A Faster Algorithm for the Free Energy in One-Dimensional Quantum Systems

• URL: http://arxiv.org/abs/2402.19030v1
• Date: Thu, 29 Feb 2024 10:42:18 GMT
• Title: A Faster Algorithm for the Free Energy in One-Dimensional Quantum Systems
• Authors: Samuel O. Scalet
• Abstract summary: We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed. We propose an algorithm outperforming this resultally and give rigorous bounds on its runtime.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed [Fawzi et al., 2022]. Combining several algorithmic techniques previously used for related problems, we propose an algorithm outperforming this result asymptotically and give rigorous bounds on its runtime. Our main techniques are the use of Araki expansionals, known from results on the nonexistence of phase transitions, and a matrix product operator construction. We also review a related approach using the Quantum Belief Propagation [Kuwahara et al., 2018], which in combination with our findings yields an equivalent result.

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)
• On the quantum time complexity of divide and conquer [42.7410400783548]
  We study the time complexity of quantum divide and conquer algorithms for classical problems. We apply these theorems to an array of problems involving strings, integers, and geometric objects.
  arXiv  Detail & Related papers  (2023-11-28T01:06:03Z)
• Hybrid classical-quantum branch-and-bound algorithm for solving integer linear problems [0.0]
  Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. The solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. We propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits.
  arXiv  Detail & Related papers  (2023-11-16T09:19:01Z)
• A Universal Quantum Algorithm for Weighted Maximum Cut and Ising Problems [0.0]
  We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system.
  arXiv  Detail & Related papers  (2023-06-10T23:28:13Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Concise and Efficient Quantum Algorithms for Distribution Closeness Testing [0.2741266294612775]
  We study the impact of quantum computation on the fundamental problem of testing the property of distributions. We propose the currently best quantum algorithms for this problem under the metrics of $l1$-distance and $l2$-distance.
  arXiv  Detail & Related papers  (2023-02-13T04:03:59Z)
• 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)
• Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis [59.545114016224254]
  Quantum algorithms for topological data analysis seem to provide an exponential advantage over the best classical approach. We show that the central task of TDA -- estimating Betti numbers -- is intractable even for quantum computers. We argue that an exponential quantum advantage can be recovered if the input data is given as a specification of simplices.
  arXiv  Detail & Related papers  (2022-09-28T17:53:25Z)
• Limitations of variational quantum algorithms: a quantum optimal transport approach [11.202435939275675]
  We obtain extremely tight bounds for standard NISQ proposals in both the noisy and noiseless regimes. The bounds limit the performance of both circuit model algorithms, such as QAOA, and also continuous-time algorithms, such as quantum annealing.
  arXiv  Detail & Related papers  (2022-04-07T13:58:44Z)
• 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)
• Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra [53.46106569419296]
  We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression. We argue that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise.
  arXiv  Detail & Related papers  (2020-11-09T01:13:07Z)

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.