Towards Quantum Computational Mechanics

• URL: http://arxiv.org/abs/2312.03791v3
• Date: Mon, 07 Oct 2024 12:53:24 GMT
• Title: Towards Quantum Computational Mechanics
• Authors: Burigede Liu, Michael Ortiz, Fehmi Cirak,
• Abstract summary: We show how quantum computing can be used to solve representative element volume (RVE) problems in computational homogenisation. Our quantum RVE solver attains exponential acceleration with respect to classical solvers.
• Score: 1.530480694206666
• License:
• Abstract: The advent of quantum computers, operating on entirely different physical principles and abstractions from those of classical digital computers, sets forth a new computing paradigm that can potentially result in game-changing efficiencies and computational performance. Specifically, the ability to simultaneously evolve the state of an entire quantum system leads to quantum parallelism and interference. Despite these prospects, opportunities to bring quantum computing to bear on problems of computational mechanics remain largely unexplored. In this work, we demonstrate how quantum computing can indeed be used to solve representative volume element (RVE) problems in computational homogenisation with polylogarithmic complexity of $\mathcal{O}((\log N)^c)$, compared to $\mathcal{O}(N^c)$ in classical computing. Thus, our quantum RVE solver attains exponential acceleration with respect to classical solvers, bringing concurrent multiscale computing closer to practicality. The proposed quantum RVE solver combines conventional algorithms such as a fixed-point iteration for a homogeneous reference material and the Fast Fourier Transform (FFT). However, the quantum computing reformulation of these algorithms requires a fundamental paradigm shift and a complete rethinking and overhaul of the classical implementation. We employ or develop several techniques, including the Quantum Fourier Transform (QFT), quantum encoding of polynomials, classical piecewise Chebyshev approximation of functions and an auxiliary algorithm for implementing the fixed-point iteration and show that, indeed, an efficient implementation of RVE solvers on quantum computers is possible. We additionally provide theoretical proofs and numerical evidence confirming the anticipated $\mathcal{O} \left ((\log N)^c \right)$ complexity of the proposed solver.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum Circuit Learning on NISQ Hardware [0.0]
  Current quantum computers are small and error-prone systems. Fault-tolerant quantum computers are not expected to be available in the near future. We show that exemplary QCL circuits with up to three qubits are executable on the IBM quantum computer.
  arXiv  Detail & Related papers  (2024-05-03T13:00:32Z)
• 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)
• 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)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• The Future of Quantum Computing with Superconducting Qubits [2.6668731290542222]
  We see a branching point in computing paradigms with the emergence of quantum processing units (QPUs) Extracting the full potential of computation and realizing quantum algorithms with a super-polynomial speedup will most likely require major advances in quantum error correction technology. Long term, we see hardware that exploits qubit connectivity in higher than 2D topologies to realize more efficient quantum error correcting codes.
  arXiv  Detail & Related papers  (2022-09-14T18:00:03Z)
• 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)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices [0.0]
  We introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical methods for the energies. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
  arXiv  Detail & Related papers  (2020-04-23T18:35:26Z)
• Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers [0.0]
  We combine the so-called seniority-zero, or paired-electron, approximation of computational quantum chemistry with techniques for simulating molecular chemistry on gate-based quantum computers. We show that using the freed-up quantum resources for increasing the basis set can lead to more accurate results and reductions in the necessary number of quantum computing runs.
  arXiv  Detail & Related papers  (2020-01-31T19:44:37Z)

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.