Hardware Realization of a Hamiltonian Simulation Algorithm for Time-Domain Maxwells Equations

• URL: http://arxiv.org/abs/2604.25229v3
• Date: Mon, 04 May 2026 05:35:39 GMT
• Title: Hardware Realization of a Hamiltonian Simulation Algorithm for Time-Domain Maxwells Equations
• Abstract summary: We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to time-domain Maxwells equations.<n>The electromagnetic fields are discretized using finite-difference operators, and the resulting non-unitary matrices are mapped to Bell-basis Trotter blocks.
• Score: 0.5321738009179028
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic fields are discretized using finite-difference operators, and the resulting non-unitary matrices are mapped to Bell-basis Trotter blocks, enabling efficient circuit construction. We introduce a measurement procedure that retrieves not only field amplitudes, but also physical directions of the electric and magnetic field values at select spatial points. Implementing this logic on quantum hardware relies on relative-phase-based sign reconstruction. Numerical results obtained using IonQ QPU, show good agreement with analytical solutions of benchmark problems in two dimensions and on simulators; in three dimensions. We further extend our approach to compute fields scattered from simple bodies, by enforcing appropriate boundary conditions. Our work lays the foundational steps towards realizing quantum-hardware solutions for computational electromagnetics.

Related papers

• Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization [42.22857110018992]
  We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential.<n>We combine Hamiltonian-preserving schemes by Jin and Wen in Commun. Math. Sci. 3(3), 285-315 (2005) with the Schrdingerization method, which embeds the resulting nonunitary semi-discrete dynamics into a unitary Schrdinger type system.
  arXiv  Detail & Related papers  (2026-06-13T02:49:05Z)
• Quantum Signal Processing for Linear PDEs: Circuit Design and Experimental Validation [1.814099487268094]
  We develop end-to-end implementations of quantum circuits compiled to machine-level instructions.<n>We experimentally demonstrate that the QSP-augmented algorithm can provide accurate solutions under realistic hardware constraints.
  arXiv  Detail & Related papers  (2026-05-29T21:21:32Z)
• Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions [45.88028371034407]
  Block encoding provides the standard method for accessing matrix data within quantum circuits.<n>We present a unified framework for efficiently block encoding finite-difference discretizations of the Laplacian.
  arXiv  Detail & Related papers  (2026-03-12T19:35:16Z)
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks [0.0]
  We present an efficient classical algorithm for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions.<n>Exact diagonalization of the unitary circuit in combination with Networks allows simulation of the wave equation with a resolution of $1013$ grid points on a laptop.
  arXiv  Detail & Related papers  (2025-04-15T13:36:08Z)
• Compact quantum algorithms for time-dependent differential equations [0.0]
  We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems.<n>We generate hybrid quantum-classical algorithms that efficiently perform matrix-vector multiplication and matrix inversion operations.
  arXiv  Detail & Related papers  (2024-05-16T02:14:58Z)
• Polynomial-time Solver of Tridiagonal QUBO, QUDO and Tensor QUDO problems with Tensor Networks [41.94295877935867]
  We present a quantum-inspired tensor network algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization problems.<n>We also solve the more general quadratic unconstrained discrete optimization problems with one-neighbor interactions in a lineal chain.
  arXiv  Detail & Related papers  (2023-09-19T10:45:15Z)
• Forward and Backward Constrained Bisimulations for Quantum Circuits using Decision Diagrams [3.788308836856851]
  We develop efficient methods for the simulation of quantum circuits on classic computers. In particular, we show that constrained bisimulation can boost decision-diagram-based quantum circuit simulation by several orders of magnitude.
  arXiv  Detail & Related papers  (2023-08-18T12:40:47Z)
• Quantum simulation of Maxwell's equations via Schr\"odingersation [27.193565893837356]
  We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr"odingersation approach. Instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework.
  arXiv  Detail & Related papers  (2023-08-16T14:52:35Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Simulation of Thermal Relaxation in Spin Chemistry Systems on a Quantum Computer Using Inherent Qubit Decoherence [53.20999552522241]
  We seek to take advantage of qubit decoherence as a resource in simulating the behavior of real world quantum systems. We present three methods for implementing the thermal relaxation. We find excellent agreement between our results, experimental data, and the theoretical prediction.
  arXiv  Detail & Related papers  (2020-01-03T11:48:11Z)

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.