A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer

• URL: http://arxiv.org/abs/2211.14064v2
• Date: Wed, 24 May 2023 09:07:17 GMT
• Title: A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer
• Authors: Mazen Ali and Matthias Kabel
• Abstract summary: Partial differential equations (PDEs) are used in material or flow simulation. The most promising route to useful deployment of quantum processors in the short to near term are so-called hybrid variational quantum algorithms (VQAs) We conduct an extensive study of utilizing VQAs on real quantum devices to solve the simplest prototype of a PDE -- the Poisson equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation. Currently, the most promising route to useful deployment of quantum processors in the short to near term are so-called hybrid variational quantum algorithms (VQAs). Thus, variational methods for PDEs have been proposed as a candidate for quantum advantage in the noisy intermediate scale quantum (NISQ) era. In this work, we conduct an extensive study of utilizing VQAs on real quantum devices to solve the simplest prototype of a PDE -- the Poisson equation. Although results on noiseless simulators for small problem sizes may seem deceivingly promising, the performance on quantum computers is very poor. We argue that direct resolution of PDEs via an amplitude encoding of the solution is not a good use case within reach of today's quantum devices -- especially when considering large system sizes and more complicated non-linear PDEs that are required in order to be competitive with classical high-end solvers.

Related papers

• A New Variational Quantum Algorithm Based on Lagrange Polynomial Encoding to Solve Partial Differential Equations [0.0]
  Partial Differential Equations (PDEs) serve as the cornerstone for a wide range of scientific endeavours. Finding solutions to PDEs often exceeds the capabilities of traditional computational approaches. Recent advances in quantum computing have triggered a growing interest from researchers for the design of quantum algorithms for solving PDEs.
  arXiv  Detail & Related papers  (2024-07-23T10:11:44Z)
• Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance [7.501820750179541]
  This paper introduces the variational quantum eigensolver (VQE) to solve portfolio optimization problems in finance. We implement the HDC experiments on the superconducting quantum computer Wu Kong with up to 55 qubits. The HDC scheme shows great potential for achieving quantum advantage in the NISQ era.
  arXiv  Detail & Related papers  (2024-03-07T07:45:47Z)
• Variational Quantum Eigensolvers with Quantum Gaussian Filters for solving ground-state problems in quantum many-body systems [2.5425769156210896]
  We present a novel quantum algorithm for approximating the ground-state in quantum many-body systems. Our approach integrates Variational Quantum Eigensolvers (VQE) with Quantum Gaussian Filters (QGF) Our method shows improved convergence speed and accuracy, particularly under noisy conditions.
  arXiv  Detail & Related papers  (2024-01-24T14:01:52Z)
• 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-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)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• 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)
• 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)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)
• Large-scale quantum hybrid solution for linear systems of equations [0.0]
  We introduce and implement a hybrid quantum algorithm for solving linear systems of equations with exponential speedup. We solve experimentally a $217$-dimensional problem on superconducting IBMQ devices, a record for linear system solution on quantum computers.
  arXiv  Detail & Related papers  (2020-03-28T11:23:05Z)

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.