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Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
Recently proposed analog solvers based on dynamical systems, such as Ising machines, are promising platforms for large-scale combinatorial optimization. Yet, given the heuristic nature of the field, there is very limited insight on…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
Ising machines, including quantum annealing machines, are promising next-generation computers for combinatorial optimization problems. However, due to hardware limitations, most Ising-type hardware can only solve objective functions…
We give a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT as well as problems where the objective function is a weighted sum of products of Ising variables, all terms of the…
A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real…
Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for…
A new class of energy-efficient digital microprocessor is being developed which is susceptible to thermal noise and consequently operates in probabilistic rather than conventional deterministic mode. Hybrid computing systems which combine…
The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from…
We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
Ising machines have emerged as accelerators for combinatorial optimization. To enable practical deployment, this work aims to reduce time-to-solution by addressing three challenges: (1) hardware topology, (2) spin selection and update…
Quantum algorithms face significant challenges due to qubit susceptibility to environmental noise, and quantum error correction typically requires prohibitive resource overhead. This paper proposes that quantum algorithms may possess…
As a natural variant of the $k$-SAT problem, NAE-$k$-SAT additionally requires the literals in each clause to take not-all-equal (NAE) truth values. In this paper, we study the worst-case time complexities of solving NAE-$k$-SAT and…
Analog Ising machines have been proposed as heuristic hardware solvers for combinatorial optimization problems, with the potential to outperform conventional approaches, provided that their hyperparameters are carefully tuned. Their…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…