A Framework to Formulate Pathfinding Problems for Quantum Computing

• URL: http://arxiv.org/abs/2404.10820v1
• Date: Tue, 16 Apr 2024 18:00:06 GMT
• Title: A Framework to Formulate Pathfinding Problems for Quantum Computing
• Authors: Damian Rovara, Nils Quetschlich, Robert Wille,
• Abstract summary: We propose a framework to automatically generate QUBO formulations for pathfinding problems. It supports three different encoding schemes that can easily be compared without requiring manual reformulation efforts. The resulting QUBO formulations are robust and efficient, reducing the previously tedious and error-prone reformulation process.
• Score: 2.9723999564214267
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With the applications of quantum computing becoming more and more widespread, finding ways that allow end users without experience in the field to apply quantum computers to solve their individual problems is becoming a crucial task. However, current optimization algorithms require problem instances to be posed in complex formats that are challenging to formulate, even for experts. In particular, the Quadratic Unconstrained Binary Optimization (QUBO) formalism employed by many quantum optimization algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA), involves the mathematical rewriting of constraints under strict conditions. To facilitate this process, we propose a framework to automatically generate QUBO formulations for pathfinding problems. This framework allows users to translate their specific problem instances into formulations that can be passed directly to quantum algorithms for optimization without requiring any expertise in the field of quantum computing. It supports three different encoding schemes that can easily be compared without requiring manual reformulation efforts. The resulting QUBO formulations are robust and efficient, reducing the previously tedious and error-prone reformulation process to a task that can be completed in a matter of seconds. In addition to an open-source Python package available on https://github.com/cda-tum/mqt-qubomaker, we also provide a graphical user interface accessible through the web (https://cda-tum.github.io/mqt-qubomaker/), which can be used to operate the framework without requiring the end user to write any code.

Related papers

• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Enhancing Quantum Algorithms for Quadratic Unconstrained Binary Optimization via Integer Programming [0.0]
  In this work, we integrate the potentials of quantum and classical techniques for optimization. We reduce the problem size according to a linear relaxation such that the reduced problem can be handled by quantum machines of limited size. We present numerous computational results from real quantum hardware.
  arXiv  Detail & Related papers  (2023-02-10T20:12:53Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• A Realizable GAS-based Quantum Algorithm for Traveling Salesman Problem [2.208581695286558]
  The paper proposes a quantum algorithm for the traveling salesman problem (TSP) based on the Grover Adaptive Search (GAS) The strategy fully considers the reversibility requirement of quantum computing, overcoming the difficulty that the used qubits cannot be simply overwritten or released. For the seven-node TSP, we only need 31 qubits, and the success rate in obtaining the optimal solution is 86.71%.
  arXiv  Detail & Related papers  (2022-12-06T03:54:07Z)
• Towards an Automated Framework for Realizing Quantum Computing Solutions [3.610459670994051]
  We envision a framework that allows users to employ quantum computing solutions in an automatic fashion. We provide proof-of-concept implementations for two different classes of problems which are publicly available on GitHub.
  arXiv  Detail & Related papers  (2022-10-26T18:00:01Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• A Hybrid Quantum-Classical Algorithm for Robust Fitting [47.42391857319388]
  We propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs. We present results obtained using an actual quantum computer.
  arXiv  Detail & Related papers  (2022-01-25T05:59:24Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• Quantum constraint learning for quantum approximate optimization algorithm [0.0]
  This paper introduces a quantum machine learning approach to learn the mixer Hamiltonian required to hard constrain the search subspace. One can directly plug the learnt unitary into the QAOA framework using an adaptable ansatz. We also develop an intuitive metric that uses Wasserstein distance to assess the performance of general approximate optimization algorithms with/without constraints.
  arXiv  Detail & Related papers  (2021-05-14T11:31:14Z)
• Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms [0.0]
  We apply the divide-and-conquer approach to reduce the original problem to a collection of smaller problems. This technique can be applied to any QUBO instance and leads to either an all-classical or a hybrid quantum-classical approach.
  arXiv  Detail & Related papers  (2021-01-19T19:00:40Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.