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Ranking the binding of small molecules to protein receptors through physics-based computation remains challenging. Though inroads have been made using free energy methods, these fail when the underlying classical mechanical force fields are…
For extreme low-bit quantization of large language models (LLMs), Double Binary Factorization (DBF) is attractive as it enables efficient inference without sacrificing accuracy. However, the scaling parameters of DBF are too restrictive;…
The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…
In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have…
As deep learning (DL) techniques become integral to various applications, ensuring model fairness while maintaining high performance has become increasingly critical, particularly in sensitive fields such as medical diagnosis. Although a…
Quantum machine learning carries the promise to revolutionize information and communication technologies. While a number of quantum algorithms with potential exponential speedups have been proposed already, it is quite difficult to provide…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the…
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a selfconsistent field (SCF) solution of large eigenvalue…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
Quantum computing and machine learning are state-of-the-art technologies that have been investigated intensively in both academia and industry. The hybrid technology of these two ingredients is expected to be a powerful tool to solve…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
Subspace clustering (SC) aims to cluster data lying in a union of low-dimensional subspaces. Usually, SC learns an affinity matrix and then performs spectral clustering. Both steps suffer from high time and space complexity, which leads to…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
Let $n = \mathrm{p}\!\cdot\!\mathrm{q}$ (p < q) and $\Delta = \lvert p-q \rvert$, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any…
Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To…
Compute-and-Forward (C&F) has been proposed as an efficient strategy to reduce the backhaul load for the distributed antenna systems. Finding the optimal coefficients in C&F has commonly been treated as a shortest vector problem (SVP),…
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an $m$-by-$n$ nonnegative matrix $X$ and an integer $k$, the PSD factorization…