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arxiv: 2606.23324 · v1 · pith:F2M36JI7new · submitted 2026-06-22 · 🪐 quant-ph

Fast quantum-state transfer in Su-Schrieffer-Heeger chains beyond the noninteracting regime

Fran\c{c}ois Impens , David Gu\'ery-Odelin This is my paper

Pith reviewed 2026-06-26 07:56 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum state transferSu-Schrieffer-Heeger chainshortcuts to adiabaticityBose-Hubbard modelinteracting topological systemsmean-field approximationnonlinear phase cancellation
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The pith

Tunable phases in next-nearest-neighbor hoppings remove nonlinear obstructions to fast state transfer in interacting Su-Schrieffer-Heeger chains

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

The paper shows that making the phase of next-nearest-neighbor shortcut hoppings tunable overcomes the nonlinear phase accumulation that prevents shortcuts to adiabaticity in interacting systems. In the mean-field regime this creates an exact nonlinear shortcut where one quadrature maintains the dark-state trajectory and the orthogonal quadrature cancels interaction self-phase modulation. For the full Bose-Hubbard model the mean-field protocol helps but falls short of unit fidelity due to many-body effects, yet direct many-body optimization with complex hoppings achieves near-perfect transfer. This matters because it provides a way to achieve fast high-fidelity transport in interacting topological quantum systems without being limited to the noninteracting case.

Core claim

By rendering the next-nearest-neighbor shortcut hopping phase tunable in Su-Schrieffer-Heeger chains, the obstruction from nonlinear phase accumulation is removed. In the mean-field regime this yields an exact nonlinear shortcut, and when applied to the full Bose-Hubbard dynamics with optimization in the many-body space, complex phase-tunable hoppings recover near-perfect fidelity.

What carries the argument

The tunable phase of the next-nearest-neighbor hopping, which splits into two quadratures to separately control the dark-state trajectory and cancel interaction-induced self-phase modulation.

Load-bearing premise

The interaction-induced self-phase modulation can be exactly canceled by the orthogonal quadrature of the tunable next-nearest-neighbor hopping without introducing new many-body errors that cannot be compensated by further optimization.

What would settle it

A numerical simulation or experiment measuring whether fidelity reaches near unity when optimizing complex phase-tunable next-nearest-neighbor hoppings directly in the many-body Hilbert space for Bose-Hubbard SSH transfer, versus saturation without such phase control.

Figures

Figures reproduced from arXiv: 2606.23324 by David Gu\'ery-Odelin, Fran\c{c}ois Impens.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Simple SSH chain with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Nonlinear NNN-assisted shortcut for state trans [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Full nonlinear vs real-valued shortcut in the non [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Many-body PMP protocol with complex site [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Simplified NNN-assisted quantum-state transfer [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Restricted-control PMP transfer in a simple linear [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

Shortcuts to adiabaticity have made topological edge-state transfer fast in the single-particle regime, but their extension to interacting systems is obstructed by nonlinear phase accumulation. We show that this obstruction can be removed in Su-Schrieffer-Heeger chains by making the next-nearest-neighbor shortcut hopping phase tunable. In the mean-field regime, this yields an exact nonlinear shortcut: one hopping quadrature keeps the state on the instantaneous dark-state trajectory, while the orthogonal quadrature cancels the interaction-induced self-phase modulation. The resulting protocol is nonperturbative in the mean-field interaction strength. When applied to the full Bose-Hubbard dynamics, the mean-field shortcut remains beneficial but saturates below unit fidelity, exposing genuinely many-body corrections beyond the product-state picture. We then optimize the transfer directly in the many-body Hilbert space and find that complex, phase-tunable next-nearest-neighbor hoppings recover near-perfect fidelity. Our results show that hopping phases are not merely a technical refinement, but a key control resource for fast and high-fidelity transport in interacting topological systems.

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 develops shortcuts to adiabaticity for quantum state transfer in interacting Su-Schrieffer-Heeger (SSH) chains. It shows that tunable phases in next-nearest-neighbor (NNN) shortcut hoppings remove the obstruction from nonlinear phase accumulation. In the mean-field regime an exact nonlinear shortcut is constructed by using orthogonal quadratures of the complex NNN hopping; one keeps the state on the dark-state trajectory while the other cancels interaction-induced self-phase modulation. When applied to the full Bose-Hubbard dynamics the mean-field protocol improves fidelity but saturates below unity; direct many-body optimization with complex NNN hoppings then recovers near-perfect fidelity, indicating that hopping phases constitute a key control resource beyond the product-state approximation.

Significance. If the central claims hold, the work supplies a concrete, nonperturbative construction that extends shortcuts to adiabaticity into the interacting regime and isolates the role of complex hoppings as an independent control degree of freedom. The separation between mean-field success and many-body corrections, together with the explicit optimization in the full Hilbert space, provides a falsifiable benchmark for future many-body STA protocols in topological lattices.

major comments (2)
  1. [Abstract and many-body optimization results] Abstract (final paragraph) and the many-body optimization section: the headline claim that 'complex, phase-tunable next-nearest-neighbor hoppings recover near-perfect fidelity' and that phases are 'a key control resource' is not supported by a control experiment in which the same many-body optimization is performed with real-valued (phase-fixed) NNN hoppings. Without this baseline it remains possible that amplitude optimization alone suffices, rendering the phase tunability non-essential to the reported fidelity gain.
  2. [Mean-field regime derivation] Mean-field derivation (section describing the nonlinear shortcut): the statement that the orthogonal quadrature 'exactly cancels the interaction-induced self-phase modulation' without introducing new many-body errors is asserted but the explicit cancellation condition and the resulting fidelity bound are not shown; a concrete equation relating the two quadratures to the interaction term would be required to substantiate the 'exact' and 'nonperturbative' character of the shortcut.
minor comments (2)
  1. [Abstract] The abstract states that the mean-field shortcut 'saturates below unit fidelity' but supplies neither the numerical value of the saturation nor error bars; these data should appear in the corresponding figure or table.
  2. Notation for the complex NNN hopping amplitudes is introduced without an explicit definition of the real and imaginary parts; a short equation or parenthetical clarification would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and the recommendation for major revision. The two major comments identify important gaps in evidentiary support and derivation clarity. We address each point below and will revise the manuscript to incorporate the requested controls and explicit equations.

read point-by-point responses

  1. Referee: [Abstract and many-body optimization results] Abstract (final paragraph) and the many-body optimization section: the headline claim that 'complex, phase-tunable next-nearest-neighbor hoppings recover near-perfect fidelity' and that phases are 'a key control resource' is not supported by a control experiment in which the same many-body optimization is performed with real-valued (phase-fixed) NNN hoppings. Without this baseline it remains possible that amplitude optimization alone suffices, rendering the phase tunability non-essential to the reported fidelity gain.

    Authors: We agree that a direct control optimization restricted to real-valued NNN hoppings is required to isolate the contribution of phase tunability. In the revised manuscript we will perform this additional many-body optimization (identical protocol and Hilbert-space search but with phase fixed at zero) and include a side-by-side fidelity comparison. This will either confirm that phase freedom is essential for near-unit fidelity or quantify the incremental gain, thereby placing the claim on firmer ground. revision: yes

  2. Referee: [Mean-field regime derivation] Mean-field derivation (section describing the nonlinear shortcut): the statement that the orthogonal quadrature 'exactly cancels the interaction-induced self-phase modulation' without introducing new many-body errors is asserted but the explicit cancellation condition and the resulting fidelity bound are not shown; a concrete equation relating the two quadratures to the interaction term would be required to substantiate the 'exact' and 'nonperturbative' character of the shortcut.

    Authors: We accept that the mean-field section would be strengthened by an explicit derivation of the cancellation. In the revision we will insert the concrete equations that decompose the complex NNN hopping into orthogonal quadratures, show how one quadrature enforces the instantaneous dark-state condition while the second exactly cancels the interaction-induced phase accumulation, and derive the resulting fidelity bound that remains unity for arbitrary mean-field interaction strength. This will make the nonperturbative character of the shortcut fully transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs a new protocol by making NNN hopping phases tunable, derives the mean-field shortcut from the instantaneous dark-state condition plus quadrature cancellation of self-phase modulation, and performs direct many-body optimization. No load-bearing step reduces to a fitted parameter renamed as prediction, no self-citation chain justifies the central claim, and no ansatz is smuggled via prior work. The abstract and described derivation chain are independent of the target fidelity result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the mean-field approximation for the interacting dynamics and on the assumption that the many-body Hilbert space optimization can be performed without prohibitive computational cost. No free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Mean-field approximation accurately captures the leading interaction effects in the Bose-Hubbard SSH chain for the purpose of shortcut design
    Invoked when stating that the mean-field shortcut is exact and remains beneficial for full Bose-Hubbard dynamics
  • domain assumption Next-nearest-neighbor hoppings with controllable complex phases are experimentally realizable without additional decoherence
    Implicit in the proposal to use tunable phases as the control resource

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Reference graph

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