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Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
We consider the problem of finding the optimal coefficient vector that maximizes the computation rate at a relay in the compute-and-forward scheme. Based on the idea of sphere decoding, we propose a highly efficient algorithm that finds the…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of…
The low-rank matrix approximation problem with respect to the component-wise $\ell_1$-norm ($\ell_1$-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
In the Correlation Clustering problem we are given $n$ nodes, and a preference for each pair of nodes indicating whether we prefer the two endpoints to be in the same cluster or not. The output is a clustering inducing the minimum number of…
Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of…
We give simple deterministic reductions demonstrating the NP-hardness of approximating the nearest codeword problem and minimum distance problem within arbitrary constant factors (and almost-polynomial factors assuming NP cannot be solved…
The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical…
Vector quantization, which discretizes a continuous vector space into a finite set of representative vectors (a codebook), has been widely adopted in modern machine learning. Despite its effectiveness, vector quantization poses a…
While a Quantum Approximate Optimization Algorithm (QAOA) is intended to provide a quantum advantage in finding approximate solutions to combinatorial optimization problems, noise in the system is a hurdle in exploiting its full potential.…
Optimizing the mRNA codon has an essential impact on gene expression for a specific target protein. It is an NP-hard problem; thus, exact solutions to such optimization problems become computationally intractable for realistic problem sizes…
Perfect Domination Problem (PDP), a canonical challenge in combinatorial optimization, finds critical applications in real-world systems such as error-correcting codes, wireless communication networks, and social networks. Decades of…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
We present the variational separability verifier (VSV), which is a novel variational quantum algorithm (VQA) that determines the closest separable state (CSS) of an arbitrary quantum state with respect to the Hilbert-Schmidt distance (HSD).…