Related papers: Solving Challenging Large Scale QAPs
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
Quantum algorithms implemented on near-term devices require qubit mapping due to noise and limited qubit connectivity. In this paper we propose a strategy called algorithm-oriented qubit mapping (AOQMAP) that aims to bridge the gap between…
The aircraft loading optimization problem is a computationally hard problem with the best known classical algorithm scaling exponentially with the number of objects. We propose a quantum approach based on a multi-angle variant of the QAOA…
Quantum computers are increasing in size and quality, but are still very noisy. Error mitigation extends the size of the quantum circuits that noisy devices can meaningfully execute. However, state-of-the-art error mitigation methods are…
The rapid development of neutral atom quantum hardware provides a unique opportunity to design hardware-centered algorithms for solving real-world problems aimed at establishing quantum utility. In this work, we study the performance of two…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
This paper presents two novel approaches for solving the set cover problem (SCP) with multiple inequality constraints on quantum annealers. The first method uses the augmented Lagrangian approach to represent the constraints, while the…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…
Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…
Solving large-scale linear systems problems is a cornerstone in scientific and industrial computing. Classical iterative solvers face increasing difficulty as the number of unknowns becomes large, while fully quantum linear solvers require…
Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in…
Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific…
We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
The Quantum Approximate Optimization Algorithm (QAOA) is a well-known hybrid quantum-classical algorithm for combinatorial optimization problems. Improving QAOA involves enhancing its approximation ratio while addressing practical…
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…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Treating uncertainties in models is essential in many fields of science and engineering. Uncertainty quantification (UQ) on complex and computationally costly numerical models necessitates a combination of efficient model solvers, advanced…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to…