Practical Quantum Computing: solving the wave equation using a quantum approach

• URL: http://arxiv.org/abs/2003.12458v2
• Date: Mon, 14 Jun 2021 13:46:05 GMT
• Title: Practical Quantum Computing: solving the wave equation using a quantum approach
• Authors: Adrien Suau, Gabriel Staffelbach, Henri Calandra
• Abstract summary: We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. Our implementation proves experimentally that some PDE can be solved on a quantum computer.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit. On the other side, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the "direct" quantum algorithm: the wave equation solver devised in [PCS. Costa, S. Jordan, A. Ostrander, Phys. Rev. A 99, 012323, 2019]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great details the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

Related papers

• A quantum annealing approach to the minimum distance problem of quantum codes [0.0]
  We introduce an approach to compute the minimum distance of quantum stabilizer codes by reformulating the problem as a Quadratic Unconstrained Binary Optimization problem. We demonstrate practical viability of our method by comparing the performance of purely classical algorithms with the D-Wave Advantage 4.1 quantum annealer.
  arXiv  Detail & Related papers  (2024-04-26T21:29:42Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity [1.0360348400670518]
  We show that a minimal SWAP-gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing.
  arXiv  Detail & Related papers  (2024-02-01T10:32:05Z)
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
  Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-10-11T15:59:54Z)
• Verifiably Exact Solution of the Electronic Schr\"odinger Equation on Quantum Devices [0.0]
  We present an algorithm that yields verifiably exact solutions of the many-electron Schr"odinger equation. We demonstrate the algorithm on both quantum simulators and noisy quantum computers.
  arXiv  Detail & Related papers  (2023-03-01T19:00:00Z)
• Quantum-inspired optimization for wavelength assignment [51.55491037321065]
  We propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. Our results pave the way to the use of quantum-inspired algorithms for practical problems in telecommunications.
  arXiv  Detail & Related papers  (2022-11-01T07:52:47Z)
• Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer [13.528362112761805]
  We show the largest-to-date execution of a quantum optimization algorithm that preserves constraints on quantum hardware. We execute XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace, using up to 20 qubits and a two-qubit gate depth of up to 159. We discuss the respective trade-offs of the algorithms and implications for their execution on near-term quantum hardware.
  arXiv  Detail & Related papers  (2022-06-13T16:21:04Z)
• 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)
• Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
  Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task. Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate. The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
  arXiv  Detail & Related papers  (2021-06-06T13:15:25Z)
• VQE Method: A Short Survey and Recent Developments [5.9640499950316945]
  The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been successfully applied to solve the electronic Schr"odinger equation for a variety of small molecules. Modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze.
  arXiv  Detail & Related papers  (2021-03-15T16:25:36Z)
• 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)

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.