{"id":"de465880-7cac-45e0-b95b-cb9f8a009794","arxiv_id":"2607.11483","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"SUSY-inspired brick-wall circuits support both edge-localized and ballistically propagating strong zero modes that can be steered by mass parameters and used for quantum-information transport.","lead":"Quantum circuits whose two-qubit gates are the S-matrix of a supersymmetric 1+1D field theory host strong zero modes that can stick to edges or travel ballistically when masses are staggered. The ballistic modes let experimenters route a qubit of information across a register while splitting it across spatially separated Majoranas, giving quadratic noise protection.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The central claim is a free-fermion construction: in the large-γ, small-θ regime the micromotion generated by the zeroth-order Dzyaloshinskii–Moriya bricks (Eq. 12) dresses the first-order generators so that ker A becomes four-dimensional, yielding a pair of approximately conserved Majoranas—one edge-localized, one defect-guided and ballistically mobile. Because the circuits are matchgates, every step (analytic kernel, Gaussian evolution of Γ, explicit transfer unitary of SM G) is exact within the free-fermion algebra; the only approximation is the exponential smallness of the residual commutator at finite γ, which the authors already flag. The reader correctly identified this as the weakest assumption, yet it does not undermine the claim as stated. The noise study (SM F,H) is preliminary but is presented as such and is not required for the existence or routing results. Consequently the ACCEPT verdict with high confidence stands; no adjustment is warranted.","tokens_in":19535,"tokens_out":527,"duration_ms":5618,"concrete_test":"Independently recompute the kernel of OF−1 for the single-heavy-mass configuration at L=8, α=1, θ=0.1, γ=30 (and again at γ=10) using the explicit SO(2L) matrices of SM D; confirm that two of the four near-zero modes match the analytic forms (18)–(21) to machine precision and that the associated magnetization signature remains ballistic under the 2L-layer micromotion.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (exact conservation only at γ→∞) is already stated by the authors and is not load-bearing for the central claim. The paper works throughout in the free-fermion/matchgate setting, derives the four-dimensional kernel of A (and of OF) analytically in the large-γ limit via micromotion dressing of Heff (Eqs. 11–13 and SM E), and supplies exact Gaussian numerics for finite but large γ=30 that exhibit the expected ballistic signature. The QI-routing protocol (Fig. 3, SM G) is an explicit finite-depth circuit that maps one Dirac fermion built from the pair of localized SZM onto another; its correctness follows from the same free-fermion algebra once the approximate conservation is granted. No internal inconsistency or hidden assumption that would invalidate the construction for the stated regime was found.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript constructs brick-wall quantum circuits whose two-qubit gates are the S-matrix of a supersymmetric 1+1D QFT. Because the gates are matchgates the dynamics is free-fermionic; the associated Floquet operator UF therefore induces an orthogonal rotation OF on the 2L-dimensional Majorana space. In the simultaneous small-rapidity (Hamiltonian) and large mass-ratio limits the kernel of the first-order generator becomes four-dimensional, yielding two exact and two approximate strong zero modes. One pair remains localized at a boundary while the second pair is transported ballistically by the Floquet micromotion generated by a Dzyaloshinskii–Moriya term. The authors give explicit analytic expressions for the modes in both staggered and single-heavy-mass configurations, confirm the ballistic signature with exact Gaussian covariance-matrix numerics, and construct a finite-depth (2L-3-layer) protocol that transfers one logical qubit encoded in a Dirac fermion built from the localized pair. Robustness under selected parity-preserving noise is examined in the Supplemental Material.","tokens_in":19833,"tokens_out":882,"duration_ms":8142,"significance":"The work supplies a concrete, analytically controlled mechanism for ballistically propagating strong zero modes inside free-fermion circuits and converts that mechanism into an explicit quantum-information routing protocol. The derivation of the micromotion-dressed effective Hamiltonian (Eq. 13 and SM E) is careful, the four-dimensional kernel is obtained by direct linear algebra rather than fitting, and the numerics are exact within the Gaussian formalism. These features make the construction a useful addition to the literature on free-fermion Floquet circuits and on protected information transport, even though the setting remains free-fermionic and the approximate modes become exact only as γ\to∞.","major_comments":[{"comment":"The central claim of ballistic propagation and the QI-routing protocol rest on approximate SZM that become exact only for γ\to∞ (Eqs. 16–17, 20–21). While the authors correctly state this, the main text and SM F/H present numerical evidence only for a single large value γ=30 and for two parity-preserving noise channels. A short quantitative scan of the residual commutator ||[UF,Ψ̃]|| versus γ (or of the fidelity of the transfer protocol versus γ) would make the practical range of the construction transparent and would strengthen the load-bearing claim that the modes remain useful at finite but large mass ratio.","section":null}],"minor_comments":[{"comment":"The abstract and introduction use both “Dzyaloshinskii Moriya” and “Dzyaloshinskii–Moriya”; a single hyphenated spelling should be adopted throughout.","section":null},{"comment":"Figure 2 caption and SM F refer to “local magnetization” ⟨Zj⟩ as the diagnostic of the SZM; a one-sentence reminder that this is the (2j-1,2j) entry of the covariance matrix would help readers unfamiliar with the Gaussian formalism.","section":null},{"comment":"In SM G the three-step transfer protocol is described clearly, but the explicit values of the boundary parameter β and of the mass string after layer L-1 are given only in prose; a short table or circuit diagram annotation would improve reproducibility.","section":null},{"comment":"References [39], [41], [42], [44], [45] appear with future arXiv numbers or “sciPost submission” labels; these should be updated or flagged as preprints at the time of publication.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a natural and technically solid extension of the authors’ earlier SciPost Phys. 17, 087 (2024) work. The free-fermion restriction is acknowledged and does not undermine the internal claims. I see no novelty or citation issues that would affect the editorial decision."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The new piece is the controlled ballistic SZM that rides the Floquet micromotion of the SUSY S-matrix gates. Edge-localized SZMs in free-fermion systems are familiar; the extra pair that appears once the mass ratio is large, and that can be steered by the heavy-mass location and the sign of β, is not. They give an explicit finite-depth circuit (2L-3 layers) that moves one logical qubit encoded in a pair of those modes from one end of the register to the other.\n\nWhat they do well is keep everything inside the exact matchgate/Gaussian setting. The SO(2L) rotations, the micromotion dressing of Heff (their Eq. 13 and SM E), and the four-dimensional kernel of A (or of OF-1) are derived cleanly. The numerics are exact covariance evolution, not approximate. The Dzyaloshinskii–Moriya origin of the routing is transparent. The noise discussion (SM F,H) is preliminary but honest: quadratic protection against local Z noise when the information is split across two modes, and clear vulnerability to bit-flip-type errors.\n\nSoft spots are real but proportional. Conservation is only exponential for finite γ; they work at γ=30 and state the limit. The noise study is limited to a few parity-preserving channels. No public code. None of that undercuts the central algebraic claim. The paper sits squarely inside free-fermion circuits and Floquet engineering; it does not claim a new platform beyond matchgates.\n\nThis is for people who already care about strong zero modes, dual-unitary or integrable circuits, or protected transport in free-fermion hardware. A serious referee should see it. I would accept it for peer review and would cite the routing construction if I were writing on Floquet Majorana protocols.","headline":"Clean free-fermion construction of steerable, ballistically propagating SZMs plus an explicit QI-routing protocol; solid within matchgate circuits, not oversold.","tokens_in":20376,"tokens_out":459,"would_cite":true,"duration_ms":5903,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Supersymmetry-inspired circuits host strong zero modes that can be steered ballistically and used to move a logical qubit.","keywords":["strong zero modes","quantum circuits","supersymmetry","Floquet micromotion","Dzyaloshinskii-Moriya","quantum information transport","free fermions","matchgates"],"falsifier":"Compute the exact commutator of the candidate propagating operator with the full Floquet unitary at finite mass ratio: if the commutator does not fall exponentially with the mass ratio, or if the white magnetization trace fails to track the heavy-mass location under the stated protocol, the claim fails.","tokens_in":20475,"feed_emoji":"⚛️","tokens_out":904,"duration_ms":7837,"temperature":0.7,"pith_summary":"The paper builds brick-wall quantum circuits whose two-qubit gates are the elastic S-matrices of a supersymmetric 1+1D field theory. These circuits are free-fermionic and therefore admit exact or approximate strong zero modes—operators that commute with the Floquet evolution and anticommute with parity. In isotropic mass configurations one finds a delocalized mode and a boundary-localized mode. In anisotropic (staggered or single-heavy-mass) configurations the Floquet micromotion generated by a large Dzyaloshinskii–Moriya term enlarges the kernel, producing a second pair of modes. One of these modes stays localized while the other propagates ballistically, following the location of the heavy mass. Encoding a logical qubit in a Dirac fermion built from the pair lets the circuit transfer one qubit of information across an L-site register in 2L−3 layers, with quadratic rather than linear sensitivity to certain single-qubit noise.","feed_headline":"Circuits steer strong zero modes to move a logical qubit","feed_subtitle":"Mass anisotropy and Floquet micromotion turn conserved Majoranas into a ballistic quantum-information bus","key_machinery":"Floquet micromotion: the nontrivial zeroth-order (in rapidity) partial products of circuit layers that permute Majorana operators according to a strong Dzyaloshinskii–Moriya rotation; this dressing enlarges the kernel of the effective generator and steers the propagating strong zero mode.","core_discovery":"In the large mass-ratio, small-rapidity regime of the brick-wall circuit the kernel of the Floquet generator becomes four-dimensional and contains a pair of approximately conserved Majorana operators, one of which remains localized while the other propagates ballistically under the micromotion generated by the Dzyaloshinskii–Moriya term; the pair can be used to transfer one logical qubit across an L-site register in 2L−3 layers.","pith_inferences":["Because the circuits are matchgate, the entire protocol is efficiently classically simulable via covariance matrices, so any experimental claim can be cross-checked on a classical computer before hardware runs.","If the mass-ratio requirement can be relaxed by approximate or dressed zero modes, the same routing idea might transfer to near-term hardware with only moderate anisotropy.","The quadratic noise protection suggests a natural comparison with other Majorana-based encodings that also split information across distant sites."],"forward_implications":["A concrete circuit protocol moves one logical qubit from one end of an L-site register to the other in 2L−3 layers by steering a pair of strong zero modes.","Encoding the logical qubit in spatially separated Majoranas yields quadratic rather than linear infidelity under certain single-qubit phase errors.","The number and location of strong zero modes can be tuned by the mass pattern and the sign of the boundary gates.","The same micromotion mechanism may generate additional conserved operators in other free-fermionic brick-wall circuits that contain chiral hopping terms."],"fun_headline_variants":["Brick-wall circuits launch ballistic strong zero modes","SUSY gates yield movable Majorana zero modes for qubit transfer","DM micromotion drives strong zero modes across circuit registers","Propagating SZMs ferry one logical qubit in 2L-3 layers","Localized and ballistic SZMs coexist in mass-anisotropic circuits"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The extra strong zero modes become exactly conserved only in the infinite mass-ratio limit; for any finite ratio they are only approximately conserved, and the numerical demonstrations use a large but finite ratio.","fun_headline_variants_meta":{"raw":{"variants":["Brick-wall circuits launch ballistic strong zero modes","SUSY gates yield movable Majorana zero modes for qubit transfer","DM micromotion drives strong zero modes across circuit registers","Propagating SZMs ferry one logical qubit in 2L-3 layers","Localized and ballistic SZMs coexist in mass-anisotropic circuits"]},"model":"grok-4.5","effort":"low","cost_usd":0.0061,"raw_usage":{"total_tokens":1502,"prompt_tokens":680,"num_sources_used":0,"completion_tokens":86,"cost_in_usd_ticks":61000000,"prompt_tokens_details":{"text_tokens":680,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":736,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":680,"tokens_out":86,"duration_ms":6394,"temperature":1.0,"reasoning_tokens":736,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T05:16:59.134347+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Compute the exact commutator of the candidate propagating operator with the full Floquet unitary at finite mass ratio: if the commutator does not fall exponentially with the mass ratio, or if the white magnetization trace fails to track the heavy-mass location under the stated protocol, the claim fails.","supporting_citations":[],"review_version":1}