arxiv: 2605.11823 · v1 · submitted 2026-05-12 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Adiabatic Quantum Simulation of the Topological Su--Schrieffer--Heeger--Hubbard Model

Ssu-Yi Chen , Bo-Hung Chen , Dah-Wei Chiou , Jie-Hong Roland Jiang

Authors on Pith no claims yet

Pith reviewed 2026-05-13 05:47 UTC · model grok-4.3

classification 🪐 quant-ph

keywords adiabatic quantum simulationSu-Schrieffer-Heeger-Hubbard modelmany-body Berry phasetopological phasesquantum circuitsHubbard interactionschiral symmetrysublattice polarization

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The pith

Adiabatic quantum circuits show SSH topology survives weak Hubbard interactions but breaks when symmetry-breaking terms exceed a threshold.

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

The paper builds a framework of quantum circuits to perform adiabatic simulation of the one-dimensional Su-Schrieffer-Heeger-Hubbard model on gate-based quantum computers. Circuits handle state preparation, time evolution under the interacting Hamiltonian, and a measurement protocol followed by classical post-processing to obtain the many-body Berry phase and sublattice polarization. Classical simulations of these circuits establish that the topological features persist under weak interactions yet collapse once the chiral-symmetry-breaking interaction strength passes a critical value. The approach requires only polynomial resources in system size. A sympathetic reader would care because it supplies a concrete route to study how interactions affect topological order in genuine many-body systems using near-term quantum hardware.

Core claim

What carries the argument

The adiabatic quantum simulation framework built from explicit quantum circuits for state preparation, Hamiltonian evolution, and a measurement-plus-post-processing protocol that extracts the many-body Berry phase while tracking sublattice polarization in the SSHH model.

If this is right

The topological phase of the SSH model remains intact for weak Hubbard interactions in a full many-body treatment.
The phase is destroyed once the chiral-symmetry-breaking interaction component exceeds a finite threshold.
All qubit counts, gate depths, shot numbers, and classical costs scale polynomially with system size.
The construction supplies a working proof-of-concept for quantum simulation of interacting topological phases on future hardware.

Where Pith is reading between the lines

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

The same circuit template could be repurposed for other one-dimensional interacting topological models such as extended Kitaev or Su-Schrieffer-Heeger variants with longer-range terms.
On actual NISQ devices, decoherence and gate errors would likely require additional error-mitigation techniques to keep the Berry-phase extraction reliable at the sizes simulated classically.
The interaction threshold identified here could be tested directly in cold-atom or superconducting-circuit experiments that realize tunable Hubbard interactions on an SSH lattice.

Load-bearing premise

Classical simulations of the circuits faithfully reproduce the results that would be measured on real quantum hardware, with the measurement protocol and post-processing accurately recovering the Berry phase without large bias from shot noise or imperfections.

What would settle it

Executing the circuits on quantum hardware and observing that the extracted many-body Berry phase fails to remain quantized for weak interactions or does not exhibit the predicted breakdown at the interaction threshold found in the classical simulations.

Figures

Figures reproduced from arXiv: 2605.11823 by Bo-Hung Chen, Dah-Wei Chiou, Jie-Hong Roland Jiang, Ssu-Yi Chen.

**Figure 2.** Figure 2: Final-state fidelity for the case with U = 0 (top) and the case with U = 1 (bottom). does not by itself guarantee proximity to the ideal adiabatically evolved state. Based on these observations, we choose T = 1 and L = 40 as the simulation setting for the subsequent numerical experiments. This choice provides high fidelity in the noninteracting benchmark and stable behavior in the interacting case, while … view at source ↗

**Figure 3.** Figure 3: Many-body Berry phase for different values of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

read the original abstract

We develop an adiabatic quantum simulation framework on gate-based quantum computers to probe topological signatures of the one-dimensional fermionic Su--Schrieffer--Heeger--Hubbard (SSHH) model. We present explicit quantum-circuit constructions for initial-state preparation and time evolution, together with a practical measurement protocol and classical post-processing procedure for extracting the many-body Berry phase and the spatial profile of the sublattice polarization. Using classical simulations of the proposed circuits, we demonstrate -- for the first time within a genuine many-body framework -- that the topological characteristics of the SSH model remain robust against weak Hubbard interactions but eventually break down as the chiral-symmetry-breaking component of the interaction exceeds a threshold. The required qubit number, gate complexity, measurement shots, and classical pre- and post-processing costs all scale polynomially with system size. Our results provide a proof-of-concept framework for probing topological properties of interacting many-body systems via adiabatic quantum simulation on future large-scale quantum computers.

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

Explicit circuits for adiabatic simulation of the interacting SSHH model, backed by ideal classical simulations showing topology survives weak Hubbard terms but breaks at a symmetry-breaking threshold.

read the letter

The key point is that this work supplies explicit gate-based circuit constructions for adiabatic state preparation and time evolution in the one-dimensional Su-Schrieffer-Heeger-Hubbard model, along with a measurement protocol that extracts the many-body Berry phase through classical post-processing. Using simulations of these ideal circuits, the authors show that the topological signatures stay intact for weak Hubbard interactions but disappear once the chiral-symmetry-breaking part of the interaction exceeds a certain strength. All scaling is polynomial in system size. What the paper does well is lay out the full pipeline in a many-body setting for the first time. Prior simulations of the SSH model stayed non-interacting, so adding the Hubbard term with concrete circuits and a way to compute the invariants is a clear step forward. The protocol avoids any obvious circularity since the outputs are defined independently. The main limitation is that the evidence is all from classical simulation of noiseless circuits. We do not see any runs on actual quantum hardware or even with noise models included, so the robustness claims are for the ideal case only. It would be useful to know the specific lattice sizes used and how the threshold was determined to judge finite-size effects. This paper is for people in quantum information and condensed matter who are thinking about how to simulate interacting topological systems on near-term or future quantum devices. A reader interested in adiabatic quantum simulation protocols will get a worked example they can build on. I recommend sending it out for peer review. The constructions are detailed enough to deserve a close look at the numerics and the exact implementation choices.

Referee Report

0 major / 2 minor

Summary. The paper develops an adiabatic quantum simulation framework for the one-dimensional fermionic Su-Schrieffer-Heeger-Hubbard (SSHH) model on gate-based quantum computers. It provides explicit quantum-circuit constructions for initial-state preparation and time evolution under the SSHH Hamiltonian, together with a measurement protocol and classical post-processing to extract the many-body Berry phase and the spatial profile of the sublattice polarization. Classical simulations of these ideal circuits are used to demonstrate that topological characteristics remain robust against weak Hubbard interactions but break down once the chiral-symmetry-breaking component of the interaction exceeds a threshold. Resource costs (qubits, gates, shots, and classical processing) scale polynomially with system size.

Significance. If the results hold, the work supplies a concrete proof-of-concept for probing topological invariants in genuinely interacting many-body systems via adiabatic quantum simulation, extending prior non-interacting SSH studies. The explicit circuit constructions, independent measurement protocol, and use of exact classical simulations of ideal circuits are strengths that directly validate the framework for the finite sizes considered. Polynomial scaling is a positive indicator for future hardware feasibility. The stress-test concern about faithful representation on noisy hardware does not land, as the paper reports only ideal classical simulations rather than hardware runs.

minor comments (2)

[Abstract] The abstract would benefit from a brief statement of the system sizes simulated and the precise criterion used to identify the interaction threshold, even if these details appear in the main text.
[Measurement protocol section] Notation for the many-body Berry phase and its extraction via post-processing could be made fully explicit with a short equation or pseudocode block to aid reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript on the adiabatic quantum simulation framework for the SSHH model. The referee correctly notes the explicit circuit constructions, the use of classical simulations of ideal circuits to demonstrate robustness of topological signatures to weak interactions, the breakdown beyond a symmetry-breaking threshold, and the polynomial resource scaling. We also appreciate the clarification that concerns regarding noisy hardware do not apply, as our results are based on exact classical simulations rather than hardware execution. Since no specific major comments are provided in the report, we have no individual points to address.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs explicit gate-based quantum circuits for adiabatic state preparation and time evolution under the SSHH Hamiltonian, defines a measurement protocol with classical post-processing to extract the many-body Berry phase and sublattice polarization, and then performs classical simulations of these ideal circuits to demonstrate the claimed robustness of topological invariants. These steps form a self-contained forward chain: the circuits and protocol are defined independently of the final topological claim, the simulations compute the direct consequences of the model and protocol for finite sizes, and the reported breakdown threshold emerges as an output of the simulation rather than a fitted input or self-referential definition. No load-bearing self-citations, ansatzes smuggled via prior work, or renamings of known results are present in the derivation; the results are falsifiable via the stated simulation procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the adiabatic theorem and the validity of the Berry-phase extraction protocol are invoked without further justification visible here.

axioms (1)

domain assumption The adiabatic theorem applies to the time-dependent Hamiltonian used in the simulation
Invoked to justify slow evolution from initial to final state.

pith-pipeline@v0.9.0 · 5481 in / 1320 out tokens · 38842 ms · 2026-05-13T05:47:17.266220+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We develop an adiabatic quantum simulation framework... explicit quantum-circuit constructions for initial-state preparation and time evolution... many-body Berry phase... sublattice polarization... topological characteristics remain robust against weak Hubbard interactions but eventually break down as the chiral-symmetry-breaking component exceeds a threshold.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

U(T,0) = T exp(-i/ℏ ∫ H(t) dt) ... first-order Trotter decomposition ... U_ℓ = exp(-i δt/ℏ (2ℓ-1)/(2L) H_1) exp(-i δt/ℏ H_0)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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