{"id":"5fbefaf0-8fd1-487b-a999-edf36780f53b","arxiv_id":"2606.16055","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"Native nonlinear qubit-readout couplings alone neither eliminate nor reliably suppress readout-induced leakage; auxiliary modes reintroduce multiphoton channels whose rates vary by orders of magnitude over <7% frequency shifts.","lead":"Nonlinear qubit-readout couplings in superconducting circuits do not automatically suppress drive-induced leakage; auxiliary modes often reintroduce multiphoton resonances. Leakage rates can change by more than an order of magnitude when the readout frequency is shifted by less than 7%, so device design must place those modes carefully.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the reader's already-flagged cooldown-comparability assumption.","rationale":"The Reader correctly isolates the multi-cooldown comparison as the weakest link while recognizing that the Floquet comparison, selection-rule spectroscopy, and order-of-magnitude leakage contrast form a coherent, experimentally grounded argument. No stronger load-bearing concern (e.g., misidentification of transitions, failure of the Floquet model, or circular use of the same data for both prediction and validation) emerges from the full manuscript and SM. The concrete test above would tighten the remaining uncertainty without requiring new hardware; until then the CONDITIONAL verdict with high confidence is appropriate and should stand.","tokens_in":27471,"tokens_out":505,"duration_ms":5889,"concrete_test":"Re-fit the dimon Hamiltonian parameters independently to the level spectra of cooldown I and cooldown III; re-run the Floquet hybridization map of Fig. 4(a) with each set; if the predicted critical power for the [2,3:3] resonance still differs by ≳10\times between the two fitted models at the experimental frequencies, the attribution to spectral placement remains intact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that native nonlinear couplings alone neither eliminate nor necessarily suppress drive-induced leakage, and that leakage can vary by orders of magnitude for <~7% frequency shifts—is supported by three independent pillars: (i) Floquet landscapes for four Hamiltonians (Fig. 2), (ii) symmetric/asymmetric DUST spectroscopy that maps auxiliary-mode-enabled resonances (Fig. 3 and SM), and (iii) the two-cooldown leakage benchmark (Table I, Fig. 4). The only load-bearing soft spot is the one already identified by the Reader: that Exp 1 (7.513 GHz) and Exp 2 (7.025 GHz) differ solely in intended resonator frequency. Junction aging shifts ωq by tens of MHz across cooldowns, and package/TLS environments can drift; the paper keeps χ and κ nominally matched and shows the Floquet prediction of a [2,3:3] resonance at the first frequency, but does not quantify residual aging or mode-drift contributions to the >10\times leakage change. No deeper internal inconsistency, circular derivation, or unsupported selection-rule claim appears.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper argues that native nonlinear qubit–readout couplings (ideal cosine-cosine, balanced cross-Kerr, and mediated cosine-cosine) do not automatically eliminate or suppress drive-induced multiphoton leakage relative to linear hybridization. Floquet simulations of the four model Hamiltonians show that ideal cosine-cosine yields the sparsest resonance landscape via selection rules, yet realistic mediation by auxiliary modes reintroduces dense parasitic channels. Pump-probe spectroscopy on a dimon device maps allowed versus symmetry-forbidden transitions under symmetric/asymmetric drives, and a repeated-readout leakage benchmark on two cooldowns (readout frequencies differing by <7 %) demonstrates leakage rates that change by more than an order of magnitude when a predicted multiphoton resonance is avoided. The authors conclude that the benefits of nonlinear couplings appear only after deliberate spectral engineering of auxiliary and parasitic modes.","tokens_in":27715,"tokens_out":1024,"duration_ms":19829,"significance":"Leakage is a dominant correlated error for surface-code QEC; any architecture that claims intrinsic Purcell protection or stricter selection rules must therefore be stress-tested against multiphoton resonances. The work supplies a concrete, falsifiable methodology—Floquet branch analysis of the full multi-mode Hamiltonian, symmetry-resolved DUST spectroscopy, and frequency-swept leakage benchmarking—that can be applied to other nonlinear-coupling proposals. The experimental demonstration that a <7 % shift in readout frequency changes leakage by >10\times is immediately actionable for device design. Strengths include the systematic comparison of four Hamiltonians (Fig. 2), the clear experimental separation of allowed versus forbidden processes (Fig. 3), and the quantitative Table I that links a specific Floquet resonance to measured leakage.","major_comments":[{"comment":"The load-bearing experimental claim that leakage varies by orders of magnitude for a <7 % frequency change rests on the comparison of Exp 1 (ω_r/2π = 7.513 GHz) and Exp 2 (7.025 GHz) across successive cooldowns (Table I, Fig. 4). While χ and κ are kept nominally matched and Floquet predicts a [2,3:3] resonance only at the first frequency, the SM reports qubit-frequency aging of tens of MHz (6.271 → 6.209 GHz) and notes that package/TLS environments can drift. Without a quantitative bound on residual aging or mode-drift contributions (e.g., re-running Floquet with the aged parameters or additional DUST maps on both cooldowns), the attribution of the entire >10\times improvement solely to the intended multiphoton landscape remains incompletely controlled.","section":"Sensitivity to the choice of readout frequency; Table I and Fig. 4"},{"comment":"Transition labels [x,y:n] in Fig. 3 and the SM spectroscopy are obtained by fitting EJ, ECJ, ECs to the low-lying spectrum and then performing Floquet branch analysis. The SM itself notes that higher levels deviate because of higher harmonics of the potential and hybridization with cavity modes. A short sensitivity analysis (how much do the resonance loci move under plausible parameter variations or inclusion of the next harmonic) would confirm that the dominant auxiliary-mode channels remain correctly identified and that the denser landscape of Fig. 2(d) is robust.","section":"Impact of auxiliary modes; Fig. 3 and SM"}],"minor_comments":[{"comment":"Citation numbering in the main text and SM is inconsistent (multiple distinct papers share the label [11], [19], etc.). A clean renumbering would improve readability.","section":"References throughout"},{"comment":"Fig. 2 color scale and hybridization-parameter definition Θ(jt) are clear, but the caption could explicitly state that the color bar is logarithmic so that the relative density of resonances is immediately visible.","section":"Fig. 2"},{"comment":"In the SM, the active-reset cost function (S25) uses an integral to 10τ; a one-sentence justification for the upper limit would help reproducibility.","section":"SM, Readout settings"},{"comment":"The shorthand [q,m:d] is introduced late; defining it once in the main text near Fig. 3 would avoid forcing the reader to the SM.","section":"Impact of auxiliary modes"}],"recommendation":"minor_revision","confidential_remarks":"The cooldown-comparability issue is real but addressable with existing data or a short additional simulation; it does not undermine the overall narrative. The manuscript is a natural fit for a high-impact quant-ph journal (PRL/PRX Quantum style)."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is simple: native cosine-cosine or balanced cross-Kerr couplings do not automatically fix readout-induced leakage. Once you include the auxiliary modes that actually realize those couplings, the multiphoton spectrum gets denser, and leakage can jump by more than an order of magnitude when the readout frequency moves by less than 7%. That is a concrete design rule for anyone building high-power, low-leakage readout for QEC.\n\nWhat is new is the side-by-side Floquet landscape of four Hamiltonians (linear, balanced cross-Kerr, ideal cos-cos, mediated cos-cos) plus a clean experimental demonstration on a dimon device. Fig. 2 shows the ideal cos-cos case is sparsest, while the mediated version reintroduces a thicket of joint [q,m:n] resonances. The symmetric/asymmetric pump-probe spectroscopy (Fig. 3 and SM) maps allowed versus forbidden transitions and confirms the auxiliary mode is the culprit. The two-cooldown leakage benchmark (Table I) then shows the practical cost: same device, nominally matched χ and κ, leakage drops from ~2–6% to ~0.1% when the resonator is moved off a predicted [2,3:3] resonance. The math is standard Floquet branch analysis; the data chain is coherent; citations cover the relevant prior work without padding.\n\nThe soft spot is exactly the one the reader flagged: Exp 1 and Exp 2 are successive cooldowns. Junction aging shifts ωq by tens of MHz, and package/TLS environments can drift. The paper keeps χ and κ similar and shows the Floquet prediction lines up with the bad frequency, but it does not quantify residual aging or mode-drift contributions. That is a real caveat, not a fatal one; a single-cooldown tunable resonator would have been cleaner, but the spectroscopy and simulations already stand on their own.\n\nThis is for people who design or simulate superconducting readout and care about leakage in surface-code cycles. It deserves a serious referee. I would cite the frequency-sensitivity result and the comparative Floquet plots. Send it out.","headline":"Solid experimental warning that mediated nonlinear readout couplings re-crowd the multiphoton landscape and can make leakage swing by >10\times for a <7% frequency shift; the two-cooldown comparison is the only real soft spot.","tokens_in":28369,"tokens_out":548,"would_cite":true,"duration_ms":6397,"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":"Native nonlinear qubit-readout couplings neither eliminate drive-induced leakage nor reliably suppress it; without careful engineering of auxiliary modes they often make leakage worse, and leakage rates still swing by orders of magnitude wi","keywords":["superconducting circuits","qubit readout","drive-induced leakage","multiphoton resonances","nonlinear couplings","cosine-cosine interaction","Floquet analysis","Purcell protection"],"falsifier":"Repeat the leakage-benchmarking experiment on a single cooldown while continuously tuning the readout frequency across the same ~7% window (or fabricate an otherwise identical device with a tunable resonator) and check whether leakage still jumps by more than tenfold exactly where the Floquet map predicts the [2,3:3] resonance.","tokens_in":28353,"feed_emoji":"⚡","tokens_out":980,"duration_ms":12967,"temperature":0.7,"pith_summary":"Superconducting qubit readout is limited by drive-induced multiphoton transitions that push the qubit into leakage states, creating correlated errors that damage quantum error correction. Nonlinear couplings such as cosine-cosine interactions look attractive because they promise intrinsic Purcell protection and stricter selection rules than ordinary linear hybridization. This paper shows that, in real devices, those couplings alone do not remove the unwanted transitions and frequently introduce new parasitic channels through auxiliary or package modes. Floquet simulations and pump-probe spectroscopy map a dense landscape of resonances whose strength remains highly sensitive to the precise readout frequency. Two experiments on the same device that differ by less than 7% in resonator frequency exhibit more than an order-of-magnitude difference in measured leakage. The practical message is that the advertised benefits of nonlinear readout appear only when every relevant auxiliary mode is deliberately placed and parasitic modes are eliminated.","feed_headline":"Nonlinear readout couplings can raise leakage by 10×","feed_subtitle":"Even a 7% shift in resonator frequency flips leakage rates; auxiliary modes must be engineered, not ignored.","key_machinery":"Floquet steady-state branch analysis of the driven multi-mode Hamiltonian, quantified by the hybridization parameter Θ that flags multiphoton resonances as avoided crossings between dressed computational and leakage states; this is used both to compare idealized coupling schemes and to identify the joint qubit-mediator transitions observed in spectroscopy.","core_discovery":"In realistic superconducting circuits, native nonlinear qubit-readout couplings (ideal cosine-cosine, balanced cross-Kerr, or mediated cosine-cosine) neither eliminate nor systematically suppress drive-induced multiphoton leakage. Auxiliary modes required to realize the nonlinear interaction enlarge the Hilbert space and reintroduce dense families of allowed resonances; leakage rates can still change by more than an order of magnitude when the readout frequency is shifted by less than 7%.","pith_inferences":["The same frequency-crowding problem will appear in any multi-mode circuit that relies on mediated nonlinear interactions (parametric gates, beamsplitters, or couplers), not only in readout.","High-frequency readout (ωr/ωq ≳ 5–10) may still be the simplest practical route to sparse multiphoton landscapes even for nonlinear couplings, because matrix elements to high-lying well states vanish.","Automated Floquet-plus-HFSS co-design loops that jointly place qubit, mediator, resonator and package modes could become standard before tape-out of nonlinear-readout chips."],"forward_implications":["Device design for nonlinear readout must treat auxiliary-mode frequencies and anharmonicities as first-class optimization parameters, not afterthoughts.","Single-frequency leakage characterization is insufficient; any claim of improved QND performance requires a frequency-sweep map of multiphoton resonances.","Package and parasitic modes must be identified and detuned or suppressed before the selection-rule advantages of cosine-cosine coupling can be realized.","Readout-frequency placement windows free of low-order joint resonances can be opened by deliberate linearization or frequency engineering of the mediator mode."],"fun_headline_variants":["Nonlinear couplings raise leakage 10× without mode engineering","Under 7% readout shift swings leakage rates by 10×","Auxiliary modes reintroduce multiphoton leakage paths","Native nonlinear links fail to suppress drive-induced leakage","Leakage varies orders of magnitude with tiny frequency tweaks"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The two successive cooldowns that change only the intended readout-resonator frequency leave every other device parameter (junction aging, package modes, TLS bath, dispersive shift, linewidth) sufficiently unchanged that the observed order-of-magnitude leakage difference can be attributed solely to the multiphoton landscape predicted by the Floquet model.","fun_headline_variants_meta":{"raw":{"variants":["Nonlinear couplings raise leakage 10× without mode engineering","Under 7% readout shift swings leakage rates by 10×","Auxiliary modes reintroduce multiphoton leakage paths","Native nonlinear links fail to suppress drive-induced leakage","Leakage varies orders of magnitude with tiny frequency tweaks"]},"model":"grok-4.5","effort":"low","cost_usd":0.003574,"raw_usage":{"total_tokens":1151,"prompt_tokens":737,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":35740000,"prompt_tokens_details":{"text_tokens":737,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":351,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":737,"tokens_out":63,"duration_ms":3152,"temperature":1.0,"reasoning_tokens":351,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T13:53:31.607300+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Repeat the leakage-benchmarking experiment on a single cooldown while continuously tuning the readout frequency across the same ~7% window (or fabricate an otherwise identical device with a tunable resonator) and check whether leakage still jumps by more than tenfold exactly where the Floquet map predicts the [2,3:3] resonance.","supporting_citations":[],"review_version":1}