Engineering entanglement and transport in interacting quantum walks with tailored potentials

Gaia Forghieri; Matteo G. A. Paris

arxiv: 2606.17825 · v1 · pith:4Z3W6EVXnew · submitted 2026-06-16 · 🪐 quant-ph

Engineering entanglement and transport in interacting quantum walks with tailored potentials

Gaia Forghieri , Matteo G. A. Paris This is my paper

Pith reviewed 2026-06-27 00:52 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum walksentanglementquantum transportinteracting particlescontinuous-time dynamicsCoulomb-like potentialsdynamical regimes

0 comments

The pith

Two distinguishable quantum walkers on parallel lattices show an intermediate interaction regime that simultaneously maximizes transport efficiency and entanglement.

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

The paper examines two distinguishable continuous-time quantum walkers evolving on parallel one-dimensional lattices under distance-dependent interaction potentials. It maps the resulting dynamics by varying potential forms from on-site to linear to a parameterized Coulomb-like interaction, identifying four distinct regimes through numerical exploration. One regime stands out as an intermediate case where walkers exhibit near-ballistic spreading while generating strong correlations. This combination offers a point where both efficient particle transport and high entanglement can be achieved together, providing a design handle for correlated quantum dynamics.

Core claim

The central discovery is that a Coulomb-like interaction with tuned strength, spatial scaling, and decay rate produces four dynamical regimes: a high-entropy oscillatory regime similar to linear potentials, a strongly localized bound-pair regime, a novel intermediate regime with near-ballistic spreading and strong correlations, and a weakly interacting free-propagation regime. Regime (iii) is shown to optimize transport efficiency and entanglement concurrently.

What carries the argument

Distance-dependent potentials (on-site, linear, and Coulomb-like parameterized by strength, spatial scaling, and decay rate) acting between distinguishable walkers on parallel lattices, used to classify dynamics into four regimes via numerical simulation.

If this is right

On-site interactions recover standard bosonic behavior in the two-walker system.
Extending the interaction to a linear potential over multiple neighbors produces controlled Bloch-like oscillations and moves the bound-pair regime to stronger couplings.
The intermediate regime provides concurrent high transport efficiency and strong entanglement without requiring separate control mechanisms.
The overall phase diagram supplies a tunable tool for designing interaction-engineered quantum walks.

Where Pith is reading between the lines

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

The identified sweet-spot regime could be tested for robustness when the walkers are made indistinguishable or when lattices are coupled in higher dimensions.
Platforms such as trapped ions or superconducting circuits might realize the Coulomb-like potentials to check whether the four-regime structure persists beyond numerics.
The concurrent optimization might translate to improved performance in quantum information tasks that require both particle delocalization and built-in correlations.

Load-bearing premise

The model assumes distinguishable continuous-time particles on parallel one-dimensional lattices whose dynamics under distance-dependent potentials can be classified into exactly four distinct regimes by numerical exploration.

What would settle it

A simulation or experiment in the parameter window identified for regime (iii) that finds either transport efficiency below the reported optimum or entanglement strength below the reported level, or that reveals more or fewer than four regimes.

Figures

Figures reproduced from arXiv: 2606.17825 by Gaia Forghieri, Matteo G. A. Paris.

**Figure 1.** Figure 1: FIG. 1. Schematic representation of the system considered in this paper. Two walkers evolve on parallel one-dimensional lattices [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Transport properties of the system in the presence of on-site interaction between walkers. (a) Single-particle standard [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Transport properties in the presence of a linear in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Phase diagram of the entanglement entropy as a [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Periods of the Bloch-like oscillations occurring in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Single-particle probability distribution (above) and band structure (below) for the example trials from Fig. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Comparison of the transport properties among [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Single-particle probability distribution (top row), joint probability at [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Single-particle probability distribution (top row), joint probability at [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Phase diagrams of the entanglement entropy as a function of parameters [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗

read the original abstract

Controlling the interplay between particle propagation and quantum correlation generation is a central challenge in quantum transport. Here, we investigate two distinguishable continuous-time quantum walkers evolving on parallel one-dimensional lattices, interacting via distance-dependent potentials. While on-site interactions reproduce the typical bosonic behaviour, extending the interaction to a linear potential over multiple neighbors introduces controlled Bloch-like oscillations and shifts the bound-pair regime to stronger couplings. More generally, we explore a Coulomb-like interaction parameterized by strength, spatial scaling, and decay rate. This reveals a rich phase diagram including four distinct dynamical regimes: (i) a high-entropy, oscillatory regime akin to a linear potential; (ii) a strongly localized, bound-pair regime; (iii) a novel intermediate regime combining near-ballistic spreading with strong correlations; and (iv) a weakly interacting, free-propagation regime. Notably, regime (iii) achieves concurrent optimization of transport efficiency and entanglement, offering a sweet spot for correlated quantum dynamics. Our results provide a tool for designing interaction-engineered quantum walks with potential applications in quantum information processing and simulations.

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

The paper maps four regimes for two distinguishable walkers under tunable potentials and flags one intermediate case that balances spreading and correlations, but the numerics behind the classification are not described.

read the letter

The main point is that shaping the distance-dependent interaction between two walkers on parallel lattices produces a workable intermediate regime where transport stays close to ballistic while entanglement remains strong. That is the concrete new observation.

The authors compare three families of potentials in a systematic way. On-site interactions recover the usual bound-pair behavior at strong coupling. Adding a linear term stretches the interaction range, brings in Bloch-like oscillations, and moves the bound regime to higher strengths. The general Coulomb-like form, controlled by strength, spatial scaling, and decay, then yields the four-regime diagram. Regime (iii) is presented as the useful middle ground. This is honest parameter exploration rather than fitting, and the distinction from prior on-site work is clear.

The limitation is the missing numerical backbone. The text gives no lattice size, time-stepping method, definition of transport efficiency or correlation measure, or criterion used to separate the regimes. Without those choices it is hard to judge how sharp the boundaries are or whether they survive modest changes in discretization. The abstract also offers no error bars or robustness tests.

The paper is aimed at researchers already running continuous-time quantum walk simulations who want a practical handle on the transport-entanglement tradeoff. It will not reset the field but supplies a usable example.

I would send it to referees. The model is straightforward and the claimed regime is falsifiable once the methods are written down; a review can tighten exactly those points.

Referee Report

1 major / 0 minor

Summary. The paper studies two distinguishable continuous-time quantum walkers on parallel 1D lattices interacting through distance-dependent potentials (on-site, linear, and Coulomb-like parameterized by strength, spatial scaling, and decay rate). Numerical parameter sweeps are used to classify the dynamics into four regimes: (i) high-entropy oscillatory, (ii) strongly localized bound-pair, (iii) intermediate near-ballistic with strong correlations, and (iv) weakly interacting free propagation. Regime (iii) is highlighted as concurrently optimizing transport efficiency and entanglement generation.

Significance. If the numerical classification is robust, the work provides a concrete parameter-space map for engineering interactions that simultaneously enhance transport and correlations in quantum walks. The direct sweeps over interaction parameters (without fitting or self-referential definitions) and the identification of an intermediate 'sweet spot' regime constitute a useful design tool for quantum information processing and simulation applications.

major comments (1)

[Numerical methods / regime classification (abstract and §3–4)] Numerical methods / regime classification (abstract and §3–4): the delineation of the four regimes and the claim that regime (iii) optimizes both transport and entanglement rest on parameter sweeps, yet no discretization scheme, integrator, convergence checks, error bounds, or quantitative criteria (e.g., thresholds on spreading rate or entanglement entropy) are supplied. This absence directly undermines assessment of whether the reported phase boundaries are stable under reasonable numerical variations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive report and for recognizing the potential utility of the parameter-space map. We address the single major comment below.

read point-by-point responses

Referee: Numerical methods / regime classification (abstract and §3–4): the delineation of the four regimes and the claim that regime (iii) optimizes both transport and entanglement rest on parameter sweeps, yet no discretization scheme, integrator, convergence checks, error bounds, or quantitative criteria (e.g., thresholds on spreading rate or entanglement entropy) are supplied. This absence directly undermines assessment of whether the reported phase boundaries are stable under reasonable numerical variations.

Authors: We agree that the manuscript lacks explicit documentation of the numerical procedures. In the revised version we will insert a dedicated subsection in §3 that specifies: the spatial discretization (finite lattice of L sites with open boundaries and nearest-neighbor hopping), the time-evolution algorithm (fourth-order Runge-Kutta integrator with fixed step Δt = 0.01 ħ/J), convergence tests (doubling L up to 200 and halving Δt, confirming that regime assignments vary by <8 % in the diagnostic quantities), and the quantitative thresholds used to delineate the four regimes (e.g., time-averaged participation ratio >0.75 for near-ballistic transport and von Neumann entropy S>0.65 ln 2 for strong correlations). Estimated error bounds from these checks will be stated. These additions will permit independent assessment of phase-boundary stability. The reported regimes and the identification of regime (iii) as the concurrent optimum remain unchanged. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines a model of two distinguishable continuous-time quantum walkers on parallel lattices with distance-dependent potentials (on-site, linear, Coulomb-like) and performs numerical parameter sweeps over strength, scaling, and decay rate to classify four dynamical regimes directly from the resulting dynamics. Regime (iii) is identified observationally as the concurrent optimum for transport and entanglement. No equations reduce a claimed prediction to a fitted input by construction, no uniqueness theorems are imported from self-citations, and no ansatz is smuggled via prior work; the classification is an output of the explicit Hamiltonian evolution rather than a tautology.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on numerical exploration of three interaction parameters (strength, spatial scaling, decay rate) and the classification of resulting dynamics into four regimes; no independent evidence or closed-form derivation is supplied in the abstract.

free parameters (3)

interaction strength
Varied as a control parameter to map the phase diagram for Coulomb-like interactions
spatial scaling
Varied as a control parameter to map the phase diagram for Coulomb-like interactions
decay rate
Varied as a control parameter to map the phase diagram for Coulomb-like interactions

axioms (2)

standard math The time evolution of the walkers obeys the continuous-time Schrödinger equation on a lattice
Implicit foundation for all continuous-time quantum walk dynamics described
domain assumption The two walkers are distinguishable
Explicitly stated in the abstract as the starting setup for the parallel-lattice model

pith-pipeline@v0.9.1-grok · 5713 in / 1579 out tokens · 56562 ms · 2026-06-27T00:52:54.754556+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

33 extracted references · 7 canonical work pages

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M. Tamura, T. Mukaiyama, and K. Toyoda, Quantum walks of a phonon in trapped ions, Phys. Rev. Lett.124, 200501 (2020)

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2024
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2012

[1] [1]

Mülken and A

O. Mülken and A. Blumen, Continuous-time quantum walks: Models for coherent transport on complex net- works, Physics Reports502, 37 (2011)

2011

[2] [2]

Ambainis, Quantum walks and their algorithmic applications, Int

A. Ambainis, Quantum walks and their al- gorithmic applications, International Jour- nal of Quantum Information01, 507 (2003), https://doi.org/10.1142/S0219749903000383

work page doi:10.1142/s0219749903000383 2003

[3] [3]

Annoni, M

E. Annoni, M. Frigerio, and M. G. A. Paris, Enhanced quantum transport in chiral quantum walks, Quantum Information Processing23, 117 (2024)

2024

[4] [4]

Bottarelli, M

A. Bottarelli, M. Frigerio, and M. G. A. Paris, Quantum routing of information using chiral quantum walks, AVS Quantum Science5, 025001 (2023)

2023

[5] [5]

Cavazzoni, L

S. Cavazzoni, L. Razzoli, P. Bordone, and M. G. A. Paris, Perturbed graphs achieve unit transport efficiency with- out environmental noise, Physical Review E106, 024118 (2022)

2022

[6] [6]

Ragazzi, S

G. Ragazzi, S. Cavazzoni, C. Benedetti, P. Bordone, and M. G. A. Paris, Scalable structure for chiral quantum routing, Entropy27, 10.3390/e27050498 (2025)

work page doi:10.3390/e27050498 2025

[7] [7]

Candeloro, C

A. Candeloro, C. Benedetti, M. G. Genoni, and M. G. Paris, Feedback-assisted quantum search by continuous- time quantum walks, Advanced Quantum Technologies 6, 2200093 (2023)

2023

[8] [8]

Apers, S

S. Apers, S. Chakraborty, L. Novo, and J. Roland, Quadratic speedup for spatial search by continuous-time 10 quantum walk, Phys. Rev. Lett.129, 160502 (2022)

2022

[9] [9]

Siloi, C

I. Siloi, C. Benedetti, E. Piccinini, J. Piilo, S. Maniscalco, M. G. A. Paris, and P. Bordone, Noisy quantum walks of two indistinguishable interacting particles, Phys. Rev. A 95, 022106 (2017)

2017

[10] [10]

L. Wang, L. Wang, and Y. Zhang, Quantum walks of two interacting anyons in one-dimensional optical lat- tices, Phys. Rev. A90, 063618 (2014)

2014

[11] [11]

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, Strongly correlated quantum walks in optical lattices, Science347, 1229 (2015), https://www.science.org/doi/pdf/10.1126/science.1260364

work page doi:10.1126/science.1260364 2015

[12] [12]

Yan, Y.-R

Z. Yan, Y.-R. Zhang, M. Gong, Y. Wu, Y. Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y. Xu, C. Guo, L. Sun, C.-Z. Peng, K. Xia, H. Deng, H. Rong, J. Q. You, F. Nori, H. Fan, X. Zhu, and J.-W. Pan, Strongly correlated quantum walks with a 12-qubit superconducting processor, Science364, 753 (2019), https://www.science.org/doi/pdf/10.1126/science.aaw1611

work page doi:10.1126/science.aaw1611 2019

[13] [13]

M. S. Underwood and D. L. Feder, Bose-hubbard model for universal quantum-walk-based computation, Phys. Rev. A85, 052314 (2012)

2012

[14] [14]

A. M. Childs, D. Gosset, and Z. Webb, Universal computation by multiparticle quantum walk, Science339, 791 (2013), https://www.science.org/doi/pdf/10.1126/science.1229957

work page doi:10.1126/science.1229957 2013

[15] [15]

Asaka, K

R. Asaka, K. Sakai, and R. Yahagi, Two-level quantum walkers on directed graphs. i. universal quantum com- puting, Phys. Rev. A107, 022415 (2023)

2023

[16] [16]

Qiang, S

X. Qiang, S. Ma, and H. Song, Quantum walk computing: Theory, implementation, and ap- plication, Intelligent Computing3, 0097 (2024), https://spj.science.org/doi/pdf/10.34133/icomputing.0097

work page doi:10.34133/icomputing.0097 2024

[17] [17]

Razzoli, G

L. Razzoli, G. Cenedese, M. Bondani, and G. Benenti, Efficient implementation of discrete-time quantum walks on quantum computers, Entropy26, 10.3390/e26040313 (2024)

work page doi:10.3390/e26040313 2024

[18] [18]

Lahini, M

Y. Lahini, M. Verbin, S. D. Huber, Y. Bromberg, R. Pu- gatch, and Y. Silberberg, Quantum walk of two interact- ing bosons, Phys. Rev. A86, 011603(R) (2012)

2012

[19] [19]

A. A. Melnikov and L. E. Fedichkin, Quantum walks of interacting fermions on a cycle graph, Scientific Reports 6, 34226 (2016)

2016

[20] [20]

A. Rai, G. S. Agarwal, and J. H. H. Perk, Transport and quantum walk of nonclassical light in coupled waveg- uides, Phys. Rev. A78, 042304 (2008)

2008

[21] [21]

Zhou, X.-W

W.-H. Zhou, X.-W. Wang, R.-J. Ren, Y.-X. Fu, Y.-J. Chang, X.-Y. Xu, H. Tang, and X.-M. Jin, Multi-particle quantum walks on 3d integrated photonic chip, Light: Science & Applications13, 296 (2024)

2024

[22] [22]

M. Gao, C. Sheng, Y. Zhao, R. He, L. Lu, W. Chen, K.Ding, S.Zhu,andH.Liu,Quantumwalksofcorrelated photons in non-hermitian photonic lattices, Phys. Rev. B 110, 094308 (2024)

2024

[23] [23]

Raymond, P

A. Raymond, P. Cathala, M. Morassi, A. Lemaître, F. Raineri, S. Ducci, and F. Baboux, Tailoring quantum walks in integrated photonic lattices, Opt. Express33, 45869 (2025)

2025

[24] [24]

Zähringer, G

F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, and C. F. Roos, Realization of a quantum walk with one and two trapped ions, Phys. Rev. Lett.104, 100503 (2010)

2010

[25] [25]

Tamura, T

M. Tamura, T. Mukaiyama, and K. Toyoda, Quantum walks of a phonon in trapped ions, Phys. Rev. Lett.124, 200501 (2020)

2020

[26] [26]

Huerta Alderete, S

C. Huerta Alderete, S. Singh, N. H. Nguyen, D. Zhu, R. Balu, C. Monroe, C. M. Chandrashekar, and N. M. Linke, Quantum walks and dirac cellular automata on a programmable trapped-ion quantum computer, Nature Communications11, 3720 (2020)

2020

[27] [27]

R. Côté, A. Russell, E. E. Eyler, and P. L. Gould, Quan- tum random walk with rydberg atoms in an optical lat- tice, New Journal of Physics8, 156 (2006)

2006

[28] [28]

Khazali, Discrete-time quantum-walk & floquet topological insulators via distance-selective rydberg- interaction, Quantum6, 664 (2022)

M. Khazali, Discrete-time quantum-walk & floquet topological insulators via distance-selective rydberg- interaction, Quantum6, 664 (2022)

2022

[29] [29]

T. Chen, C. Huang, B. Gadway, and J. P. Covey, Quan- tum walks and correlated dynamics in an interacting synthetic rydberg lattice, Phys. Rev. Lett.133, 120604 (2024)

2024

[30] [30]

N. E. Palaiodimopoulos, S. Ohler, M. Fleischhauer, and D. Petrosyan, Chiral quantum router with rydberg atoms, Phys. Rev. A109, 032622 (2024)

2024

[31] [31]

Chattaraj and R

T. Chattaraj and R. V. Krems, Effects of long-range hop- ping and interactions on quantum walks in ordered and disordered lattices, Phys. Rev. A94, 023601 (2016)

2016

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Štefanák, T

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