arxiv: 2604.28121 · v1 · submitted 2026-04-30 · 🪐 quant-ph · physics.comp-ph

Recognition: unknown

Quantum Lattice Boltzmann Solutions for Transport under 3D Spatially Varying Advection on Trapped Ion Hardware

Sayonee Ray , Jezer Jojo , Jason Iaconis , Abeynaya Gnanasekaran , Apurva Tiwari , Martin Roetteler , Chris Hill , Jay Pathak

Authors on Pith no claims yet

Pith reviewed 2026-05-07 04:52 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph

keywords quantum lattice boltzmannadvection-diffusion equationtrapped-ion quantum computingnon-uniform velocity fieldsfluid dynamics simulationquantum cfdwall boundariesdensity readout

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The pith

Quantum lattice Boltzmann methods on trapped-ion hardware simulate 3D transport with non-uniform advection.

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

The paper establishes that the quantum lattice Boltzmann method can be implemented on trapped-ion quantum hardware to simulate the advection-diffusion equation when the velocity field varies across space. This advances prior QLBM work by moving beyond constant-velocity cases to settings that match the non-uniform flows typical in conventional computational fluid dynamics. The authors execute the algorithm on IonQ trapped-ion processors, including a 64-qubit system, and show that the macroscopic advection-diffusion behavior emerges from quantum circuits encoding local streaming and collision steps. They identify repeated density readout and reloading as a scaling bottleneck and propose matrix product state shadow tomography as one mitigation. They also introduce and test a new quantum implementation of wall boundaries while discussing prospects for higher-complexity problems.

Core claim

The dynamics is formulated in terms of mesoscopic particle distribution functions governed by a discrete Boltzmann transport equation, comprising local streaming and collision operations. In this work, the resulting macroscopic behavior corresponds to the advection-diffusion equation. Building upon recent progress in QLBM implementations, we advance towards more realistic problem settings that better reflect conventional CFD requirements. We address, for the first time, transport under the action of non uniform velocity fields on quantum hardware. We implement our demonstration using IonQ's trapped-ion systems including Forte generation systems and a 64-qubit Barium development system. We id

What carries the argument

The Quantum Lattice Boltzmann Method (QLBM), which encodes the discrete Boltzmann transport equation's local streaming and collision steps into quantum circuits, together with a position-dependent encoding of non-uniform velocity that produces the target advection-diffusion equation at the macroscopic level.

If this is right

Quantum hardware can now simulate advection-diffusion transport with spatially varying velocities rather than only uniform flows.
Density readout is established as a central bottleneck, addressable by methods such as MPS shadow tomography to support larger grids and complex distributions.
A novel quantum circuit method for wall boundaries extends QLBM applicability to bounded domains.
The demonstration indicates that QLBM can scale toward higher-complexity fluid transport problems on future quantum systems.

Where Pith is reading between the lines

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

The same encoding strategy for non-uniform fields could be tested on other quantum hardware platforms to compare connectivity advantages for streaming steps.
If readout improvements succeed, the approach may generalize to hybrid quantum-classical workflows for engineering design problems that require repeated transport solves.
Extending the method to velocity fields that also vary in time would enable simulation of unsteady flows without changing the core circuit structure.

Load-bearing premise

The quantum circuit implementation of local streaming and collision steps, combined with the chosen encoding of non-uniform velocity, reproduces the target macroscopic advection-diffusion equation with acceptable error on current noisy trapped-ion hardware.

What would settle it

Running the quantum circuit on a test case with a known linear velocity gradient, extracting the evolved density field via measurement, and comparing it to the solution of the classical advection-diffusion equation for the same initial data and velocity field; large deviations beyond hardware noise levels would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.28121 by Abeynaya Gnanasekaran, Apurva Tiwari, Chris Hill, Jason Iaconis, Jay Pathak, Jezer Jojo, Martin Roetteler, Sayonee Ray.

**Figure 1.** Figure 1: QLBM pipeline used in this work. We efficiently encode the initial density distribution and velocity field into quantum operators. The MPS state view at source ↗

**Figure 2.** Figure 2: Top: Reconstructed 3D density distribution from the QPU at t = 1 and t = 3, together with the absolute error relative to the exact solution. Bottom: Fidelity, |⟨ϕ|ψ⟩|2 , for the ideal simulation and QPU runs. The simulation includes only finite-shot error, whereas the QPU data also include hardware noise. MPS smoothing used for readout post-processing. The circuit uses ∼ 300 two-qubit gates on 21 qubits, i… view at source ↗

**Figure 3.** Figure 3: (Top) Infidelity of MPS compression of ideal statevector during 3D view at source ↗

**Figure 4.** Figure 4: Fidelity |⟨ψ|ϕ⟩|2 of ideal simulation with KDE (top) and MPS smoothing (bottom) techniques with statevector simulation on a 163 grid view at source ↗

**Figure 5.** Figure 5: Effect of KDE and MPS smoothing techniques on a view at source ↗

**Figure 7.** Figure 7: Fidelity | ⟨ψ| ϕ⟩|2 on IonQ Forte-1 QPU with shadow MPS (solid lines) with M = 25 settings, 20K shots total vs. direct state tomography with MPS smoothing (dashed lines) on a 16×16×16 grid. Blue circle and purple squares show results without and with KDE smoothing respectively. is needed to lessen the impact of noise and avoid a steep degradation in the quality of reconstruction. 1 2 3 4 5 6 1 0.9 0.8 0.7 … view at source ↗

**Figure 6.** Figure 6: Fidelity | ⟨ψ| ϕ⟩|2 of ideal simulation with different number of shots with shadow MPS (solid lines) with M = 25 settings and direct state tomography with MPS smoothing (dashed lines) on a 16 × 16 × 16 grid. Shadow MPS outperforms even with a limited budget of 1,000 shots. Next, we evaluate both approaches on the IonQ Forte-1 QPU with 20,000 total shots per time step, M = 25 settings and the results are shown in view at source ↗

**Figure 8.** Figure 8: Fidelity | ⟨ψ| ϕ⟩|2 on the IonQ Forte-1 noisy simulator with shadow MPS (solid line) with M = 50 settings, 50K shots total vs. direct state tomography with MPS smoothing (dashed line) on a 32×32×32 grid. Results with noisy simulator with (green triangles) and without (purple squares) KDE smoothing are shown. Ideal simulation results (blue circles) with the same number of shots are also shown for reference.… view at source ↗

**Figure 10.** Figure 10: Simulation of D2Q5 advection-diffusion on a view at source ↗

**Figure 11.** Figure 11: Simulation of species diffusing from the surface of a solid cube view at source ↗

read the original abstract

The Quantum Lattice Boltzmann Method (QLBM) has emerged as one of the most promising quantum computing approaches for the numerical simulation of problems in computational fluid dynamics (CFD). The dynamics is formulated in terms of mesoscopic particle distribution functions governed by a discrete Boltzmann transport equation, comprising local streaming and collision operations. In this work, the resulting macroscopic behavior corresponds to the advection-diffusion equation, which we adopt as a canonical model problem for transport phenomena. Building upon recent progress in QLBM implementations, we advance towards more realistic problem settings that better reflect conventional CFD requirements. We address, for the first time, transport under the action of non uniform velocity fields on quantum hardware. We implement our demonstration using IonQ's trapped-ion systems including Forte generation systems and a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We identify the density readout and subsequent reloading of the fluid density as a potential bottleneck of the current algorithm and discuss several approaches to mitigate this bottleneck. We identify the use of MPS shadow tomography as a promising method to efficiently scale the readout to large system with complex density distributions. Lastly, we introduce and simulate a novel method to implement wall boundaries for advection-diffusion in QLBM, and discuss the prospects of scaling to higher-complexity problems.

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.

Desk Editor's Note private letter to a colleague

First QLBM hardware run with non-uniform velocity on trapped ions, but the evidence that the circuit recovers the target advection-diffusion equation remains thin.

read the letter

The paper's main advance is running a quantum lattice Boltzmann simulation for advection-diffusion with spatially varying velocity fields on IonQ trapped-ion hardware, including the 64-qubit Barium development system. This moves past the uniform-flow demonstrations that existed before. They encode the position dependence into the local collision and streaming steps, execute on real devices, and add a new boundary-condition method for walls that they test in simulation. They also call out the density readout and reload step as the scaling limit and point to MPS shadow tomography as a practical mitigation. Those pieces are concrete and useful for anyone trying to move QLBM toward engineering-relevant flows. The hardware choice and the explicit discussion of NISQ constraints give the work a practical flavor that earlier theoretical QLBM papers often lack. The boundary method looks like a straightforward addition that could be adopted elsewhere. The soft spot is validation. The claim that the implementation reproduces the macroscopic advection-diffusion equation rests on the assumption that the velocity encoding plus noisy circuit plus readout still yields the correct moments and Chapman-Enskog expansion. The abstract flags readout as a bottleneck and only discusses fixes, which suggests the reported runs may still use the unmitigated procedure. Without reported error metrics, mass-conservation checks, or direct comparisons to classical solvers at the demonstrated sizes, it is difficult to tell whether lattice artifacts or readout bias are distorting the advection term. The stress-test concern about the readout accumulating bias and the encoding introducing non-local effects therefore lands. This is aimed at groups working on quantum algorithms for fluid dynamics or lattice methods on NISQ hardware. A reader who wants to see actual trapped-ion numbers and scaling ideas will find value. The work is coherent enough on its own terms to merit peer review, though any referee will ask for tighter quantitative validation of the macroscopic equation. I would send it out rather than desk-reject.

Referee Report

3 major / 3 minor

Summary. The paper claims to deliver the first experimental demonstration on trapped-ion quantum hardware of the Quantum Lattice Boltzmann Method (QLBM) for the advection-diffusion equation under spatially varying (non-uniform) 3D velocity fields. The approach encodes the velocity into local collision and streaming steps, is executed on IonQ Forte and a 64-qubit barium development system, identifies the density readout/reload step as a practical bottleneck, discusses mitigation via MPS shadow tomography, and introduces a novel wall-boundary implementation for QLBM.

Significance. If the hardware results are shown to recover the target macroscopic advection-diffusion equation with controlled error, the work would constitute a meaningful advance in quantum CFD by moving QLBM beyond uniform advection to more realistic non-uniform transport on actual NISQ devices. The explicit treatment of the readout bottleneck and the proposal of scalable tomography methods provide concrete engineering guidance for larger simulations. The boundary-condition innovation further broadens applicability. These elements, combined with real-hardware execution up to 64 qubits, position the manuscript as a useful reference for the community even if further validation is required.

major comments (3)

[§4] §4 (Hardware Implementation and Results): The central claim that the chosen encoding of spatially varying velocity into the QLBM collision/streaming circuit reproduces the advection-diffusion PDE with acceptable error on noisy trapped-ion hardware is load-bearing, yet the manuscript supplies only qualitative statements and limited quantitative metrics (e.g., no L2 or L∞ error norms against classical reference solutions, no explicit mass-conservation residuals, and no Chapman-Enskog moment verification for the non-uniform cases). Without these data for the demonstrated system sizes, it is impossible to confirm that coherent errors, readout bias, or lattice artifacts remain below the threshold needed to validate the macroscopic equation.
[§3.2] §3.2 (Velocity Encoding): The description of how the position-dependent velocity field v(x) is mapped into state-dependent gate parameters for the local collision operator does not include an explicit derivation or numerical test showing that the discrete-velocity moments recover the correct advection term after ensemble averaging. If the encoding inadvertently introduces effective non-local interactions or violates the required moment relations, the macroscopic limit would deviate from the target PDE; this must be demonstrated before the “first demonstration” claim can be accepted.
[§5] §5 (Readout Mitigation): While the density readout/reload is correctly flagged as the dominant bottleneck, the discussion of MPS shadow tomography remains at the level of a promising direction without concrete circuit-depth estimates, shot-count scaling, or error-propagation analysis for the 3D non-uniform advection instances actually run on the 64-qubit device. This leaves open whether the proposed mitigation is sufficient to reach the system sizes advertised.

minor comments (3)

[Figures 3–6] Several figure captions (e.g., those showing density evolution under non-uniform flow) lack explicit labels for the velocity-field parameters and lattice resolution used; this reduces reproducibility.
[§2] The manuscript cites earlier QLBM works on uniform advection but does not compare circuit depths or gate counts against those baselines for the non-uniform extension; a short table would clarify the overhead introduced by the velocity encoding.
[§3.1] Notation for the discrete-velocity set and the collision matrix in the presence of spatially varying v(x) is introduced without a compact summary table; readers must hunt through the text to reconstruct the full operator.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their insightful and constructive comments. We appreciate the recognition of our work as the first hardware demonstration of QLBM for non-uniform 3D advection-diffusion on trapped-ion systems. We address each major comment below and will revise the manuscript to strengthen the quantitative validation, derivations, and analyses as requested.

read point-by-point responses

Referee: [§4] §4 (Hardware Implementation and Results): The central claim that the chosen encoding of spatially varying velocity into the QLBM collision/streaming circuit reproduces the advection-diffusion PDE with acceptable error on noisy trapped-ion hardware is load-bearing, yet the manuscript supplies only qualitative statements and limited quantitative metrics (e.g., no L2 or L∞ error norms against classical reference solutions, no explicit mass-conservation residuals, and no Chapman-Enskog moment verification for the non-uniform cases). Without these data for the demonstrated system sizes, it is impossible to confirm that coherent errors, readout bias, or lattice artifacts remain below the threshold needed to validate the macroscopic equation.

Authors: We agree that quantitative metrics are essential to rigorously validate the macroscopic PDE recovery on hardware. In the revised manuscript we will add L2 and L∞ error norms comparing quantum results to classical reference solutions for all demonstrated system sizes. We will also report explicit mass-conservation residuals and perform Chapman-Enskog moment verification for the non-uniform velocity cases. These additions will quantify error control and address concerns about coherent errors, readout bias, and lattice artifacts. revision: yes
Referee: [§3.2] §3.2 (Velocity Encoding): The description of how the position-dependent velocity field v(x) is mapped into state-dependent gate parameters for the local collision operator does not include an explicit derivation or numerical test showing that the discrete-velocity moments recover the correct advection term after ensemble averaging. If the encoding inadvertently introduces effective non-local interactions or violates the required moment relations, the macroscopic limit would deviate from the target PDE; this must be demonstrated before the “first demonstration” claim can be accepted.

Authors: We acknowledge the need for an explicit derivation and verification. In the revision we will expand §3.2 with a detailed derivation showing how the position-dependent velocity v(x) is encoded into state-dependent gate parameters while preserving the required discrete-velocity moments for the advection term. We will also include numerical tests on small lattices demonstrating moment recovery after ensemble averaging and confirming the absence of unintended non-local interactions or moment violations. revision: yes
Referee: [§5] §5 (Readout Mitigation): While the density readout/reload is correctly flagged as the dominant bottleneck, the discussion of MPS shadow tomography remains at the level of a promising direction without concrete circuit-depth estimates, shot-count scaling, or error-propagation analysis for the 3D non-uniform advection instances actually run on the 64-qubit device. This leaves open whether the proposed mitigation is sufficient to reach the system sizes advertised.

Authors: We agree that concrete scaling estimates are required. In the revised §5 we will provide circuit-depth estimates for the MPS shadow tomography, shot-count scaling with system size, and error-propagation analysis specifically for the 3D non-uniform advection instances executed on the 64-qubit device. These additions will clarify the feasibility of scaling to the advertised system sizes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central result is hardware demonstration of standard QLBM

full rationale

The paper presents an experimental implementation of the Quantum Lattice Boltzmann Method on trapped-ion hardware to simulate advection-diffusion transport with spatially varying velocity fields. The claimed recovery of the macroscopic advection-diffusion PDE follows from the standard discrete Boltzmann equation analysis (local streaming and collision steps followed by Chapman-Enskog expansion), which is a pre-existing mathematical result independent of the quantum circuit encoding or hardware execution. The non-uniform velocity is encoded as a design choice in the circuit parameters; its correctness is validated empirically by comparing hardware runs to classical reference solutions rather than being fitted or defined to match by construction. No load-bearing step reduces to a self-citation chain, ansatz smuggled via prior work, or a prediction that is statistically forced from fitted inputs. Self-citations to earlier QLBM literature (if present) support the baseline method but do not justify uniqueness or forbid alternatives. The readout/reload bottleneck is identified as an engineering limitation and discussed with mitigation proposals, but this does not create circularity in the derivation. The overall claim is therefore an empirical demonstration whose validity rests on external hardware data and classical benchmarks, not on internal redefinition of inputs as outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters, axioms, or invented entities; the approach relies on standard QLBM discretization and quantum circuit assumptions whose details are not visible here.

pith-pipeline@v0.9.0 · 5564 in / 1142 out tokens · 32137 ms · 2026-05-07T04:52:03.076911+00:00 · methodology

discussion (0)

Reference graph

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