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REVIEW 4 major objections 6 minor 103 references

Hyperbolic Quantum Processor

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Hyperbolic-material resonators can make distant silicon qubits interact strongly enough for 99 percent fidelity gates.

desk verdict A creative architecture whose headline numbers rest on self-cited unpublished preprints and an unverified high-wavevector loss assumption; not publishable as written, but serious enough to referee. read the letter →

arxiv 2412.14098 v1 pith:ZWP5ZGPZ submitted 2024-12-18 quant-ph cond-mat.mes-hallphysics.optics

Evgenii E. Narimanov , Eugene A. Demler This is my paper · ORCID
classification quant-phcond-mat.mes-hallphysics.optics
keywords hyperbolicmaterialshexagonalboronnitridephononpolaritonsquantumgatesspin-exchangecouplingdonorqubitsinsiliconstrongliquidnitrogenoperation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

What carries the argument

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 $h_* \ll h \lesssim h_c$.

What would settle it

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.

Watch

Extended reading notes

Core claim

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$^2$.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

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.

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 (4)
  1. [Section V, Eqs. (7)-(9)] 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.
  2. [Section V, Eqs. (24)-(25); footnote [62]] 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.
  3. [Section VI, fidelity claim] 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.
  4. [Abstract and Section VIII, density claim] 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.
minor comments (6)
  1. [Throughout] 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".
  2. [Section V, Eq. (11)] 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.
  3. [Section VI] 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.
  4. [Fig. 5 caption] The caption defines the spacer thickness as "b" while the text and equations use h; please unify the notation.
  5. [References] 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.
  6. [Fig. 6 caption] 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.

Circularity Check

2 steps flagged · score 5.0 of 10

The central Hyperbolic Super-Resonance coupling and the auto-focusing geometry rest on two unpublished self-citations, but the J/Gamma ratio itself is not fitted and retains independent Green-function content.

  1. self citation load bearing [Section V, Eq. (8), with the mode-degeneracy claim preceding Eq. (7)]
    "Such infinite mode degeneracies in hyperbolic resonators also arise in other geometries,[68] ... In particular, for the hyperbolic Super-Resonance in a metal-clad cylindrical hyperbolic resonator (see Fig. 3(b)) we obtain: ... at the HSR frequency for the corresponding Jaynes-Cummings model [72] coupling coefficient g we obtain [68] ℏg = ..."

    The paper's strong-coupling estimates ℏg ≈ 0.1–0.15ℏω, and hence the central claim that J is comparable to the optical photon energy, import the coupling formula (8) from Ref. [68], an unpublished preprint by one of the present authors. The companion assertion that infinite mode degeneracies ('hyperbolic Super-Resonance') occur in these geometries is likewise attributed to [68]. The manuscript gives no independent derivation, numerical check, or externally verifiable statement of Eq. (8), so the central enabling physics is carried by a self-citation whose content is not established in the present text.

  2. self citation load bearing [Section IV, Eqs. (3)–(4), 'auto-focusing' statement]
    "With essentially unlimited [62] propagating wavenumbers in a hyperbolic medium (see Eqn. (1) and Fig. 2(a)), the spatial spectrum of the electromagnetic fields radiated by a point source, is primarily supported by the waves that are confined to the waveguide by total internal reflection, which will then lead to the natural “auto-focusing” [63] into multiple focal spots separated by the distance Δz = ..."

    Equation (3) and the 'auto-focusing' picture place the donor qubits at the resonator's focal spots and determine the inter-qubit separation used in the proposed architecture of Figs. 4–5. The effect is attributed to Ref. [63], another unpublished preprint by one of the authors, and Eqs. (3)–(4) are presented without derivation in this paper. If the focusing premise fails, the multi-qubit geometry loses its stated basis, so this is a second load-bearing self-citation, although less central than Eq. (8).

full rationale

No fitted-input-called-prediction or self-definitional reduction is present: the J/Γ ratio is obtained from a Green-function calculation (Eqs. (15) and (30)–(35)) combined with experimental hBN loss values, and the claimed h_c/h_* ≈ 100 is a parameter substitution, not a fit to the 99% fidelity target. The circularity concern is narrower but real: the enabling Hyperbolic Super-Resonance and the quantitative coupling formula (8) used for the strong-coupling estimates are attributed to Ref. [68], an unpublished preprint by one author, and the auto-focusing focal geometry is attributed to Ref. [63], another unpublished preprint by the same author. The manuscript does not provide independent derivations at those points, so the headline interaction strength inherits part of its content from self-citations. Because the subsequent J and Γ calculations in the supplementary material and the experimentally based loss parameter are independent of those self-citations, the circularity is moderate rather than total.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particle, force, or conserved quantity. The Hyperbolic Super-Resonance is a predicted phenomenon, not an entity. The ledger instead shows a set of chosen geometric and material parameters and several domain assumptions that the quantitative claims depend on.

free parameters (4)
  • Donor transition dipole moment p ~ e * 1 nm = p ~ e*1 nm, r_eg ~ 1-2 nm
    Used in Eqns. (6), (8), and (9); controls J ~ p^2 and g ~ p. Taken as a representative value for 1s to 2p donor transitions, but not measured for the specific transitions in Fig. 6.
  • Spacer thickness h between qubit and hBN resonator = 3-5 nm in estimates, must satisfy h* << h <= h_c
    Enters Eqns. (9), (18), (20)-(23). The result is sensitive to h because J ~ 1/h^3 and Gamma ~ 1/h^3. The value is chosen by hand within the claimed allowed window.
  • Resonator radius R and length d = R up to ~50 nm, d ~ 50 nm
    Set by the HSR condition Eq. (7) and used in the margin estimate h_c/h_star ~ 100 via Eq. (24). These dimensions are chosen for the order-of-magnitude design.
  • Loss parameter Im sqrt(-epsilon_perp/epsilon_par) = about 0.03 for natural hBN, 0.01 for isotopically enriched hBN
    Taken from literature values, but assumed temperature-independent and k-independent. The linear dependence of h_c/h_star on 1/Im makes this parameter load-bearing for the claimed 100-fold operating margin.
assumptions (4)
  • domain assumption Quasistatic approximation for hyperbolic nanostructures reduces Maxwell's equations to a scalar potential equation.
    Used throughout the supplementary Green-function calculation. Valid only for wavevectors much larger than omega/c, which is the regime the paper relies on.
  • domain assumption Local continuum permittivity for hBN remains valid up to wavevectors k ~ 1/a with no spatial dispersion.
    The paper notes a natural wavenumber cutoff at 1/a but otherwise treats hBN as a local medium. Nonlocal phonon response at atomic scale could change the loss and the mode degeneracy.
  • ad hoc to paper Semiclassical EBK quantization and ray-optical integrability give the exact mode degeneracy behind Eq. (7) and the coupling Eq. (8).
    This is the central theoretical input, cited to unpublished preprint [68]. The paper states the degeneracy is exact only in the large-wavenumber limit, and it is assumed to survive finite absorption and finite unit-cell size.
  • domain assumption The qubit dynamics can be described by a Markovian Lindblad master equation with rates from the dyadic Green function under the rotating-wave approximation.
    Used to write Eqns. (12)-(15). It is standard for weak coupling and wideband reservoirs, but the ultra-strong coupling regime J ~ hbar-omega may strain the rotating-wave and Markov approximations.

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Cite this review

Pith. "Pith review of Hyperbolic Quantum Processor." pith.science (2026). https://pith.science/paper/ZWP5ZGPZ

@misc{pith2026241214098,
  author       = {Pith},
  title        = {Pith review of: Hyperbolic Quantum Processor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZWP5ZGPZ}},
  note         = {Machine review of arXiv:2412.14098}
}
read the original abstract

Achieving strong coherent interaction between qubits separated by large distances holds the key to many important developments in quantum technology, including new designs of quantum computers, new platforms for quantum simulations and implementation of large scale quantum optical networks. However, the inherent mismatch between the spatial dimensions of a quantum emitter and the photon wavelength fundamentally limits the transmission of quantum entanglement over long distances. Here we demonstrate, that long-range qubit entanglement can be readily achieved when qubit interactions are mediated by optical polariton waves in a hyperbolic material, due to the phenomenon of the Hyperbolic Super-Resonance. We show that in this regime the resulting quantum gate fidelity that exceeds 99%, can be achieved with the use of qubits based on well known deep donors in silicon when their interactions are mediated by polariton fields in the substrate formed by a hyperbolic material (such as e.g. hexagonal boron nitride. At the physical level the proposed system is essentially a silicon-based optoelectronic chip, and it's readily accessible to the existing methods of semiconductor nanofabrication, leading to the integration densities of well over 10^8. qubits/cm^2, and therefore opening the way to scalable and fault-tolerant error correction in quantum computation. Furthermore, we demonstrate that, due to the optical time scales that define the duration of the gate operation in the proposed system, and sub-nanosecond time of the decoherence in deep donors in silicon at the liquid nitrogen temperatures, the proposed Hyperbolic Quantum Processor does not require dilution refrigeration and therefore offers a pathway to bring quantum computation to the realm of conventional engineering.

Figures

Figures reproduced from arXiv: 2412.14098 by the authors.

Figure 1
Figure 1. FIG. 1. Hyperbolic Quantum Processor operation. Panel (a): the quantum transition frequencies [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Light from a point dipole emission in a hyperbolic [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The hyperbolic Super-Resonance. Panel (a): the conceptual introduction. Compared to the frequency range with [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Long-range dipole-dipole interaction mediated by [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Panel (a): two quantum emitters (e.g. chalcogene [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The dielectric permittivity of the natural hexagonal boron nitride in its lower-frequency (a) and higher-frequency (b) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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Works this paper leans on

103 extracted references · 77 canonical work pages

  1. [63]

    M. C. Collodo, J. Herrmann1, N. Lacroix et al . Implementation of Conditional Phase Gates Based on Tunable ZZ Interactions. Phys. Rev. Lett. 125, 240502 (2020)

    work page 2020

  2. [68]

    E. E. Narimanov, Hyperbolic Auto-Focusing: Long-Range Dipole-Dipole Interaction in Hyperbolic Waveguides, preprint

    work page

  3. [62]

    number of modes at the same frequency - see Fig. 3(a). Such infinite mode degeneracies in hyperbolic resonators also arise in other geometries,[68] as long as the corresponding ray-optical dynamics remains integrable – which can be shown in a straightforward manner, using the transformation to action-angle variables, as in the derivation of Einstein-Brill...

  4. [80]

    Selective Radiance

    A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble and D. E. Chang, Exponential Improvement in Photon Storage Fidelities Using Subradiance and “Selective Radiance” in Atomic Arrays. Phys. Rev. X 7, 031024 (2017). 12

    work page 2017

  5. [1]

    H. J. Kimble, The quantum internet. Nature 453, 1023 - 1030 (2008)

    2008

  6. [2]

    Cirac, P

    J.I. Cirac, P. Zoller, Quantum computations with cold trapped ions Physical review letters 74 (20), 4091 (1995)

    1995

  7. [3]

    Porras, J.I

    D. Porras, J.I. Cirac, Effective quantum spin systems with trapped ions. Physical review letters92 (20), 207901 (2004)

    2004

  8. [4]

    C. Hung, A. Gonz´ alez-Tudela, J.I. Cirac, H.J. Kimble, Quantum spin dynamics with pairwise-tunable, 10 long-range interactions, Proc. Natl. Acad. Sci. 113 (34) E4946 - E4955 (2016)

    2016

Show all 103 references
  1. [5]

    M.Arrazola, V

    J. M.Arrazola, V. Bergholm, K. Br´ adler et al. Quantum circuits with many photons on a programmable nanophotonic chip. Nature 591, 54 - 60 (2021)

    2021

  2. [6]

    Cai and V

    W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications, (Springer, 1st edition, 2009)

    2009

  3. [7]

    Ezratty, Perspective on superconducting qubit quantum computing

    O. Ezratty, Perspective on superconducting qubit quantum computing. Eur. Phys. J. A 59, 94 (2023)

    2023

  4. [8]

    Kielpinski, C

    D. Kielpinski, C. Monroe & D. J. Wineland, Architecture for a large-scale ion-trap quantum computer. Nature 417 (6890) 709 - 711 (2002)

    2002

  5. [9]

    S. J. Evered, D. Bluvstein et al ., High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 622, 268 - 272 (2023)

    2023

  6. [10]

    Gonz´ alez-Tudela, P

    A. Gonz´ alez-Tudela, P. A. Huidobro, L. Mart ´ ın-Moreno, C. Tejedor and F. J. Garc ´ ıa-Vidal, Reversible dynamics of single quantum emitters near metal-dielectric interfaces. Phys. Rev. Lett. 110, 126801 (2013)

    2013

  7. [11]

    Janzen, R

    E. Janzen, R. Stedman, G. Grossmann, and H. G. Grimmeiss, High-resolution studies of sulfur- and selenium-related donor centers in silicon. Phys. Rev. B 29 (4), 1907 - 1918 (1984)

    1984

  8. [12]

    Steger, A

    M. Steger, A. Yang, M. L. W. Thewalt, M. Cardona, H. Riemann, N. V. Abrosimov, M. F. Churbanov, A. V. Gusev, A. D. Bulanov, I. D. Kovalev, A. K. Kaliteevskii, O. N. Godisov, P. Becker, H.-J. Pohl, E. E. Haller and J. W. Ager, High-resolution absorption spectroscopy of the deep...

    2009

  9. [13]

    R. J. S. Abraham,A. DeAbreu, K. J. Morse, V. B. Shuman, L. M. Portsel, A. N. Lodygin, Yu. A. Astrov, N. V. Abrosimov, S. G. Pavlov, H.-W. H¨ ubers, S. Simmons and M. L. W. Thewalt, Further investigations of the deep double donor magnesium in silicon. Physical Review B 98, 0452...

    2018

  10. [14]

    Karaiskaj, J

    D. Karaiskaj, J. A. H. Stotz, T. Meyer, M. L.W. Thewalt, and M. Cardona, Impurity Absorption Spectroscopy in 28Si: The Importance of Inhomogeneous Isotope Broadening. Physical Review B 90 (18), 186402 (2003)

    2003

  11. [15]

    K. J. Morse, R. J. S. Abraham, A. DeAbreu, C. Bowness, T. S. Richards, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, M. L. W. Thewalt, S. Simmons, A photonic platform for donor spin qubits in silicon. Science Advances 3, e1700930 (2017)

    2017

  12. [16]

    C. R. Pidgeon and B. N. Murdin, Silicon as a model ion trap: Time domain measurements of donor Rydberg states. Proc. Nat. Acad. Sci. 105 (31), 10649–10653 (2008)

    2008

  13. [17]

    Caldwell, A

    J. Caldwell, A. Kretinin, Y. Chen et al., Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride. Nat Commun 5, 5221 (2014)

    2014

  14. [18]

    S. Dai, Q. Ma, T. Andersen et al. Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material. Nat Commun 6, 6963 (2015)

    2015

  15. [19]

    P. Li, M. Lewin, A. Kretinin et al. , Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing. Nat. Commun. 6, 7507 (2015)

    2015

  16. [20]

    I. H. Lee, M. He, X. Zhang et al. Image polaritons in boron nitride for extreme polariton confinement with low losses. Nat. Commun. 11, 3649 (2020)

    2020

  17. [21]

    H. H. Sheinfux, L. Orsini, M. Jung et al. , High-quality nanocavities through multimodal confinement of hyperbolic polaritons in hexagonal boron nitride. Nat. Mater. 23, 499 - 505 (2024)

    2024

  18. [22]

    Yoxall, M

    E. Yoxall, M. Schnell, A. Y. Nikitin et al. Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity. Nature Photonics 9, 674 - 678 (2015)

    2015

  19. [23]

    T. Low, A. Chaves, J. D. Caldwell et al . Polaritons in layered two-dimensional materials. Nature Materials 16, 182 - 194 (2017)

    2017

  20. [24]

    D. N. Basov, M. M. Fogler, and F. J. Garc ´ ıa de Abajo. Polaritons in van der Waals materials. Science 354 (6309), 195 (2016)

    2016

  21. [25]

    G. Ni, A. S. McLeod, Z. Sun et al. Long-Lived Phonon Polaritons in Hyperbolic Materials. Nano Lett. 21, 5767 - 5773 (2021)

    2021

  22. [26]

    A. J. Sternbach, S. L. Moore, A. Rikhter et al. Negative refraction in hyperbolic hetero-bicrystals. Science 379, 555 - 557 (2023)

    2023

  23. [27]

    H. Wang, A. Kumar, S. Dai et al. Planar hyperbolic polaritons in 2D van der Waals materials. Nature Communications 15, 69 (2024)

    2024

  24. [28]

    A. J. Sternbach, S. H. Chae, S. Latini et al. Programmable hyperbolic polaritons in van der Waals semiconductors. Science 371, 617 - 620 (2021)

    2021

  25. [29]

    G. Jia, J. Luo, H. Wang et al. Two-dimensional natural hyperbolic materials: From polaritons modulation to applications. Nanoscale 14, 17096 - 17118 (2022)

    2022

  26. [30]

    V. A. Podolskiy and E. E. Narimanov, Strongly anisotropic waveguide as a nonmagnetic left-handed system. Phys. Rev. B 71, 201101(R) (2005)

    2005

  27. [31]

    A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco and C. Gmachl, Negative refraction in semiconductor metamaterials, Nature Materials 6, 948 (2007)

    2007

  28. [32]

    Galfsky, J

    T. Galfsky, J. Gu, E.E. Narimanov, V.M. Menon, Photonic hypercrystals for control of light–matter interactions. Proc. Natl. Acad. Sci. 114 (20) 5125 - 5129 (2017)

    2017

  29. [33]

    M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, Bulk photonic metamaterial with hyperbolic dispersion. Appl. Phys. Lett. 94 (15), 151105 (2009)

    2009

  30. [34]

    J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, Optical negative refraction in bulk metamaterials of nanowires. Science321 (5891), 930 (2008)

    2008

  31. [35]

    L. V. Alekseyev, V. A. Podolskiy, E. E. Narimanov, Homogeneous Hyperbolic Systems for Terahertz and Far-Infrared Frequencies, Advances in OptoElectronics 2012, 267564 (2012)

    2012

  32. [36]

    Schubert, T

    M. Schubert, T. E. Tiwald, and C. M. Herzinger, Infrared dielectric anisotropy and phonon modes of sapphire. Phys. Rev. B 61, 8187 (2000)

    2000

  33. [37]

    Kuroda, K

    N. Kuroda, K. Tsugawa and H. Yokoi, Negative Refraction of Infrared Waves and Rays in Sapphire α-Al2O3. Journal of the Physical Society of Japan 81, 114706 (2012)

    2012

  34. [38]

    Kleverman, K

    M. Kleverman, K. Bergman and H. G. Grimmeiss, Photothermal investigations of magnesium-related donors in silicon. Semicond. Sci.Technol. 1, 49 (1986). 11

    1986

  35. [39]

    freezes out

    that removes photon-on-impurity scattering, and by lowering the system temperature that “freezes out” the phonon-phonon scattering.[49] The polar crystals with hyperbolic response therefore offer an a powerful platform with extreme light-matter coupling of quantum emitters, wi...

    2024 arXiv

  36. [40]

    Jacob, L

    Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, Optical Hyperlens: Far-field imaging beyond the diffraction limit. Optics Express 14, 8247 (2006)

    2006

  37. [41]

    Salandrino, N

    A. Salandrino, N. Engheta, Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations. Phys Rev B, 74, 075103 (2006)

    2006

  38. [42]

    de Waele, S

    R. de Waele, S. P. Burgos, A. Polman, and H. A. Atwater, Plasmon Dispersion in Coaxial Waveguides from Single-Cavity Optical Transmission Measurements Nano Letters 9 (8), 2832 - 2837 (2009)

    2009

  39. [43]

    Z. Liu, H. Lee, Y. Xiong, C. Sun, X. Zhang, Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 315(5819), 1686 (2007)

    2007

  40. [44]

    Giles, S

    A. Giles, S. Dai, I. Vurgaftman et al. Ultralow-loss polaritons in isotopically pure boron nitride. Nature Mater 17, 134 - 139 (2018)

    2018

  41. [45]

    I. I. Smolyaninov, and E. E. Narimanov, Metric Signature Transitions in Optical Metamaterials. Phys. Rev. Lett. 105, 067402 (2010)

    2010

  42. [46]

    Jacob, I

    Z. Jacob, I. I. Smolyaninov, E. E. Narimanov, Broadband Purcell effect: Radiative decay engineering with metamaterials. Appl. Phys. Lett. 100 (18), 181105 (2012)

    2012

  43. [47]

    H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V. M. Menon, Topological transitions in metamaterials. Science 336 (6078), 205 - 209 (2012)

    2012

  44. [48]

    auto-focusing

    remove this singularity. IV. LONG RANGE DIPOLE-DIPOLE INTERACTION IN HYPERBOLIC NANOSTRUCTURES We begin by considering the setup that, while challenging to realize in real experimental environment, clearly illustrates the underlying physics and allows a straightforward theoret...

  45. [49]

    J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, X. Zhang, Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies. Nat. Commun. 1, 143 (2010)

    2010

  46. [50]

    G. W. Ludwig, Paramagnetic Resonance Study of a Deep Donor in Silicon. Physical Review 137 (5A), A1520 - A1530 (1965)

    1965

  47. [51]

    Swartz, D.H

    J.C. Swartz, D.H. Lemmon and R.N. Thomas, Optical Excitation Spectra of Selenium-doped Silicon. Solid State Communications 36, 331 - 334 (1980)

    1980

  48. [52]

    multi-elliptical

    the lifetimes approaching 200 ps. However, the hyperbolic Super-Resonance also leads to the increased decoherence due to material absorption in the hyperbolic resonator, described by the decay rates Γij in Eqn. (14), so that to turn the system of donor atom cubits coupled to a...

  49. [53]

    E. E. Narimanov, Hyperbolic modes of a conductor-dielectric interface. Phys. Rev. A 99, 023827 (2019)

    2019

  50. [54]

    Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids , (Oxford University Press; reprint edition, 2001)

    J. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids , (Oxford University Press; reprint edition, 2001)

    2001

  51. [55]

    Mundada, G

    P. Mundada, G. Zhang, T. Hazard, and A. Houck. Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit. Phys. Rev. Applied 12, 054023 (2019)

    2019

  52. [56]

    Foxen, C

    B. Foxen, C. Neill, A. Dunsworth et al . Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms. Phys. Rev. Lett. 125, 120504 (2020)

    2020

  53. [57]

    N. Q. Vinh, P. T. Greenland, K. Litvinenko, B. Redlich, A. F. G. van der Meer, S. A. Lynch, M. Warner A. M. Stoneham, G. Aeppli, D. J. Paul, C. R. Pidgeon and B. N. Murdin, Silicon as a model ion trap: Time domain measurements of donor Rydberg states. Proc. Nat. Acad. Sci. 105...

    2008

  54. [58]

    P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin3, C. R. Pidgeon, B. Redlich, N. Q. Vinh & G. Aeppli, Coherent control of Rydberg states in silicon. Nature 465, 1057 - 1061 (2010)

    2010

  55. [59]

    F. Yan, P. Krantz, Y. Sung et al. Tunable Coupling Scheme for Implementing High-Fidelity Two-Qubit Gates. Phys. Rev. Applied 10, 054062 (2018)

    2018

  56. [60]

    Negirneac, H

    V. Negirneac, H. Ali, N. Muthusubramanian et al. High-Fidelity Controlled- Z Gate with Maximal Intermediate Leakage Operating at the Speed Limit in a Superconducting Quantum Processor. Phys. Rev. Lett. 126, 220502 (2021)

    2021

  57. [61]

    E. E. Narimanov and A. V. Kildishev, Naturally Hyperbolic. Nature Photonics 9, 214 - 216 (2015)

    2015

  58. [64]

    D. C. McKay, Stefan Filipp, Antonio Mezzacapo et al. Universal Gate for Fixed-Frequency Qubits via a Tunable Bus Phys. Rev. Applied 6, 064007 (2016)

    2016

  59. [65]

    Y. Sung, L. Ding, J. Braum¨ uller et al. Realization of High-Fidelity CZ and ZZ -Free iSW AP Gates with a Tunable Coupler. Phys. Rev. X 11, 021058 (2021)

    2021

  60. [66]

    Riolo, A

    R. Riolo, A. Tomadin, G. Mazza et al. Tuning Fermi Liquids with Sub-wavelength Cavities. Preprint arXiv:2403.20067

    arXiv

  61. [67]

    The finite size of the material unit cell a imposed an upper limit on the wavenumber, kmax ∼ 1/a

  62. [69]

    A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, F. Nori, Ultrastrong coupling between light and matter. Nature Reviews Physics 1, 19 (2019)

    2019

  63. [70]

    Tomadin, A

    A. Tomadin, A. Principi, J. C. W. Song, L. S. Levitov, and M. Polini, Accessing phonon polaritons in hyperbolic crystals by angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 115, 087401 (2015)

    2015

  64. [71]

    Z. Sun, A. Guti´ errez-Rubio, D. N. Basov and M. M. Fogler, Hamiltonian Optics of Hyperbolic Polaritons in Nanogranules. Nano Lett. , 15, 4455 - 4460 (2015)

    2015

  65. [72]

    extended

    coupling coefficient g we obtain [68] ℏg = 1 − cos πm 2 2 r p2ℏω 3dh2 , (8) where the integer m is the order of the Super-Resonance (see Eqn. (7)). For a quantum emitter based on deep donor impurities in silicon, with the characteristic dipole moment p ∼ e · 1 nm, the dipole-r...

    2000

  66. [73]

    The corresponding mode spacings statistics varies from the Poissonian to the Wigner-Dyson distributions,[70] depending on whether the underlying ray dynamics is integrable or chaotic.[69, 71]

  67. [74]

    E. E. Narimanov, Hyperbolic Super-Resonance: semiclassical theory, preprint

  68. [75]

    Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer; 1st edition (1990)

    M. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer; 1st edition (1990)

    1990

  69. [76]

    E. E. Narimanov, Chaos in hyperspace: ray dynamics in media with hyperbolic dispersion Proceedings SPIE 7392, 739205 (2009)

    2009

  70. [77]

    Jaynes and F.W

    E.T. Jaynes and F.W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE. 51 (1), 89 - 109 (1963)

    1963

  71. [78]

    A. K. Ramdas and S. Rodriguez, Spectroscopy of the solid-state analogues of the hydrogen atom: donors and acceptors in semiconductors. Rep. Prog. Phys. 44, 1297 (1981)

    1981

  72. [79]

    Asenjo-Garcia, J

    A. Asenjo-Garcia, J. D. Hood, D. E. Chang and H. J. Kimble, Atom-light interactions in quasi-one-dimensional nanostructures: A Green’s-function perspective. Phys. Rev. A 95, 033818 (2017)

    2017

  73. [81]

    Gruner and D.-G

    T. Gruner and D.-G. Welsch. Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers-Kronig dielectrics. Phys. Rev. A 53, 1818 (1996)

    1996

  74. [82]

    H. T. Dung, L. Kn¨ oll, and D.-G. Welsch. Resonant dipole-dipole interaction in the presence of dispersing and absorbing surroundings. Phys. Rev. A 66, 063810 (2002)

    2002

  75. [83]

    S. Y. Buhmann and D.-G. Welsch. Dispersion forces in macroscopic quantum electrodynamics. Prog. Quantum Electron. 31, 51 (2007)

    2007

  76. [84]

    (Intext Educational Publishers; 1st edition, 1971)

    Chen-to Tai, Dyadic Green Functions in Electromagnetic Theory. (Intext Educational Publishers; 1st edition, 1971)

    1971

  77. [85]

    T. Abad, J. Fern´ andez-Pend´ as, A. F. Kockum and G. Johansson, Universal Fidelity Reduction of Quantum Operations from Weak Dissipation Phys. Rev. Lett. 129, 150504 (2022)

    2022

  78. [86]

    O. Katz, L. Feng, A. Risinger, C. Monroe, M. Cetina, Demonstration of three- and four-body interactions between trapped-ion spins. Nature Physics 19, 1452 (2023)

    2023

  79. [87]

    H. G. Stemp et al., Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits. Nature Communications 15, 8415 (2024)

    2024

  80. [88]

    J. P. Dehollain et al. , Optimization of a solid-state electron spin qubit using gate set tomography. N. J. Phys. 18, 103018 (2016)

    2016

  81. [89]

    Koiller, X

    B. Koiller, X. Hu, & D. S. Sarma, Exchange in silicon-based quantum computer architecture. Phys. Rev. Lett. 88, 027903 (2001)

    2001

  82. [90]

    Voisin et al

    B. Voisin et al. , Valley interference and spin exchange at the atomic scale in silicon. Nat. Commun. 11, 6124 (2020)

    2020

  83. [91]

    B Joecker, A. D. Baczewski, J. K. Gamble, A. Saraiva & M. Andrea, Full configuration interaction simulations of exchange-coupled donors in silicon using multi-valley effective mass theory. N. J. Phys. 23, 073007 (2021)

    2021

  84. [92]

    Pajot, G

    B. Pajot, G. Grossmann, M. Astier and C. Naud, Highly Excited States of Donor Centres in Silicon. Solid State Communications 54 (1), 57 - 60 (1985)

    1985

  85. [93]

    S. R. Schofield, N. J. Curson, M. Y. Simmons, F. J. Rueß, T. Hallam, L. Oberbeck, and R. G. Clark, Atomically Precise Placement of Single Dopants in Si. Phys. Rev. Lett. 91, 136104 (2003)

    2003

  86. [94]

    Holmes, B

    D. Holmes, B. Wilhelm, A. M. Jakob, X. Yu, F. E. Hudson, K. M. Itoh, A. S. Dzurak, D. N. Jamieson, A. Morello, Improved Placement Precision of Donor Spin Qubits in Silicon using Molecule Ion Implantation. Adv Quantum Technol. 7, 2300316 ( 2024)

    2024

  87. [95]

    M. A. Sakib, B. Triplett, W.Harris et al, Purcell-Induced Bright Single Photon Emitters in Hexagonal Boron Nitride Nano Letters24 (40), 12390 - 12397 (2024)

    2024

  88. [96]

    Fukamachi, P

    S. Fukamachi, P. Sol ´ ıs-Fern´ andez, K. Kawaharaet al. Large-area synthesis and transfer of multilayer hexagonal boron nitride for enhanced graphene device arrays. Nat Electron 6, 126 - 136 (2023)

    2023

  89. [97]

    Gorman, M.G

    M.A.Broome, S.K. Gorman, M.G. House et al. Two-electron spin correlations in precision placed donors in silicon. Nat. Commun. 9, 980 (2018)

    2018

  90. [98]

    P. W. Shor, Scheme for reducing decoherence in quantum computer memory. Physical Review A 52 (4), R2493 - R2496 (1995)

    1995

  91. [99]

    D. E. Chang, A. S. Sørensen, E. A. Demler and M. D. Lukin, A single-photon transistor using nanoscale surface plasmons. Nature Physics 3 (11), 807 - 812 (2007)

    2007

  92. [100]

    Firstenberg, T

    O. Firstenberg, T. Peyronel, Q.-Y. Liang et al. Attractive photons in a quantum nonlinear medium. Nature 502, 71 - 75 (2013)

    2013

  93. [101]

    D. E. Chang, V. Vuleti´ c and M. D. Lukin. Quantum nonlinear optics – photon by photon. Nature Photonics 8, 685 - 694 (2014)

    2014

  94. [102]

    D.E.Chang, J. S. Douglas, A. Gonz´ alez-Tudela et al. Quantum matter built from nanoscopic lattices of atoms and photons. Rev. Mod. Phys. 90, 031002 (2018)

    2018

  95. [103]

    bounce points

    L. Zhang, V. Walther, K. Mølmer, and Thomas Pohl, Quantum 6, 674 (2022). SUPPLEMENT AR Y MA TERIAL Electrodynamics in Hyperbolic Media From the late 19th century when optical interferometers brought the dawn of modern physics, offering a peak into the nature and the chemical c...

    2022

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