (if it exists) for a 3SAT problem with high…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…
This paper proposes a novel higher-order multi-scale (HOMS) computational method, which is highly targeted for efficient, high-accuracy and low-computational-cost simulation of hygro-thermo-mechanical (H-T-M) coupling problems in…
SAT technology has proven to be surprisingly effective in a large variety of domains. However, for the Weighted CSP problem dedicated algorithms have always been superior. One approach not well-studied so far is the use of SAT in…
The signal for a highly boosted heavy resonance competing against a background of light parton jets at the LHC can be enhanced by analyzing subjets in the "fat" jet that possibly contains the heavy resonance. Three methods for doing this…
The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other…
A novel deep neural network classifier, a ``Particle transformer'' (PaRT), is introduced for the identification of highly Lorentz-boosted resonances reconstructed as single, multipronged jets in measurements and searches performed by the…
The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time,…
The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
Quantum state tomography (QST) scales exponentially in both measurement and computational cost, making full reconstruction impractical for multi-qubit systems. Existing approaches attempt to reduce this complexity, but do not explicitly…
Although Retrieval-Augmented Generation (RAG) systems have been widely applied, the privacy and security risks they face, such as data leakage and data poisoning, have not been systematically addressed yet. Existing defense strategies…