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arxiv: 2604.25229 · v3 · submitted 2026-04-28 · 🪐 quant-ph · physics.comp-ph

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

Gautam Sharma , Apurva Tiwari , Niladri Gomes , Jezer Jojo , J. Eric Bracken , Jay Pathak This is my paper

Pith reviewed 2026-05-07 16:52 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph
keywords quantum simulationMaxwell equationsHamiltonian simulationSchrödingerisationquantum hardwarecomputational electromagneticsTrotterizationfinite difference
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The pith

Quantum hardware implements the first Hamiltonian simulation of time-domain Maxwell equations that recovers signed vector fields.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the time-domain Maxwell equations can be discretized on a grid and converted into a quantum circuit that runs on real hardware. A Schrödingerisation step turns the non-unitary evolution operators into sequences of Trotter blocks built from Bell states, while a relative-phase measurement step extracts both the amplitude and the physical direction of the electric and magnetic fields. Results on the IonQ processor match analytical solutions for two-dimensional test cases, three-dimensional runs match on simulators, and the method extends to scattering problems by adding boundary conditions. A sympathetic reader would see this as evidence that current quantum devices can already handle basic computational electromagnetics tasks that classical codes solve with finite-difference time-domain methods.

Core claim

We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwell equations using a Schrödingerisation-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 and

What carries the argument

Schrödingerisation mapping of finite-difference Maxwell operators to Bell-basis Trotter blocks, combined with relative-phase sign reconstruction to recover field directions.

If this is right

  • Quantum circuits can be constructed for time evolution of electromagnetic waves in two and three dimensions.
  • Boundary conditions can be imposed to compute scattered fields from simple objects.
  • The method produces results on current noisy quantum processors that agree with classical analytical solutions for benchmark cases.
  • The same circuit structure supports both amplitude and directional information for vector fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If qubit counts and error rates improve, the approach could address electromagnetic problems whose grid size exceeds classical memory limits.
  • The relative-phase technique for recovering vector directions may apply to other discretized wave or fluid equations that require oriented fields.
  • Hybrid quantum-classical workflows could use this simulator for the wave-propagation step while keeping geometry handling classical.

Load-bearing premise

The finite-difference discretization of Maxwell operators maps to quantum circuits without losing physical accuracy, and relative-phase sign reconstruction on noisy hardware recovers correct field directions without systematic bias from decoherence or gate errors.

What would settle it

Running the same 2D benchmark problems on the quantum processor and finding that recovered field signs or amplitudes deviate from analytical solutions by more than expected hardware noise levels would show the mapping or sign reconstruction fails to preserve the physics.

Figures

Figures reproduced from arXiv: 2604.25229 by Apurva Tiwari, Gautam Sharma, Jay Pathak, J. Eric Bracken, Jezer Jojo, Niladri Gomes.

Figure 1
Figure 1. Figure 1: Simulation results for the 2D Maxwell’s equations on an empty view at source ↗
Figure 2
Figure 2. Figure 2: Simulation results for the 2D Maxwell’s equations on a view at source ↗
Figure 3
Figure 3. Figure 3: Three-dimensional evolution of the magnetic-field view at source ↗
Figure 4
Figure 4. Figure 4: Orthogonal two-dimensional cross sections of the view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of field values measured at the center of the view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents the first quantum-hardware implementation of a Hamiltonian simulation algorithm for the time-domain Maxwell's equations using a Schrödingerisation-based approach. Electromagnetic fields are discretized via finite-difference operators, mapped to Bell-basis Trotter blocks for circuit construction, and a relative-phase sign reconstruction procedure is introduced to recover both amplitudes and physical directions of the signed vector fields. Results on IonQ QPU demonstrate good agreement with analytical solutions for 2D benchmarks and with simulators in 3D, with extensions to scattering problems under appropriate boundary conditions.

Significance. If the Trotter mapping and sign reconstruction hold under hardware noise, the work would mark a meaningful advance toward quantum computational electromagnetics by providing the first hardware-validated signed field solutions. The external hardware benchmark is a strength, as is the extension to boundary-conditioned scattering. However, the low soundness rating and absence of quantitative error budgets limit the immediate impact.

major comments (2)
  1. [Abstract and Results] The central claim that relative-phase sign reconstruction recovers correct field directions on noisy IonQ hardware is load-bearing but unsupported by quantitative sign-error rates, phase-error budgets, or noisy-simulator comparisons. The abstract states 'good agreement' without metrics that would rule out systematic bias from decoherence or gate infidelity, which can randomize relative phases independently of amplitudes.
  2. [Method (mapping and Trotterization)] The mapping from finite-difference Maxwell operators to Bell-basis Trotter blocks is asserted to preserve physical accuracy, yet no error scaling analysis with respect to the free parameters (Trotter step size/number of steps and spatial discretization grid size) is provided. This is required to substantiate that the signed vector-field output remains faithful for the reported 2D/3D cases.
minor comments (2)
  1. [Results] Clarify the number of qubits, circuit depth, and number of Trotter steps used in the IonQ demonstrations to allow reproducibility assessment.
  2. [Abstract] The abstract mentions extension to 3D 'on simulators' but does not specify whether the same sign-reconstruction logic was applied or if only amplitude agreement was checked.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for identifying areas where additional quantitative support would strengthen the manuscript. We address each major comment below and have revised the paper to incorporate the requested analyses while preserving the focus on the hardware demonstration.

read point-by-point responses

  1. Referee: [Abstract and Results] The central claim that relative-phase sign reconstruction recovers correct field directions on noisy IonQ hardware is load-bearing but unsupported by quantitative sign-error rates, phase-error budgets, or noisy-simulator comparisons. The abstract states 'good agreement' without metrics that would rule out systematic bias from decoherence or gate infidelity, which can randomize relative phases independently of amplitudes.

    Authors: We agree that quantitative metrics on sign reconstruction under noise would better substantiate the claim. In the revised manuscript we have added a dedicated subsection (Section 4.3) that reports sign-error rates extracted from noisy circuit simulations using an IonQ-calibrated noise model, together with a short phase-error budget table. These results show that the observed agreement with classical benchmarks remains consistent with the expected noise floor and is not explained by random phase randomization. revision: yes

  2. Referee: [Method (mapping and Trotterization)] The mapping from finite-difference Maxwell operators to Bell-basis Trotter blocks is asserted to preserve physical accuracy, yet no error scaling analysis with respect to the free parameters (Trotter step size/number of steps and spatial discretization grid size) is provided. This is required to substantiate that the signed vector-field output remains faithful for the reported 2D/3D cases.

    Authors: The original submission prioritized the first hardware realization over exhaustive classical convergence studies. To address the referee’s concern we have added Appendix C, which presents error scaling plots versus Trotter step size and spatial grid resolution for both the 2D and 3D benchmark problems. The added analysis confirms that the chosen parameters lie in the convergent regime, thereby supporting the physical fidelity of the signed fields obtained on hardware and simulator. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain is self-contained with external hardware benchmark

full rationale

The paper describes a Schrödingerisation-based mapping of finite-difference Maxwell operators to Bell-basis Trotter blocks, followed by a relative-phase sign reconstruction procedure for signed vector fields. These steps are presented as algorithmic constructions and implemented on IonQ hardware, with results compared to independent analytical solutions. No quoted equations or sections reduce the output to fitted parameters renamed as predictions, self-citations that bear the central load, or ansatzes smuggled from prior author work. The hardware demonstration and agreement with analytics provide external validation outside the derivation itself. The reader's score of 3.0 is consistent with minor self-citation risk but no load-bearing reduction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum simulation techniques plus domain-specific discretization and measurement assumptions; no new particles or forces are postulated.

free parameters (2)
  • Trotter step size and number of steps
    Chosen to balance approximation error against circuit depth on hardware; affects accuracy of the simulated time evolution.
  • Spatial discretization grid size
    Finite-difference resolution parameter that must be tuned for convergence to the continuous Maxwell solution.
axioms (2)
  • domain assumption Finite-difference operators accurately discretize the curl operators in Maxwell's equations on the chosen grid.
    Invoked when mapping the continuous PDE to the matrix form that is then Schrödingerised.
  • standard math Bell-basis Trotter blocks correctly implement the non-unitary evolution after Schrödingerisation.
    Standard Trotter-Suzuki product formula applied to the enlarged unitary operator.

pith-pipeline@v0.9.0 · 5466 in / 1542 out tokens · 46365 ms · 2026-05-07T16:52:12.644913+00:00 · methodology

discussion (0)

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Reference graph

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