Related papers: Practical implementation of a quantum backtracking…
We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
The quantum backtracking algorithm proposed by Ashley Montanaro raised considerable interest, as it provides a quantum speed-up for a large class of classical optimization algorithms. It does not suffer from Barren-Plateaus and transfers…
We investigate quantum backtracking algorithms of a type previously introduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of unknown structure, and in certain cases exponentially outperform classical procedures (such as…
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are…
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…
Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…
In this paper, we explore the automation of services' compositions. We focus on the service selection problem. In the formulation that we consider, the problem's inputs are constituted by a behavioral composition whose abstract services…
The model of Dynamic Meta-Constraints has special activity constraints which can activate other constraints. It also has meta-constraints which range over other constraints. An algorithm is presented in which constraints can be assigned one…
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
For many problems, quantum algorithms promise speedups over their classical counterparts. However, these results predominantly rely on asymptotic worst-case analysis, which overlooks significant overheads due to error correction and the…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
We show how one can use certain deterministic algorithms for higher-value constraint satisfaction problems (CSPs) to speed up deterministic local search for 3-SAT. This way, we improve the deterministic worst-case running time for 3-SAT to…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…