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In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness…
We show that, assuming NP $\not\subseteq$ $\cap_{\delta > 0}$DTIME$\left(\exp{n^\delta}\right)$, the shortest vector problem for lattices of rank $n$ in any finite $\ell_p$ norm is hard to approximate within a factor of $2^{(\log n)^{1 -…
We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden…
Motivated by recent progress in quantum hardware and algorithms researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and…
We implement two Quantum Approximate Optimisation Algorithm (QAOA) variants for a battery revenue optimisation problem, equivalent to the weakly NP-hard Knapsack Problem. Both approaches investigate how to tackle constrained problems with…
Quantum error-correcting codes (QECCs) is at the heart of fault-tolerant quantum computing. As the size of quantum platforms is expected to grow, one of the open questions is to design new optimal codes of ever-increasing size. A related…
Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been…
We establish deterministic hardness of approximation results for the Shortest Vector Problem in $\ell_p$ norm ($\mathsf{SVP}_p$) and for Unique-SVP ($\mathsf{uSVP}_p$) for all $p > 2$. Previously, no deterministic hardness results were…
We give several improvements on the known hardness of the unique shortest vector problem. - We give a deterministic reduction from the shortest vector problem to the unique shortest vector problem. As a byproduct, we get deterministic…
We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for…
Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Protein folding is a central challenge in computational biology, with important applications in molecular biology, drug discovery and catalyst design. As a hard combinatorial optimisation problem, it has been studied as a potential target…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman (RSA) cryptography. With programmable quantum devices, adiabatic quantum computing has been proposed…
In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs.…
We introduce a new nearest-prototype classifier, the prototype vector machine (PVM). It arises from a combinatorial optimization problem which we cast as a variant of the set cover problem. We propose two algorithms for approximating its…
In this paper we consider a generalization of the classical k-center problem with capacities. Our goal is to select k centers in a graph, and assign each node to a nearby center, so that we respect the capacity constraints on centers. The…
Structured variational quantum algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have emerged as leading candidates for exploiting advantages of near-term quantum hardware. They interlace classical computation, in…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…