Related papers: Mechanisms for Quantum Advantage in Global Optimiz…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
A quadratic speedup of the quantum adiabatic algorithm (QAA) for finding independent sets (ISs) in a graph is proven analytically. In comparison to the best classical algorithm with $O(n^2)$ scaling, where $n$ is the number of vertexes, our…
We investigate the efficiency of Quantum Adiabatic Optimization when overcoming potential barriers to get from a local to a global minimum. Specifically we look at n qubit systems with symmetric cost functions f:{0, 1}^n->R where the ground…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
It is shown that quantum computer can detect the existence of root of a function almost exponentially more efficient than the classical counterpart. It is also shown that a quantum computer can produce quantum state corresponding to the…
This paper investigates the performance of the emerging non-variational Quantum Walk-based Optimisation Algorithm (NV-QWOA) for solving small instances of the Quadratic Assignment Problem (QAP). NV-QWOA is benchmarked against classical…
This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…
Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over a proposed…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
We consider some classical and quantum approximate optimization algorithms with bounded depth. First, we define a class of "local" classical optimization algorithms and show that a single step version of these algorithms can achieve the…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…
Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary near intermediate-scale quantum (NISQ) era. The quantum approximate optimisation algorithm (QAOA)…
Quantum Annealing (QA) relies on mixing two Hamiltonian terms, a simple driver and a complex problem Hamiltonian, in a linear combination. The time-dependent schedule for this mixing is often taken to be linear in time: improving on this…
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…
Demonstrating quantum advantage for combinatorial optimization requires more than standalone algorithmic results; it calls for end-to-end case studies that integrate problem modelling, quantum execution, and classical refinement into…