Sub-microsecond entangling gate between trapped ions via Rydberg interaction

Andreas P\"oschl; Chi Zhang; Fabian Pokorny; Gerard Higgins; Igor Lesanovsky; Markus Hennrich; Weibin Li

REVIEW 3 major objections 6 minor 38 references

Sub-microsecond entangling gate between trapped ions via Rydberg interaction

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Microwave-dressed Rydberg interactions entangle two trapped ions in 700 nanoseconds, producing a Bell state with 78% fidelity and a predicted error path below 0.2%.

desk verdict First real trapped-ion Rydberg entangling gate, with credible 78% fidelity and an honest error budget; the 0.2% and 100-ion projections lean on an undemonstrated zero-polarisability dressed state. read the letter →

arxiv 1908.11284 v1 pith:3QQEBYSM submitted 2019-08-29 quant-ph physics.atom-ph

Chi Zhang , Fabian Pokorny , Weibin Li , Gerard Higgins , Andreas Pöschl , Igor Lesanovsky , Markus Hennrich This is my paper · ORCID

classification quant-phphysics.atom-ph PACS 03.67.Lx32.80.Ee

keywords trapped-ionquantumcomputationRydbergionsmicrowavedressingdipole-dipoleinteractionblockadeSTIRAPBellstatesub-microsecondentanglinggate

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

The paper claims that two trapped-ion qubits can be entangled in 700 nanoseconds — about one to two orders of magnitude faster than the typical 40–100 µs gates that act through shared vibrational motion — by using the strong dipole-dipole interaction between microwave-dressed Rydberg states of ⁸⁸Sr⁺. The experiment produces a Bell state with 78% fidelity, identifies every source of error, and predicts that with technically achievable parameters the total error falls below 0.2%. The authors further calculate that residual coupling to the ions' motion contributes only about 10⁻⁴ error in a 100-ion crystal, because the gate never depends on the motional modes. If the paper is right, trapped-ion systems could gain Rydberg-level interaction speeds while keeping the long coherence and precise control that make ions attractive for quantum simulation and computation.

What carries the argument

The carrying object is the microwave-dressed Rydberg state $|+\rangle = C\big((\Delta_{\mathrm{MW}}+\sqrt{\Delta_{\mathrm{MW}}^2+\Omega_{\mathrm{MW}}^2})/\Omega_{\mathrm{MW}}\,|s\rangle+|p\rangle\big)$: the $|s\rangle$ and $|p\rangle$ components have dipole moments of opposite sign, so the dressed state possesses a permanent electric dipole that rotates with the microwave field. That rotating dipole is what converts the negligible second-order van der Waals force of Rydberg ions into a strong, tunable first-order dipole-dipole shift between two ions. The gate itself is carried by a double STIRAP (stimulated Raman adiabatic passage) sequence lasting 700 ns, with the two laser couplings varied sinusoidally so that population from $|0\rangle$ adiabatically reaches $|r\rangle$ and returns; for the pair state $|00\rangle$ the doubly-excited component $|rr\rangle$ is energy-shifted by $V_{\max}$, so $|00\rangle$ acquires the phase $\varphi = V_{\max}\int_0^T\langle rr|\rho(t)|rr\rangle\,dt \simeq \pi$, while $|01\rangle$, $|10\rangle$, and $|11\rangle$ remain dark and acquire no phase.

What would settle it

Measure the residual polarisability of the $n=60$ microwave-dressed Rydberg state by spectroscopy — the authors state they expect to reach $10^{-34}\,\mathrm{C^2\,m^2\,J^{-1}}$ precision — and run the improved gate on Doppler-cooled ions in a 100-ion crystal; if the measured polarisability exceeds that level, or the two-ion fidelity falls short of 99.8%, the projected error budget fails. A more direct check: measure the two-ion Bell-state fidelity as the crystal grows from 2 to 100 ions; the motional-error calculation predicts the fidelity should stay essentially flat once roughly ten ions are present.

Watch

Extended reading notes

Core claim

Rydberg ions have a problem: their second-order van der Waals interaction is far too weak for fast gates, scaling as $Z^{-6}$ with net core charge. The paper's central move is to couple two Rydberg states $|s\rangle$ and $|p\rangle$ with a 122 GHz microwave field, producing dressed states whose electric dipole moments rotate in the plane perpendicular to the magnetic field; two ions in the state $|r\rangle \equiv |+\rangle$ then interact at first order through $V = (1/4\pi\epsilon_0)\,\langle s|\hat{\mu}|p\rangle^2 r^{-3}\,\Omega_{\mathrm{MW}}^2/(\Delta_{\mathrm{MW}}^2+\Omega_{\mathrm{MW}}^2) \propto n^4/Z^2$, tunable from about zero to $V_{\max} \simeq 2\pi\times 1.9$ MHz at $n=46$ and 4.2 µm separation. This interaction gives Rydberg blockade — the pair state $|rr\rangle$ is shifted out of resonance and two-ion Rabi oscillations run at $\sqrt{2}$ the single-ion frequency — and it drives a 700 ns controlled-phase gate: a double STIRAP pulse takes the $|00\rangle$ component up to $|rr\rangle$ and back, accumulating phase $\varphi = V_{\max}\int_0^T \langle rr|\rho(t)|rr\rangle\,dt \simeq \pi$ while the other three pair states are untouched. The measured coherence $C = 0.72 \pm 0.04$ and population $P = 0.85 \pm 0.04$ give an entanglement fidelity of $0.78 \pm 0.03$. The error budget assigns the largest losses to technical sources — microwave power fluctuations, imperfect adiabatic passage, Rydberg decay, and laser linewidth — and predicts a total error of 0.19% for an improved setup ($n=60$, 2.3 µm separation, zero-polarisability dressed state, stabilised microwaves, stronger and narrower lasers), with coupling to crystal motion contributing about $10^{-4}$ error even in a 100-ion crystal.

Load-bearing premise

The improved-error predictions (0.19% total error and $10^{-4}$ motional error in a 100-ion crystal) assume that a microwave-dressed Rydberg state with residual polarisability below $10^{-34}\,\mathrm{C^2\,m^2\,J^{-1}}$ can actually be realised; the demonstrated 700 ns gate at 78% fidelity does not use such a state — it uses a maximally-dressed state and requires sideband cooling — so the projected performance has not itself been shown.

Editorial extensions

If this is right

Entangling gates in trapped-ion systems could run at sub-microsecond speeds, about one to two orders of magnitude faster than the standard 40–100 µs motional-mode gates, so many more operations fit within a given coherence time.
Because the gate never requires the vibrational phase-space trajectories to close, it should work in long ion strings and higher-dimensional crystals; the predicted error from coupling to motion is about $10^{-4}$ in a 100-ion crystal at intermediate temperatures (10–100 µK).
The microwave-dressed interaction is tunable between zero and $V_{\max}$ on nanosecond timescales, which the authors note may enable studies of quantum quench dynamics and out-of-equilibrium behaviour in Rydberg-ion systems.
With realistic technical upgrades — $n=60$, 2.3 µm ion separation, a zero-polarisability dressed state, stabilised microwave power, and higher laser intensities — the modelled total gate error is 0.19%, comparable to the best demonstrated ion gates but in a fraction of the time.
Operating the trap cryogenically suppresses blackbody-radiation double ionisation of the Rydberg electron, which the authors estimate otherwise limits the useful Rydberg lifetime; this would allow even higher Rydberg states and faster gates.

Reading between the lines

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

One testable next step the paper does not take is running the same gate with a zero-polarisability dressed state on Doppler-cooled ions; the reported 78% demonstration still required sideband cooling, so the improved-error path stands or falls on that state's residual polarisability being as low as assumed.
The saturation of the motional error with crystal size implies a clean experimental signature: two-ion gate fidelity should be nearly independent of crystal size from roughly ten to 100 ions, so a fidelity-versus-N scan would directly test the scalability claim.
Because the interaction strength grows as $n^4$, cryogenic operation plus higher principal quantum numbers could push gate times toward tens of nanoseconds; the paper only footnotes the obstacle — coupling to the trap's quadrupole field at high $n$ — and does not analyse the compensation it would require.
The tunable, pairwise character of the dressed interaction suggests the scheme could be extended to parallel entangling gates on selected ion pairs in a large crystal, a direction the paper gestures toward through its reference on Rydberg mode shaping but does not demonstrate.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is the first experimental demonstration of a Rydberg-interaction entangling gate in trapped ions, and the core result holds up: a 700 ns controlled-phase gate with 78% Bell fidelity, with Rabi oscillations and gate error reproduced by simulations that use no free parameters. That is a real advance over previous trapped-ion Rydberg work, which stopped at single-ion excitation and coherent control. The blockade observations, including the sqrt(2)-enhanced Rabi frequency, are clean and support the interaction picture.

The error budget is the honest part of the paper. The listed sources—Rydberg decay, laser linewidth, intermediate-state scattering, adiabatic transitions, MW power fluctuations, polarisability—sum roughly to the observed ~23% infidelity, and the dominant technical errors are traced to known hardware limitations rather than hidden assumptions. The scaling formulas in the supplement look sensible and are backed by derivations. I believe the central experimental claim.

The soft spot is the projection, not the demonstration. The abstract's "total error below 0.2%" depends on a zero-polarisability MW-dressed Rydberg state with residual polarisability below 1e-34 C^2 m^2/J. That state is not demonstrated here; the experiment uses a maximally-dressed state and needs sideband cooling. The supplement says they expect to measure the polarisability to that precision in a follow-up, citing an in-preparation paper. That is the one load-bearing extrapolation. If the residual polarisability is an order of magnitude worse, the polarisability and Doppler motional errors in the improved column climb above the 0.2% claim. This does not shake the demonstrated 78% gate, but it should temper how the headline is read.

The 100-ion motional-error estimate (~1e-4) is a plausible theoretical upper bound, and it explicitly assumes the zero-polarisability state. That assumption is clearly flagged in the supplement, so it is an unverified prediction rather than a hidden flaw. The footnote about RF quadrupole coupling at high n is similarly honest about a possible complication.

Verdict: this deserves serious peer review. A proof-of-principle result that opens a new route for fast trapped-ion gates should be published, with the experimental claims separated from the extrapolations. The authors should be asked to mark the 0.2% figure as a prediction contingent on the zero-polarisability state and to either add a pointer to the in-preparation measurement or soften the abstract. If they can demonstrate the zero-polarisability dressed state, this becomes much stronger. I would take it to a reading group and would cite the demonstrated gate; the projected numbers, only with caution.

Referee Report

3 major / 6 minor

Summary. The manuscript reports the first experimental demonstration of a sub-microsecond entangling gate between two trapped ions based on the microwave-dressed Rydberg dipole-dipole interaction. Two 88Sr+ ions are excited to a MW-dressed Rydberg state, and the resulting first-order dipole-dipole interaction (Vmax <= 2pi x 1.9 MHz at n=46, r=4.2 um) suppresses double excitation and is used in a double-STIRAP sequence to implement a 700 ns controlled-phase gate. The measured Bell state fidelity is 78 +/- 3% (parity coherence C=0.72 +/- 0.04, population P=0.85 +/- 0.04), consistent with the simulated error budget of about 23%. The authors further predict that with improved parameters (n=60, r=2.3 um, higher laser Rabi frequencies, and a zero-polarisability MW-dressed Rydberg state) the total gate error can be reduced below 0.2%, and that coupling to motional modes in a 100-ion crystal contributes only about 1e-4 error.

Significance. If correct, this work opens a new route for fast entangling gates in trapped-ion quantum computers that do not require shared motional-mode control, potentially enabling faster operations in large ion crystals. The main experimental claim - a 700 ns gate with 78% fidelity - is supported by the data and by no-free-parameter numerical simulations of the Rabi oscillations and the gate dynamics. The projection to below 0.2% error and the large-crystal scaling, however, rest on an unverified zero-polarisability dressed state and should be treated as conditional. The paper's strength is the clear identification of error sources through a simulation that closes the error budget against the measured fidelity.

major comments (3)

[Supplemental Material, Sec. III; Table I, footnote c] The improved-experiment error budget and the 100-ion motional error estimate both assume a zero-polarisability MW-dressed Rydberg state with residual polarisability |alpha| < 1e-34 C^2 m^2/J. This state is not realized or characterized in the present manuscript; the only backing cited is Ref. [3] of the supplement, which is described as 'in preparation.' Because the abstract's headline claims ('total error below 0.2%' and 'residual coupling ... ~1e-4' in a 100-ion crystal) depend on this unverified assumption, the projections are not independently supported by this paper. Please either provide a measurement of the zero-polarisability state or explicitly reframe these claims as conditional on a state that remains to be demonstrated.
[Supplemental Material, Sec. III; Table I] The required polarisability cancellation is quantitatively extreme: the n=60 Rydberg state polarisability is about 3e-30 C^2 m^2/J, so reaching |alpha| < 1e-34 C^2 m^2/J requires relative control at the 3e-5 level, while the dressed state must simultaneously retain roughly 75% of the maximal dipole moment (V = 2pi x 21.9 MHz in Table I). The manuscript provides no sensitivity analysis showing how the gate error depends on residual polarisability or on MW power stability at this operating point. I ask the authors to add such an analysis; if the residual polarisability is only one order of magnitude worse than assumed, the projected total error would rise above the 0.2% claim.
[Main text, closing paragraph; Table I] The statement that 'the sources of gate error are identified' is stronger than what is demonstrated. Table I lists contributions estimated by numerical simulation, but the individual contributions are not measured independently; only the sum is compared with the observed fidelity (78 +/- 3% vs. simulated ~77%). The authors should either provide an experimental decomposition (for example, measuring the MW power noise contribution directly) or soften the wording to 'sources of error are estimated by simulation and sum to a value consistent with the observed infidelity.' This is a moderation of the central claim rather than a request for new physics.

minor comments (6)

[Abstract] The phrase 'and produce a Bell state' should read 'and produces a Bell state' to agree with the singular subject 'gate.'
[Main text, second paragraph] The sentence 'A two-photon laser field then couples |0> to Rydberg state |r> via a two-photon laser field' is redundant; consider removing 'via a two-photon laser field' or restructuring.
[Supplemental Material, Ref. [3]] The title 'Zero-polorizability microwave-dressed Rydberg states' contains a typo: 'polorizability' should be 'polarizability.'
[Table I] The table footnotes introduce symbols such as Gamma_l, deltaOmega_MW, and alpha; please define each symbol at first use in the table or in the main text for self-containedness.
[Main text, Eq. (2)] The scaling V proportional to n^4/Z^2 is stated without derivation or reference; a brief justification for the dipole matrix element scaling would help the reader.
[Supplemental Material, Figs. 5 and 6] The axis labels indicate factors of 10^5 and 10^4 (as 'G x 10^5' and 'G x 10^4'), but in the ascii rendering the scaling is easy to miss; please ensure the printed figures show the scaling factors clearly.

Circularity Check

1 steps flagged · score 4.0 of 10

Demonstrated 700 ns gate is self-contained; projected 0.2% error and 100-ion scaling lean on an unverified, in-preparation self-cited zero-polarisability dressed state.

self citation load bearing [Supplement §III ('Gate Error Analysis and Scaling'); main-text Table I footnote; refs [3] and [26]]
"The dressed-state polarisability can be measured precisely by spectroscopy and tuned to nearly zero by tuning the MW frequency (the theory value of dressed Rydberg state polarisability is confirmed by our recent experiment [3]). For higher Rydberg states (n∼60) with narrower linewidths, we expect to measure the polarisability to a precision of 10−34 C2m2J−1 level and thus achieve a residual polarisability below this value ... In that case the error caused by polarisability in a Doppler cooled large ion crystal can be reduced below 10−4."

The improved-experiment error budget (Table I: total 0.19%) and the 100-ion motional-error estimate (~10−4) assume a zero-polarisability MW-dressed Rydberg state with residual polarisability below 10−34 C2m2J−1. The only support offered for the existence and tunability of this state is ref [3], an in-preparation paper by the same group, together with author-overlapping theory in ref [26]. This is not a machine-checked, code-reproduced, or externally falsified result. The abstract's 'total error below 0.2%' and '~10−4' scaling predictions are therefore conditional on the authors' own unpublished self-citation rather than derived from an independent, demonstrated result.

full rationale

The experimental core is self-contained: the Rabi-oscillation simulations are parameter-free ('Solid lines show results of numerical simulation using no free parameters'), with parameters taken from atomic matrix elements or independent measurements, and the 78% Bell-state fidelity is a measured value rather than a fitted output. The error budget is compared with the observed infidelity, not constructed to match it by tuning. No equation in the demonstrated gate derivation is defined in terms of its target result. The one load-bearing self-reference is the projection to 0.2% total error and ~10−4 motional error in a 100-ion crystal: both require a zero-polarisability MW-dressed Rydberg state that is not realized in this experiment, and whose feasibility is attributed to an in-preparation paper by overlapping authors (Pokorny et al., ref [3]) and to author-overlapping theory (ref [26]). That makes the headline improvement projections dependent on an unverified self-citation, but it does not make the reported 700 ns/78% gate demonstration circular.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The demonstrated gate is simulated with parameters from atomic matrix elements and independent measurements, so the central experimental claim has a low circularity burden. The main new premises in the ledger are the assumed improved-experiment parameters and the zero-polarisability dressed state, which are chosen by hand or borrowed from the same group's unpublished work and carry the scalability predictions.

free parameters (2)

Improved-experiment parameter set (n=60, r=2.3 μm, Ω1 = 2π × 1000 MHz, Ω2 = 2π × 1414 MHz, Δ = 2π × 100 MHz, Γ1,2 = 2π…
Chosen by hand as 'technically achievable' values to compute the predicted 0.19% total error (Table I, improved experiment column). Not realized in this work.
Residual polarisability of zero-polarisability dressed state = < 1e-34 C^2 m^2/J (target)
Assumed for the improved-experiment error estimate and for the 100-ion motional error calculation (Supplement §III, §IV). Support is the same group's in-preparation work, not an independent measurement.

assumptions (5)

domain assumption Dipole-dipole interaction of two identically dressed Rydberg ions is given by V = (1/4πε0)⟨s|μ|p⟩²/r³ × Ω²/(Δ²+Ω²), with higher-order terms neglected because Ω_MW >> V_max.
Main text Eq. (2) and surrounding text. The gate phase and Rabi-blockade simulations depend on this interaction model.
domain assumption Double STIRAP with detuning Δ >> V_max and Δ << Ω_max keeps the two-ion system in the two-atom dark state and returns population to |00>, so the only effect on |00> is the phase V_max∫⟨rr|ρ|rr⟩dt.
Supplement §I and Fig. 3(c). Non-adiabatic transitions and intermediate-state scattering are treated as errors.
ad hoc to paper A zero-polarisability MW-dressed Rydberg state with residual polarisability |α| < 1e-34 C^2 m^2/J can be realized and characterized.
Supplement §III ('we expect to measure the polarisability to a precision of 10^-34 C^2m^2/J') and §IV; cited to same-group in-preparation ref [3]. Load-bearing for the extrapolated error and scaling claims.
domain assumption Phonon-induced gate error can be computed to linear order in ion displacement using the Magnus expansion and tracing over a thermal phonon state; quadratic and higher-order displacement terms are neglected.
Supplement §IV, Eqs. (8)-(14). The 1e-4 motional error estimate in a 100-ion crystal rests on this approximation.
standard math Lindblad master equation with independent spontaneous decay channels from |e>, |s>, |p> to the 5S1/2 sublevels captures the decoherence.
Supplement §II. Standard open-quantum-system treatment solved with QuTiP; no free parameters stated.

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Cite this review

Pith. "Pith review of Sub-microsecond entangling gate between trapped ions via Rydberg interaction." pith.science (2026). https://pith.science/paper/3QQEBYSM

@misc{pith2026190811284,
  author       = {Pith},
  title        = {Pith review of: Sub-microsecond entangling gate between trapped ions via Rydberg interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3QQEBYSM}},
  note         = {Machine review of arXiv:1908.11284}
}

abstract

Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems with low-error entanglement gates operated via the vibrational motion of a few-ion crystal within tens of microseconds. To exceed the level of complexity tractable by classical computers the main challenge is to realise fast entanglement operations in large ion crystals. The strong dipole-dipole interactions in polar molecule and Rydberg atom systems allow much faster entangling gates, yet stable state-independent confinement comparable with trapped ions needs to be demonstrated in these systems. Here, we combine the benefits of these approaches: we report a $700\,\mathrm{ns}$ two-ion entangling gate which utilises the strong dipolar interaction between trapped Rydberg ions and produce a Bell state with $78\%$ fidelity. The sources of gate error are identified and a total error below $0.2\%$ is predicted for experimentally-achievable parameters. Furthermore, we predict that residual coupling to motional modes contributes $\sim 10^{-4}$ gate error in a large ion crystal of 100 ions. This provides a new avenue to significantly speed up and scale up trapped ion quantum computers and simulators.

Figures

Figures reproduced from arXiv: 1908.11284 by the authors.

**Figure 2.** FIG. 2. Tunable interaction between Rydberg ions. (a) Two-ion level scheme, where levels are [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Experimental sequence of the Rydberg-interaction gate. (a) Pulse sequence: two ions are [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Analysis of the two-ion state after the entangling gate operation. (a) A Ramsey-type [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. Exponent [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]

**Figure 6.** Figure 6: FIG. 6. (Color online) Exponent [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]

**Figure 7.** Figure 7: FIG. 7. (Color online) Double ionisation rate Γ [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]

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Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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(c) Simulation of one- and two-ion population dynamics during gate operation, the controlled-phase accumulated by|00⟩ is proportional to area enclosed by the|rr⟩ population curve

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