Curve fitting on a quantum annealer for an advanced navigation method

• URL: http://arxiv.org/abs/2402.15308v1
• Date: Fri, 23 Feb 2024 13:13:28 GMT
• Title: Curve fitting on a quantum annealer for an advanced navigation method
• Authors: Philipp Isserstedt, Daniel Jaroszewski, Wolfgang Mergenthaler, Felix Paul, Bastian Harrach
• Abstract summary: We consider a function that approximates a given set of data points and is written as a finite linear combination of standardized functions. In a real-word use case, we discuss the problem to find an optimized speed profile for a vessel using the framework of dynamic programming.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore the applicability of quantum annealing to the approximation task of curve fitting. To this end, we consider a function that shall approximate a given set of data points and is written as a finite linear combination of standardized functions, e.g., orthogonal polynomials. Consequently, the decision variables subject to optimization are the coefficients of that expansion. Although this task can be accomplished classically, it can also be formulated as a quadratic unconstrained binary optimization problem, which is suited to be solved with quantum annealing. Given the size of the problem stays below a certain threshold, we find that quantum annealing yields comparable results to the classical solution. Regarding a real-word use case, we discuss the problem to find an optimized speed profile for a vessel using the framework of dynamic programming and outline how the aforementioned approximation task can be put into play.

Related papers

• Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer [0.0]
  We study the projective quantum eigensolver (PQE) approach to optimizing unitary coupled cluster wave functions on quantum hardware. The algorithm uses projections of the Schr"odinger equation to efficiently bring the trial state closer to an eigenstate of the Hamiltonian. We present numerical evidence of superiority over both the optimization introduced in arXiv:2102.00345 and VQE optimized using the Broyden Fletcher Goldfarb Shanno (BFGS) method.
  arXiv  Detail & Related papers  (2024-10-19T15:03:59Z)
• A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation [8.648660469053342]
  A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. We propose a solution via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties.
  arXiv  Detail & Related papers  (2024-05-28T15:42:15Z)
• Quantum Realization of the Finite Element Method [0.0]
  This paper presents a quantum algorithm for the solution of second-order linear elliptic partial differential equations discretized by $d$-linear finite elements. An essential step in the construction is a BPX preconditioner, which transforms the linear system into a sufficiently well-conditioned one. We provide a constructive proof demonstrating that, for any fixed dimension, our quantum algorithm can compute suitable functionals of the solution to a given tolerance.
  arXiv  Detail & Related papers  (2024-03-28T15:44:20Z)
• Quantum speedups for stochastic optimization [18.32349609443295]
  We consider the problem of minimizing a continuous function given quantumvitzvariance to an oracle. We provide two new methods for the special case of minimizing a Lipsch avvitz function.
  arXiv  Detail & Related papers  (2023-08-03T07:39:10Z)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• Progress toward favorable landscapes in quantum combinatorial optimization [0.0]
  We focus on algorithms for solving the algorithm optimization problem MaxCut. We study how the structure of the classical optimization landscape relates to the quantum circuit used to evaluate the MaxCut function.
  arXiv  Detail & Related papers  (2021-05-03T18:38:53Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Gradient-Free Methods for Saddle-Point Problem [125.99533416395765]
  We generalize the approach Gasnikov et. al., 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle. Our approach reduces $fracnlog n$ times the required number of oracle calls. In the second part of the paper, we analyze the case when such an assumption cannot be made, we propose a general approach on how to modernize the method to solve this problem.
  arXiv  Detail & Related papers  (2020-05-12T16:44:27Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

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.