Quantum algorithms for solving a drift-diffusion equation

• URL: http://arxiv.org/abs/2505.21221v1
• Date: Tue, 27 May 2025 14:09:14 GMT
• Title: Quantum algorithms for solving a drift-diffusion equation
• Authors: Ellen Devereux, Animesh Datta,
• Abstract summary: We present three quantum algorithms for solving a drift-diffusion equation.<n>They rely on a quantum linear system solver, a quantum random walk, and the quantum Fourier transform.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present three quantum algorithms for solving a multi-dimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum random walk, and the quantum Fourier transform. We compare the complexities of these methods to their classical counterparts, finding that diagonalisation via the quantum Fourier transform offers a quantum computational advantage for solving linear partial differential equations at a fixed final time. We employ a multidimensional amplitude estimation process to extract the full probability distribution from the quantum computer.

Related papers

• Sequential Quantum Computing [41.94295877935867]
  We propose and experimentally demonstrate sequential quantum computing (SQC), a paradigm that utilizes multiple or heterogeneous quantum processors.<n>SQC overcomes the limitations of each type of quantum computer by combining their complementary strengths.<n>These results highlight SQC as a powerful and versatile approach for addressing complex quantum optimization problems.
  arXiv  Detail & Related papers  (2025-06-25T17:51:29Z)
• Quantum Circuits for the Black-Scholes equations via Schrödingerisation [26.57843095806779]
  We construct quantum circuits for the Black-Scholes equations.<n>We will conduct a thorough complexity analysis to highlight the quantum advantages of our approach.
  arXiv  Detail & Related papers  (2025-05-07T10:21:12Z)
• Quantum smoothed particle hydrodynamics algorithm inspired by quantum walks [0.0]
  We propose a quantum algorithm for the time-dependent smoothed particle hydrodynamics (SPH) method.<n>Our algorithm uses concepts from discrete-time quantum walks to solve the one-dimensional advection partial differential equation.<n>We construct a quantum circuit to carry out the calculations for a two-particle system over one, two and three timesteps.
  arXiv  Detail & Related papers  (2025-03-07T13:09:33Z)
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions [39.58317527488534]
  We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• Variational methods for solving high dimensional quantum systems [0.0]
  We explore the effectiveness of three variational methods for solving high-dimensional quantum systems. We apply these methods to two different quantum systems: the fermi-Hubbard model in condensed matter physics and the Schwinger model in high energy physics. We calculate the ground state of both quantum systems and compare the results obtained using the three variational methods.
  arXiv  Detail & Related papers  (2024-04-17T15:46:27Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Quantum Circuit Completeness: Extensions and Simplifications [44.99833362998488]
  The first complete equational theory for quantum circuits has only recently been introduced. We simplify the equational theory by proving that several rules can be derived from the remaining ones. The complete equational theory can be extended to quantum circuits with ancillae or qubit discarding.
  arXiv  Detail & Related papers  (2023-03-06T13:31:27Z)
• 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)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods [1.802439717192088]
  We explore utilizing quantum computers for the purpose of solving differential equations. We devise and simulate corresponding digital quantum circuits, and implement and run a 6$mathrmth$ order Gauss-Legendre collocation method. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.
  arXiv  Detail & Related papers  (2020-12-17T09:49:35Z)
• Practical Quantum Computing: solving the wave equation using a quantum approach [0.0]
  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.
  arXiv  Detail & Related papers  (2020-03-27T15:05:31Z)

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.