Related papers: A quantum algorithm for solving 0-1 Knapsack probl…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where…
In this thesis we develop FPTASs for the counting problems of m-tuples, contingency tables with two rows, and 0/1 knapsack. For the problem of counting m-tuples, we design two algorithms, one is strongly polynomial. As far as we know, these…
A combinatorial optimization problem is to find an optimal solution under the constraints. This is one of the potential applications for quantum computers. Quantum Random Access Optimization (QRAO) is the quantum optimization algorithm that…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Quantum computation has demonstrated a promising alternative to solving the NP-hard combinatorial problems. Specifically, when it comes to optimization, classical approaches become intractable to account for large-scale solutions.…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Among the genetic algorithms generally used for optimization problems in the recent decades, quantum-inspired variants are known for fast and high-fitness convergence and small resource requirement. Here the application to the patient…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…
Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce…
Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…