{"id":"de0f0154-ec35-45d8-a722-5cf15083e30b","arxiv_id":"2412.14098","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A theoretical proposal for a silicon-based Hyperbolic Quantum Processor using deep donors coupled through hyperbolic polaritons, claiming strong long-range coupling via Hyperbolic Super-Resonance and liquid-nitrogen-temperature operation.","lead":"This paper proposes a quantum processor in which qubits are deep donor atoms in silicon and interactions are carried by special polariton waves in hexagonal boron nitride. It claims gate fidelities above 99 percent, very high qubit density, and operation at liquid nitrogen temperature, all based on a predicted effect called Hyperbolic Super-Resonance.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The J/Γ margin and 99% fidelity claim rely on the local hBN permittivity with Im√(−ε⊥/ε∥)≈0.01 persisting up to atomic-scale wavevectors; large-momentum losses or nonlocality would collapse h_c/h_* and the central architecture.","rationale":"The reader's weakest assumption is essentially the one identified here: the local, homogeneous, frequency-dependent permittivity is assumed to describe hBN hyperbolic phonon-polaritons up to k ∼ 1/a, with Im sqrt(−ε_⊥/ε_∥) ≈ 0.01. I agree that this is the load-bearing point. Every quantitative headline—J comparable to ℏω, Γ ≲ J/100, fidelity above 99%, density above 10^8 cm−2—is obtained from Eqs. (7)–(9), (18), (24)–(25), and the supplementary Green's-function reduction, all of which assume a local dielectric response with a small, constant imaginary part at very large wavevectors. The paper presents no derivation of Eqs. (7)–(9) except references to unpublished preprints, and it contains no numerical verification of the high-k behavior. Real hBN, even when isotopically enriched, has finite optical-phonon damping and a lattice cutoff, so the high-momentum regime is exactly where the approximation is most fragile. A conservative recomputation with k-dependent loss and a Brillouin-zone cutoff would settle whether the 100-fold margin is genuine. I do not see a separate fatal internal inconsistency that would change this verdict; the dimensional form of Eq. (22) appears to require a cube root rather than a square root, but that is secondary and would not rescue the claim if the loss assumption fails. Therefore the reader's REJECT remains appropriate: the central numbers are not supported by the arguments supplied in the manuscript.","tokens_in":18428,"tokens_out":10236,"duration_ms":97496,"concrete_test":"Solve the quasistatic Green's function in Eqs. (26)–(29) and (30)–(34) for the cylinder geometry of Fig. 4 using a nonlocal, cutoff-regulated hBN response instead of the local permittivity: take k-dependent damping such as Im ε(q,ω) = Im ε_local(ω) + β q², and truncate the mode sum at q_c = π/a with a ≈ 0.25 nm. Recompute h_*, h_c/h_* from Eq. (24), and Γ11/J12 from Eqs. (9) and (18) for R = 20–50 nm, d = 50 nm, h = h_c/2. If the margin falls below Γ/J = 1/100 or J < 0.1ℏω, the central claim fails; if the margin survives conservative nonlocal damping, the reader's rejection is not warranted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing condition is the hierarchy h_* ≪ h ≲ h_c in Eq. (23), quantified as h_c/h_* ≈ 100 in Eq. (25). This number follows from setting h_* = d |Im sqrt(−ε_⊥/ε_∥)| with a local, homogeneous, frequency-dependent permittivity and quoting Im sqrt(−ε_⊥/ε_∥) ≈ 0.01 for isotopically enriched hBN, with further reduction at cryogenic temperatures. However, the fields that dominate the Hyperbolic Super-Resonance have wavevectors up to the inverse atomic scale (k ∼ 1/a), and the local-continuum approximation is not established in that range. hBN phonon-polaritons gain damping at large in-plane momenta, and the hyperbolic response terminates near the Brillouin-zone edge. If the effective loss at the dominant k is larger than the quoted 0.01, or if the semiclassical degeneracy behind Eq. (7) is lifted by nonlocality and absorption, then h_* is not 0.5 nm but several nanometers or more. In that case h_c/h_* drops far below 100, the window (23) cannot simultaneously provide J ≳ 0.1ℏω and Γ ≲ J/100, and the headline fidelity, density, and liquid-nitrogen operation claims lose their quantitative basis. Since Eqs. (7)–(9), (24)–(25), and the supplementary reduction (30)–(34) all rely on this local low-loss assumption, this is the most load-bearing unverified premise. The issue is not a disagreement with consensus; it is a correctness risk because the manuscript offers neither a derivation of the high-k response nor a numerical check of the high-k behavior.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a \"Hyperbolic Quantum Processor\" architecture in which deep-donor qubits in silicon interact via hyperbolic phonon-polaritons in a nearby hexagonal boron nitride (hBN) resonator. The central concept is the \"Hyperbolic Super-Resonance\" (hSR), a claimed near-exact degeneracy of a large number of high-wavevector modes in a finite hyperbolic resonator, which the authors argue produces strong, long-range, optically switchable dipole-dipole interactions J12. The paper derives effective spin-exchange couplings and decay rates through a dyadic-Green-function formalism, and claims that at the hSR one obtains J12 comparable to the optical photon energy (~100 meV), decoherence rates Γ satisfying Γ ≲ J/100, gate fidelities above 99%, qubit densities above 10^8 cm^-2, and operation at liquid nitrogen temperatures without dilution refrigeration. The architecture uses the Stark shift from off-resonant control fields to tune donor transitions into and out of the hBN hyperbolic bands, and proposes a multi-elliptical resonator geometry for multi-qubit entanglement.","tokens_in":18841,"tokens_out":9085,"duration_ms":79405,"significance":"If correct, the proposal would be a significant contribution to solid-state quantum computing: it promises silicon-compatible fabrication, long-range qubit interactions mediated by infrared polaritons, high gate fidelities, and cryogen-free operation. The paper is commendable for identifying specific donor transitions in silicon (Se, Mg, S) that spectrally overlap the hBN hyperbolic bands (Fig. 6), and for formulating the problem in the language of dyadic Green functions and Lindblad dynamics. However, the quantitative claims rest on a small set of analytical equations (Eqs. (7)-(9), (24)-(25)) that are either not derived in the manuscript or assigned to unpublished self-authored preprints, and on an unverified assumption that the local low-loss permittivity persists up to atomic-scale wavevectors. The paper does not provide machine-checked proofs, gate-level simulations, or a packing analysis; the headline fidelity and density numbers are asserted rather than demonstrated. The significance is therefore conditional on the missing derivations and on the validity of the high-wavevector locality assumption.","major_comments":[{"comment":"The central equations of the paper are the hSR condition (7), the single-emitter coupling (8), and the inter-emitter coupling (9). These are stated as \"we obtain\" or assigned to unpublished preprints [63] and [68], and no derivation is provided in the main text or the supplementary material. The supplement derives the related expressions (30)-(35) from a quasistatic Green-function calculation, but it does not derive Eq. (7) or Eq. (8). Since all subsequent quantitative claims (J12 ~ ℏω, h*, hc, the ratio in Eq. (24), and the fidelity estimate) depend on these equations, the core of the paper is not independently verifiable from the submitted text. The authors must include a complete derivation of Eqs. (7)-(9) in the supplement or cite a published derivation, rather than relying on unreviewed self-citations.","section":"Section V, Eqs. (7)-(9)"},{"comment":"The hierarchy h* ≪ h ≲ hc, quantified as hc/h* ≈ 100 in Eq. (25), assumes that the local, homogeneous, frequency-dependent permittivity of hBN, with Im sqrt(-ε⊥/ε∥) ≈ 0.01, remains valid for wavevectors up to k ~ 1/a. The paper itself notes that the wavenumber cutoff is at the inverse atomic scale (footnote [62]), and the hSR is dominated by such large wavevectors. However, the local-continuum approximation is not established in this range: hBN phonon-polaritons are expected to gain additional damping at large in-plane momenta, and the hyperbolic response terminates near the Brillouin-zone edge. If the effective loss at the dominant k is larger than 0.01, then h* is larger than 0.5 nm, the ratio hc/h* drops far below 100, and the window (23) cannot simultaneously yield J ≳ 0.1ℏω and Γ ≲ J/100. This is a load-bearing correctness risk. A quantitative test is needed, e.g., a microscopic or measured nonlocal dielectric response of hBN at k ~ 1/a, or a full-wave simulation of the resonator with a realistic high-k loss model.","section":"Section V, Eqs. (24)-(25); footnote [62]"},{"comment":"The statement that the gate fidelity is \"on the order of 99% and above\" for h ≃ hc follows only from the scaling Γ/J ~ h*/h (Eq. (19)) and the general result of Ref. [80]. The paper does not simulate the two-qubit gate dynamics described by the Hamiltonian and Lindblad operators in Eqs. (13)-(14), nor does it provide an error budget for the optical control fields (off-resonant scattering, Stark-shift misalignment), crosstalk between nearby nano-waveguides, or the finite linewidth of the super-resonance. Since fidelity is a headline quantitative claim, the authors should present a gate-level simulation or a more detailed error analysis rather than an order-of-magnitude estimate.","section":"Section VI, fidelity claim"},{"comment":"The abstract and Section VIII assert \"integration densities of well over 10^8 qubits/cm^2\" without a layout analysis. The proposed multi-elliptical resonator geometry with individual nano-waveguides (Figs. 1 and 5) must be packed with a pitch on the order of 1 μm to reach 10^8 cm^-2; the compatibility of this pitch with the resonator dimensions (R ~ 30-50 nm), the spacer thickness (h ~ 3-5 nm), and the control-waveguide network is not demonstrated. Please provide a quantitative packing analysis or soften the claim.","section":"Abstract and Section VIII, density claim"}],"minor_comments":[{"comment":"Numerous typos and grammatical errors: \"cubits\" should be \"qubits\" (Abstract, Fig. 1 and Fig. 3 captions, Section VI); \"sickness of the (silicon) spacer\" should be \"thickness\" (Section II); \"the the\" appears in Section I; the abstract uses \"it's\" instead of \"its\".","section":"Throughout"},{"comment":"The symbol e for eccentricity conflicts with the electron charge e used throughout the paper. Please use a different symbol, e.g., η or e_ell, to avoid ambiguity.","section":"Section V, Eq. (11)"},{"comment":"The sentence \"the coherence times in excess of 300 picoseconds, which are three orders of magnitude larger then the corresponding transition frequencies\" is dimensionally incorrect: a 300 ps coherence time corresponds to a rate of about 3 GHz, which is four orders of magnitude smaller than the 100 meV (≈24 THz) transition frequency. The intended statement is presumably that the decoherence rate is several orders of magnitude smaller than the transition frequency.","section":"Section VI"},{"comment":"The caption defines the spacer thickness as \"b\" while the text and equations use h; please unify the notation.","section":"Fig. 5 caption"},{"comment":"References [16] and [52] appear to be the same paper (Pidgeon and Murdin / Vinh et al., \"Silicon as a model ion trap: Time domain measurements of donor Rydberg states\"). This duplicate should be removed.","section":"References"},{"comment":"The legend entries for the donor transitions (e.g., \"Se0_x\", \"Mg^*+\", \"Si:Mgi0\") are not all defined in the caption, and the relation between the color coding and the specific transitions is unclear.","section":"Fig. 6 caption"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a proposal with strong claims but the central equations (7)-(9) are attributed to two self-authored unpublished preprints ([63] and [68]), which is a heavy circularity burden. The paper also lacks a quantitative treatment of the high-wavevector regime of hBN, which is essential for the hSR. The fidelity and density claims are not supported by simulations or layouts. The manuscript appears to be in an early draft state, with many typos and inconsistent notation. If the authors can provide the missing derivations and address the high-k loss concern, the paper could become a solid contribution; in its current form, I would not recommend publication in a top journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nTwo things you should know. First, the architecture is genuinely new: deep donor qubits in silicon coupled to hBN hyperbolic resonators, with Stark shifts used to tune qubits into and out of the hyperbolic band, aiming at long-range strong coupling and integration densities above 10^8 qubits per square centimeter. Second, the numbers that make it interesting—J around 100 meV, fidelity above 99%, h_c/h_* around 100—are not derived in this manuscript. Equations (7)–(9) are assigned to two self-authored unpublished preprints, refs. [63] and [68], and the supplement does not close that gap. That is the load-bearing issue.\n\nWhat the paper does well: it assembles a coherent physical picture, cites the relevant experimental literature on hBN phonon polaritons, isotopically enriched hBN, and deep donors in silicon, and it identifies specific donor transitions that plausibly sit in or near the hBN hyperbolic bands. Figure 6 is genuinely useful. The Green-function formalism in the supplement is standard, and the quasistatic reduction is appropriate for hyperbolic nanostructures. Using optical Stark shifts to switch interactions is borrowed from superconducting circuits, but the adaptation here makes sense.\n\nThe soft spots. Equations (7)–(9), (18), (24)–(25) are asserted with no derivation in the paper or supplement. The stress-test note is on target: the h_c/h_* ~ 100 margin assumes the local, homogeneous permittivity of hBN, with Im sqrt(-eps_perp/eps_par) ~ 0.01, holds up to atomic-scale wavevectors. hBN's hyperbolic response terminates near the Brillouin zone edge, and losses grow at large momenta; if the effective loss is a few times larger, the operating window in Eq. (23) closes, and the fidelity and density claims lose their basis. The 99% fidelity is also not a gate-level result—it is inferred from Gamma less than or about J/100, with no control-error budget, crosstalk analysis, or disorder sensitivity. These are not minor quibbles; they are exactly where the proposal lives or dies. That said, I do not see a fatal contradiction: this is a proposal, and the missing derivations could in principle be supplied.\n\nWho is this for? Researchers in quantum computing architectures and hyperbolic nanophotonics. A reading group would get a good debate out of it. My recommendation: send it to peer review, but with referees explicitly asked to verify Eqs. (7)–(9) and the high-wavevector loss assumption. If the authors can provide the derivations and a numerical check, this could be a real contribution. As written, it is not ready.","headline":"A creative architecture whose headline numbers rest on self-cited unpublished preprints and an unverified high-wavevector loss assumption; not publishable as written, but serious enough to referee.","tokens_in":19359,"tokens_out":3368,"would_cite":false,"duration_ms":31894,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Hyperbolic-material resonators can make distant silicon qubits interact strongly enough for 99 percent fidelity gates.","keywords":["hyperbolic materials","hexagonal boron nitride","phonon polaritons","quantum gates","spin-exchange coupling","donor qubits in silicon","strong coupling","liquid nitrogen operation"],"falsifier":"Measure the two-qubit exchange coupling $J_{12}$ and the decay rate $\\Gamma_{11}$ as functions of spacer thickness $h$ in a fabricated hBN cylindrical resonator with two silicon donor emitters tuned to the hSR condition of Eq. (7). The local-permittivity model predicts $J_{12}$ following Eq. (9) and $\\Gamma_{11}/J_{12} \\sim h_*/h$ for $h\\gtrsim h_*$; observing that the coupling saturates at a much lower value, or that the super-resonance peak in the trapped-intensity spectrum broadens dramatically as the resonator shrinks, would falsify the assumption and invalidate the 99 percent fidelity and $10^8$ cm$^{-2}$ density claims.","tokens_in":2261,"feed_emoji":"⚛️","tokens_out":4955,"duration_ms":102826,"temperature":0.7,"pith_summary":"This paper sets out to remove the usual bottleneck between a tiny quantum emitter and the wavelength of light. It claims that if qubits are placed next to a resonator made from a natural hyperbolic material such as hexagonal boron nitride, the polariton modes of that medium can carry an exchange interaction between two emitters over distances far beyond the atomic scale, and at a special resonance this coupling becomes comparable to the photon energy. The authors call this the Hyperbolic Super-Resonance and show, within a quasistatic Green-function calculation, that the resulting spin-exchange energy can reach tens of meV while the material-induced decoherence stays about a hundred times smaller when the spacer thickness is chosen correctly. They conclude that two-qubit gates based on deep donor atoms in silicon can reach fidelities of 99 percent and above, that integration densities above $10^8$ qubits per square centimeter are possible, and that the processor can run at liquid nitrogen temperature without dilution refrigeration. The paper is a concrete proposal, not a demonstration: every needed technology has been shown separately, but the integrated device does not yet exist.","feed_headline":"Hyperbolic resonance enables 99% fidelity qubit gates","feed_subtitle":"Silicon donor qubits couple through hBN polaritons at liquid nitrogen temperature, no dilution fridge needed.","key_machinery":"The load-bearing object is the Hyperbolic Super-Resonance (hSR): an asymptotically exact degeneracy of an extremely large number of high-wavevector polariton modes in a finite hyperbolic resonator whose ray dynamics is integrable. In the cylindrical geometry it is fixed by Eq. (7), $\\sqrt{-\\epsilon_\\perp/\\epsilon_\\parallel} = 4R/(dm)$, and it converts the broadband hyperbolic density-of-states singularity into a resonant enhancement of the dyadic Green function that connects two spatially separated dipoles. The calculation of the spin-exchange coupling and decay rates runs through Eq. (15), $J_{ij} + i\\Gamma_{ij} = 4\\pi(\\omega/c)^2 p_i^* \\cdot G(r_i,r_j,\\omega) \\cdot p_j$, evaluated in the quasistatic limit via the scalar-potential Green function of Eqs. (26)--(27); the super-resonance pole in that Green function produces the $J_{12}$ of Eq. (9). The second controlling element is the spacer thickness $h$: it suppresses the local decoherence $\\Gamma_{ii}$ (which diverges when the emitter touches the hyperbolic medium) while leaving the exchange coupling finite, which is what opens the window $h_* \\ll h \\lesssim h_c$.","core_discovery":"The central claim is that the Hyperbolic Super-Resonance (hSR) turns a finite hyperbolic resonator into a nearly degenerate multimode cavity. For a metal-clad cylindrical hBN resonator the degeneracy condition is $\\sqrt{-\\epsilon_\\perp/\\epsilon_\\parallel} = 4R/(dm)$ (Eq. 7), and at that frequency two donor-qubit dipoles on opposite sides of the resonator acquire a spin-exchange energy $J_{12} \\simeq 8p^2/(h_*^3 + 2h^3)$ (Eq. 9), where $h_* = d \\, \\mathrm{Im}\\sqrt{-\\epsilon_\\perp/\\epsilon_\\parallel}$ and $h$ is the spacer thickness. With $p \\sim e\\cdot 1$ nm, $d \\sim 50$ nm, $h \\sim 3$--$5$ nm and isotopically enriched hBN, the paper estimates $J_{12}$ at tens of meV, comparable to the $\\sim 100$--$180$ meV photon energies of the hBN hyperbolic bands, i.e. the ultra-strong coupling regime. The accompanying decoherence rate $\\Gamma_{11}$ diverges as $h\\to 0$ while $J_{12}$ stays finite, and for $h\\gtrsim h_*$ the ratio is $\\Gamma/J \\sim h_*/h$; using measured hBN loss $\\mathrm{Im}\\sqrt{-\\epsilon_\\perp/\\epsilon_\\parallel}\\simeq 0.01$ gives $h_c/h_* \\simeq 100$. The paper therefore argues that $h$ can be chosen so that $J \\gtrsim 0.1\\hbar\\omega$ and $\\Gamma \\lesssim J/100$, yielding gate fidelities of order 99% and above, and that the whole system is a silicon-based optoelectronic chip with projected densities over $10^8$ qubits/cm$^2$.","pith_inferences":["Beyond the paper: if the hSR mechanism is geometry-driven rather than material-specific, the same design should work with other low-loss natural hyperbolic crystals such as sapphire or quartz, and the formulas give a clear way to rank candidate materials by the single figure $\\mathrm{Im}\\sqrt{-\\epsilon_\\perp/\\epsilon_\\parallel}$.","Beyond the paper: the hSR line itself is a sensitive probe of nonlocal response; measuring the trapped-intensity peak of the resonator as its radius is scaled down would show whether the quasistatic local-permittivity model holds down to wavevectors of order $1/a$ or whether the degeneracy broadens and shifts first.","Beyond the paper: the effective Hamiltonian is a long-range Ising model with site-resolved on-site energies, so the same chip could serve as a programmable quantum simulator for spin models with interactions beyond nearest neighbours, a direction the paper mentions but does not develop.","Beyond the paper: the fidelity estimate assumes weak Markovian dissipation, but at $J\\sim\\hbar\\omega$ the system sits in the ultra-strong-coupling regime where non-Markovian and counter-rotating corrections can matter; a direct master-equation calculation would show whether the 99 percent figure survives or improves."],"forward_implications":["Two-qubit entangling gates between donor atoms in silicon can run at optical timescales of about 0.04 ps with fidelities around 99 percent, because the exchange coupling at the hSR is comparable to the photon energy and exceeds the decoherence rate by roughly two orders of magnitude.","Qubit interactions become optically switchable: off-resonance control fields Stark-shift a donor transition into the hBN hyperbolic band to turn on the exchange coupling, and out of it to turn it off, yielding an effective Ising spin model with tunable long-range interactions.","The physical platform is a silicon-on-hBN chip, so donor placement, hBN growth, silicon deposition, and plasmonic waveguide addressing are all technologies that have already been demonstrated independently, projecting integration densities above $10^8$ qubits/cm$^2$.","Because the gate time is set by optical periods and donor decoherence in silicon at liquid nitrogen temperature is sub-nanosecond, the processor would work at 77 K without dilution refrigeration.","At the same operating point the single-emitter coupling $g \\simeq 0.1\\omega$ puts the system in the strong-coupling regime, making the architecture a candidate for single-photon-level infrared nonlinear optics and for quantum simulation of long-range spin models."],"supporting_citations":[{"why":"Supplies the measured hBN dielectric permittivity and defines the hyperbolic phonon-polariton bands that set the operating frequencies.","marker":"[17]"},{"why":"Documents ultralow-loss hyperbolic polaritons in isotopically enriched hBN, the loss scale (Im sqrt(-eps_perp/eps_par) ~ 0.01) that produces the 100-fold margin.","marker":"[39]"},{"why":"Provides donor Rydberg-state lifetimes in silicon at elevated temperatures, the decoherence numbers used for the liquid-nitrogen operation argument.","marker":"[52]"},{"why":"Demonstrates coherent control and long coherence of Rydberg states in isotopically pure silicon, supporting the qubit platform and the 300 ps coherence estimate.","marker":"[53]"},{"why":"Derives the semiclassical mode-degeneracy condition behind the hyperbolic super-resonance, Eq. (7), and the coupling formula.","marker":"[68]"},{"why":"Supplies the Green-function formalism connecting spin-exchange coupling and decay rates to the dyadic Green function, Eq. (15).","marker":"[74]"}],"fun_headline_variants":["Hyperbolic resonance pairs distant qubits with 99% fidelity","Silicon qubit chip uses hyperbolic polaritons for 99% fidelity gates","Hyperbolic super-resonance links qubits across a chip, no dilution fridge","Hyperbolic polaritons enable long-range qubit gates at 99% fidelity"],"cache_read_input_tokens":21376,"weakest_assumption_plain":"Everything hinges on hBN behaving like a low-loss, ordinary dielectric even for polariton waves with wavelengths of just a few atomic spacings; if nonlocal dispersion or much stronger absorption appears at those wavevectors, the strong coupling, the 100-fold margin, and the 99 percent fidelity all collapse.","fun_headline_variants_meta":{"raw":{"variants":["Hyperbolic resonance pairs distant qubits with 99% fidelity","Silicon qubit chip uses hyperbolic polaritons for 99% fidelity gates","Hyperbolic super-resonance links qubits across a chip, no dilution fridge","Hyperbolic polaritons enable long-range qubit gates at 99% fidelity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000759,"raw_usage":{"total_tokens":3516,"prompt_tokens":1231,"completion_tokens":2285,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":847,"completion_tokens_details":{"reasoning_tokens":2202}},"tokens_in":847,"tokens_out":2285,"duration_ms":15582,"temperature":1.0,"reasoning_tokens":2202,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:29:27.056194+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the two-qubit exchange coupling $J_{12}$ and the decay rate $\\Gamma_{11}$ as functions of spacer thickness $h$ in a fabricated hBN cylindrical resonator with two silicon donor emitters tuned to the hSR condition of Eq. (7). The local-permittivity model predicts $J_{12}$ following Eq. (9) and $\\Gamma_{11}/J_{12} \\sim h_*/h$ for $h\\gtrsim h_*$; observing that the coupling saturates at a much lower value, or that the super-resonance peak in the trapped-intensity spectrum broadens dramatically as the resonator shrinks, would falsify the assumption and invalidate the 99 percent fidelity and $10^8$ cm$^{-2}$ density claims.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates coherent control and long coherence of Rydberg states in isotopically pure silicon, supporting the qubit platform and the 300 ps coherence estimate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the semiclassical mode-degeneracy condition behind the hyperbolic super-resonance, Eq. (7), and the coupling formula."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Green-function formalism connecting spin-exchange coupling and decay rates to the dyadic Green function, Eq. (15)."}],"review_version":1}