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arxiv: 2606.17975 · v1 · pith:FD4DDCLNnew · submitted 2026-06-16 · 🪐 quant-ph · cond-mat.mes-hall

Manipulation of Topological Corner States via Subchiral Symmetry

Hai-Tao Ding , Tianqi Chen , Leong-Chuan Kwek , Jiangbin Gong This is my paper

Pith reviewed 2026-06-27 00:21 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords subchiral symmetrytopological corner modeshigher-order topologyadiabatic transferBenalcazar-Bernevig-Hughes modelquantum simulation
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The pith

Subchiral symmetry allows selective isolation and adiabatic transfer of topological corner modes.

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

The paper shows that conventional chiral symmetry in the two-dimensional Benalcazar-Bernevig-Hughes model decomposes into four subchiral symmetries, each linked to one zero-energy corner mode. Selectively breaking these subsymmetries via controlled intercell hoppings reduces the fourfold manifold to isolated single modes step by step. Adiabatic protocols then move a single mode or a phase-preserving superposition from one corner to another. Both simulations and runs on IBM quantum processors achieve high fidelity, turning protected corner states into addressable elements.

Core claim

In the two-dimensional Benalcazar-Bernevig-Hughes model, the conventional chiral symmetry decomposes into four subchiral symmetries, each associated with one zero-energy corner mode. By selectively breaking these subsymmetries with controlled intercell hoppings, the fourfold corner-state manifold reduces step by step to single isolated modes. Adiabatic protocols transfer either a single corner state or a superposition of two corner states between selected corners while preserving the relative phase, as shown by numerical simulations and IBM quantum-processor implementations.

What carries the argument

Subchiral symmetry, the decomposition of conventional chiral symmetry into four independent subsymmetries each tied to one corner mode, which permits targeted breaking to shrink the manifold and to design transfer protocols.

If this is right

  • Single isolated corner modes become addressable by breaking specific subsymmetries one at a time.
  • Adiabatic protocols achieve high-fidelity transfer of either single states or phase-preserving superpositions between chosen corners.
  • The same control principle applies to programmable manipulation of higher-order topological states on quantum hardware.

Where Pith is reading between the lines

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

  • The approach may generalize to other two-dimensional higher-order topological models that possess analogous symmetry decompositions.
  • Phase-preserving superposition transfers could support encoding of quantum information directly in corner-state manifolds.
  • Scaling the protocols to larger lattices would test whether the required hopping precision remains experimentally feasible.

Load-bearing premise

Controlled intercell hoppings can be implemented to break individual subchiral symmetries without introducing decoherence, disorder, or unwanted couplings that would destroy topological protection or adiabatic transfer fidelity.

What would settle it

An experiment in which breaking one chosen subchiral symmetry leaves more than one corner mode at zero energy, or in which an adiabatic transfer protocol produces measurable phase drift or fidelity below the reported numerical values on a quantum processor.

Figures

Figures reproduced from arXiv: 2606.17975 by Hai-Tao Ding, Jiangbin Gong, Leong-Chuan Kwek, Tianqi Chen.

Figure 1
Figure 1. Figure 1: FIG. 1. Subchiral-symmetry-controlled manipulation of cor [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a1-a4) The energy spectrum and (b1-b4) the spatial distributions [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Transfer of corner states on the IBM quantum processor [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Higher-order topological phases provide robust corner modes, but their use requires controllable creation, isolation, and transfer of individual modes and their superpositions. Here we demonstrate, using the two-dimensional Benalcazar-Bernevig-Hughes model as an example, that subchiral symmetry provides a general control principle for manipulating topological corner modes. The conventional chiral symmetry decomposes into four subchiral symmetries, each associated with one zero-energy corner mode. By selectively breaking these subsymmetries with controlled intercell hoppings, we reduce the fourfold corner-state manifold step by step to single isolated modes. We further design adiabatic protocols that transfer either a single corner state or a superposition of two corner states between selected corners, while preserving the relative phase in the latter case. Both numerical simulations and IBM quantum-processor implementations show that the proposed protocols can be executed with high fidelity, establishing subchiral symmetry as a route to programmable higher-order topological state manipulation.

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 paper claims that the conventional chiral symmetry of the 2D Benalcazar-Bernevig-Hughes model decomposes into four independent subchiral symmetries, each associated with one zero-energy corner mode. Selectively breaking these subsymmetries via controlled intercell hoppings reduces the fourfold manifold to isolated single modes. Adiabatic protocols are introduced to transfer either a single corner state or a phase-preserving superposition between corners. Both numerical simulations and implementations on IBM quantum processors are reported to achieve high fidelity, positioning subchiral symmetry as a control principle for programmable higher-order topological state manipulation.

Significance. If the results hold, the work supplies an explicit symmetry-based route to active control and transfer of higher-order topological corner modes while preserving topological protection and relative phase. The combination of model Hamiltonians, adiabatic protocols, and hardware validation on quantum processors adds practical relevance for potential applications in robust quantum state transfer. The approach avoids fitted parameters and relies on explicit constructions.

major comments (2)
  1. [IBM quantum-processor implementations] Hardware implementation section: the high-fidelity IBM results are load-bearing for the claim of practical applicability, yet the manuscript provides insufficient detail on mapping the symmetry-breaking intercell hoppings to native gates, verification of adiabatic conditions, and confirmation that no extra couplings or decoherence lift the zero modes (directly addressing the stress-test concern on controlled intercell hoppings).
  2. [Symmetry analysis] Symmetry analysis section: the claim that the four subchiral symmetries are independent and can be broken one-by-one without affecting the others is central to the selective isolation protocol, but the manuscript does not explicitly demonstrate this independence (e.g., via commutation relations or explicit operator decomposition) in a manner that rules out cross-talk between subsymmetries.
minor comments (2)
  1. The abstract states 'high fidelity' for both numerics and hardware but does not quantify the lattice size or number of qubits used; adding these details would improve reproducibility.
  2. Figure captions for the adiabatic protocol diagrams should explicitly label the time-dependent hopping parameters to match the text description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments point by point below. Where the manuscript is missing explicit demonstrations or details, we agree to incorporate them in a revised version.

read point-by-point responses

  1. Referee: [IBM quantum-processor implementations] Hardware implementation section: the high-fidelity IBM results are load-bearing for the claim of practical applicability, yet the manuscript provides insufficient detail on mapping the symmetry-breaking intercell hoppings to native gates, verification of adiabatic conditions, and confirmation that no extra couplings or decoherence lift the zero modes (directly addressing the stress-test concern on controlled intercell hoppings).

    Authors: We agree that the hardware section would benefit from additional explicit information. In the revised manuscript we will add: (i) the explicit transpilation of the controlled intercell hoppings into native IBM gates (including the decomposition of the time-dependent terms), (ii) quantitative verification that the chosen ramp times satisfy the adiabatic condition (via both instantaneous eigenstate overlap and gap analysis), and (iii) a brief discussion of how the zero-mode protection is preserved under the measured decoherence and residual couplings on the device. These additions will directly address the stress-test concern. revision: yes

  2. Referee: [Symmetry analysis] Symmetry analysis section: the claim that the four subchiral symmetries are independent and can be broken one-by-one without affecting the others is central to the selective isolation protocol, but the manuscript does not explicitly demonstrate this independence (e.g., via commutation relations or explicit operator decomposition) in a manner that rules out cross-talk between subsymmetries.

    Authors: We acknowledge that an explicit algebraic demonstration of independence is currently absent. In the revised manuscript we will add a short subsection showing the four subchiral operators explicitly, proving that they mutually commute ([S_i, S_j] = 0 for i ≠ j) and that each can be broken independently by the corresponding intercell term without inducing cross-talk in the zero-mode subspace. This will be supported by the operator decomposition already implicit in the model but not previously written out. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via explicit models and protocols

full rationale

The paper starts from the established 2D BBH model, explicitly decomposes its chiral symmetry into four subchiral symmetries by definition in the Hamiltonian, introduces controlled intercell hoppings as symmetry-breaking terms, constructs adiabatic transfer protocols from those terms, and validates via direct numerical diagonalization plus IBM hardware runs. None of these steps reduce by construction to fitted inputs from the paper's own data, self-citations that bear the central load, or renamed known results. The claims rest on independent constructions and external benchmarks (simulations, device experiments) rather than tautological re-derivation of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard topological classification of the BBH model and the assumption that intercell hoppings can be tuned to break individual subchiral symmetries independently; no free parameters, new axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The 2D BBH model possesses a chiral symmetry that decomposes into four independent subchiral symmetries, each protecting one zero-energy corner mode.
    Invoked in the abstract as the starting point for selective breaking.

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