Polynomial-time Solver of Tridiagonal QUBO and QUDO problems with Tensor Networks

• URL: http://arxiv.org/abs/2309.10509v3
• Date: Mon, 22 Apr 2024 15:12:10 GMT
• Title: Polynomial-time Solver of Tridiagonal QUBO and QUDO problems with Tensor Networks
• Authors: Alejandro Mata Ali, Iñigo Perez Delgado, Marina Ristol Roura, Aitor Moreno Fdez. de Leceta,
• Abstract summary: We present an algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization (QUBO) problems and Quadratic Unconstrained Discrete Optimization (QUDO) problems with one-neighbor interactions. Our method is based on the simulation of a quantum state to which we will apply an imaginary time evolution and perform a series of partial traces to obtain the state of maximum amplitude.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization (QUBO) problems and Quadratic Unconstrained Discrete Optimization (QUDO) problems with one-neighbor interactions using the quantum-inspired technology of tensor networks. Our method is based on the simulation of a quantum state to which we will apply an imaginary time evolution and perform a series of partial traces to obtain the state of maximum amplitude, since it will be the optimal state. We will also deal with the degenerate case and check the polynomial complexity of the algorithm.

Related papers

• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields [0.0]
  We introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT) IST-SAT solves quantum spin glass optimization problems using high-frequency oscillating transverse fields.
  arXiv  Detail & Related papers  (2024-08-13T02:09:30Z)
• An entanglement perspective on the quantum approximate optimization algorithm [0.0]
  We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits. We also investigate the entanglement spectrum in connection with random matrix theory.
  arXiv  Detail & Related papers  (2022-06-14T17:37:44Z)
• How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization [11.095381943951539]
  We present a toolkit of methods to transform almost arbitrary problems to Quadratic unconstrained binary optimization (QUBO) We showcase the usage of our approaches on two example problems (ratio cut and logistic regression)
  arXiv  Detail & Related papers  (2022-04-23T09:43:06Z)
• A quantum-inspired tensor network method for constrained combinatorial optimization problems [5.904219009974901]
  We propose a quantum-inspired tensor-network-based algorithm for general locally constrained optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem. Our results show the effectiveness of this construction and potential applications.
  arXiv  Detail & Related papers  (2022-03-29T05:44:07Z)
• 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)
• 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)
• Polynomial unconstrained binary optimisation inspired by optical simulation [52.11703556419582]
  We propose an algorithm inspired by optical coherent Ising machines to solve the problem of unconstrained binary optimization. We benchmark the proposed algorithm against existing PUBO algorithms, and observe its superior performance. The application of our algorithm to protein folding and quantum chemistry problems sheds light on the shortcomings of approxing the electronic structure problem by a PUBO problem.
  arXiv  Detail & Related papers  (2021-06-24T16:39:31Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Multi-block ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers [3.04585143845864]
  We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization problems. We show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms) The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit.
  arXiv  Detail & Related papers  (2020-01-07T14:43:13Z)

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.