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REVIEW 3 major objections 4 minor 75 references

Performance Analysis for Crosstalk Errors between Parallel Entangling Gates in Trapped Ion Quantum Error Correction

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Crosstalk between parallel entangling gates in trapped ions is a two-qubit error that requires a distance-5 surface code.

desk verdict The distance-5 necessity claim is solid and useful, but the scaling extrapolation to 1e-10 logical error rates is built on a fitted formula that already fails against the paper's own d=5 data. read the letter →

arxiv 2501.09554 v2 pith:L7DO5GVA submitted 2025-01-16 quant-ph

Fangxuan Liu , Gaoxiang Tang , Luming Duan , Yukai Wu This is my paper · ORCID
classification quant-ph MSC 81P6881P73
keywords trapped-ionquantumcomputingcrosstalkerrorsparallelentanglinggatessurfacecodeerrorcorrectionrandomizedcompilinglogicalratetwo-dimensionalioncrystals
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 establishes that the crosstalk between entangling gates run in parallel on a two-dimensional trapped-ion crystal is a correlated two-qubit error, and that a rotated surface code of distance 3 cannot correct it even in principle. Using a distance-5 code, one crosstalk event is correctable, so the logical error rate acquires a quadratic suppression and a pseudothreshold (where the logical qubit beats the physical qubits) can exist. The paper simulates logical error rates and coherence times under crosstalk, gate infidelity, and idling errors, and shows that the optimal number of parallel gate pairs balances crosstalk against idling. It also derives a unified scaling bound for the logical error rate and argues that both slow-gate and fast-gate regimes can reach logical error rates below $10^{-10}$ with hundreds to thousands of ions. The practical consequence is that near-term trapped-ion error correction should plan for at least distance 5 once parallel entangling gates are used.

What carries the argument

The load-bearing objects are the rotated surface code with its four-layer CNOT schedule and the phonon-mediated Mølmer–Sørensen gate model. The CNOT schedule is ordered so that single-qubit errors propagate perpendicular to the logical operators; a two-qubit crosstalk event between ancilla gates becomes a weight-4 data-qubit error, which the schedule keeps correctable only when the code distance is at least 5. The gate model writes the evolution as spin-dependent displacements plus pair phases $\Theta_{ij}$, so an undesired phase is the crosstalk and residual spin-phonon entanglement becomes dephasing; randomized single-qubit rotations convert the coherent phase into a stochastic Pauli $XX$ error. The EASE algorithm supplies the amplitude-modulated pulses used to compute realistic crosstalk, and the unified bound in Eq. (12) combines gate infidelity, idling error, and crosstalk per gate $\tilde p_c=2(k-1)p_c$ into a single distance-dependent formula.

What would settle it

Run the same EASE parallel-gate pulses on a small two-dimensional ion crystal, with and without randomized compiling, and perform quantum process tomography on two simultaneous gate pairs; if the crosstalk channel retains coherent off-diagonal terms, or if the measured $d=3$ logical error rate does not scale linearly with $p_c$ while the $d=5$ rate does not scale quadratically, the central claim fails.

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Extended reading notes

Core claim

The central claim is that phonon-mediated crosstalk between parallel entangling gates is a two-qubit $XX$-type error that a distance-3 surface code cannot correct, making distance 5 the minimum code for a pseudothreshold. The argument is made concrete by simulation of a $d=5$ rotated surface code: for equal physical error rates $p$, the logical error rate scales as $p_L \propto p$ for $d=3$ and $p_L \propto p^2$ for $d=5$, with a pseudothreshold near $p\approx 1.3\times10^{-5}$. Once the coherent crosstalk phase is converted to a stochastic Pauli error by randomized compiling, the crosstalk enters as a two-qubit error with probability $p_c=\epsilon_{ij}^2$. Under EASE-designed parallel gates with realistic pulse noise, the average crosstalk is $p_c\approx1.1\times10^{-5}$, and the paper finds a break-even point where logical coherence time equals physical coherence time over a wide parameter range. The unified scaling bound $p_L \le 0.015[(p_g + 3t/8T + 1.3\tilde p_c)/0.013]^{(d+1)/2}$ then implies that logical error rates below $10^{-10}$ are reachable with a distance-41 code in the slow-gate regime or a distance-17 code in the fast-gate regime.

Load-bearing premise

Everything downstream assumes that randomized compiling fully converts the coherent crosstalk phase into a stochastic Pauli $XX$ error; if residual coherent two-qubit rotation remains, the crosstalk is stronger than the model and distance 5 may not be sufficient.

Editorial extensions

If this is right

  • A distance-3 rotated surface code has no pseudothreshold under two-qubit crosstalk: once $p_c$ is fixed, $p_L$ is lower-bounded by a value proportional to $p_c$ no matter how low gate infidelity and idling errors go.
  • The optimal parallelism level is not full parallelism: with spatially uniform crosstalk, choosing $k=O(d)$ parallel gate pairs balances the $O(d^2/k)$ idling error against the $O(k)$ crosstalk contribution.
  • In the fast-gate regime, crosstalk decays polynomially with ion-pair distance, and sublattice scheduling with $l=4$ gives $\tilde p_c=10^{-6}$, making a distance-17 code sufficient for $p_L<10^{-10}$.
  • Under realistic parameters with $p_g=10^{-3}$ and physical coherence times of $10^3$ to $10^5$ gate times, the optimized $d=5$ code exceeds the break-even point $T_L=T$ for a wide range of crosstalk rates.
  • The slow-gate regime requires a larger code, $d=41$ with thousands of ions, but still reaches the $10^{-10}$ logical error goal.

Reading between the lines

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

  • If randomized compiling is imperfect, residual coherence in the crosstalk would make the two-qubit rotation more damaging than the depolarizing model; an experiment that compares $d=3$ and $d=5$ logical error rates under full process tomography of the crosstalk channel would reveal this directly.
  • The fitted $r^{-5.87}$ decay of crosstalk in the fast-gate regime is a concrete prediction: a two-dimensional crystal experiment measuring undesired two-qubit phase as a function of ion-pair distance could confirm the boundary between the slow- and fast-gate regimes.
  • The scaling law suggests that codes with nonlocal connectivity, such as quantum LDPC codes laid out on the same crystal, could inherit the same crosstalk protection with fewer physical qubits; the paper notes long-range gates as an outlook without quantifying this.
  • Reporting crosstalk per parallel layer rather than per gate pair would make fault-tolerance comparisons clearer, since the effective crosstalk per gate grows as $2(k-1)p_c$ with the number of parallel pairs.
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Formalized claims in Lean

  1. Claim #1: The central claim is that phonon-mediated crosstalk between parallel entangling gates is a two-qubit $XX$-type error that a distance-3 surface code cannot correct, making distance 5 the minimum code for a pseudothreshold. The argument is made concrete by simulation of a $d=5$ rotated surface code: for equal physical error rates $p$, the logical error rate scales as $p_L \propto p$ for $d=3$ and $p

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper analyzes crosstalk errors between parallel entangling gates in a 2D ion crystal and their impact on rotated surface code quantum error correction. It argues that the phonon-mediated two-qubit crosstalk considered here cannot be corrected by a distance-3 code, so a distance-5 code is necessary, and it supports this claim with Stim simulations of d=3 and d=5 rotated surface codes, showing pL ~ p for d=3 and pL ~ p^2 with a pseudothreshold for d=5. The paper also optimizes the parallelism level by balancing idling errors against crosstalk, studies slow- and fast-gate spatial regimes with concrete EASE pulse sequences, and proposes a unified scaling formula, Eq. (12), to predict that logical error rates below 10^-10 can be reached with distance d=17 or d=41 in a 2D crystal of hundreds to thousands of ions.

Significance. The main qualitative conclusion, that phonon-mediated two-qubit crosstalk forces a distance-5 rotated surface code rather than distance-3, is well supported by direct simulation under the stated stochastic Pauli noise model, and it is practically relevant for 2D ion-crystal QEC. The paper has concrete strengths: it uses a physically motivated crosstalk model, performs stabilizer-circuit simulations with Stim, designs actual pulse sequences with the EASE protocol for both slow- and fast-gate regimes, and releases the pulse-sequence data on figshare. The quantitative extrapolation to large code distances, however, rests on Eq. (12), a fitted formula that is presented as an upper bound but is not conservative even at d=5; the large-distance resource claims are therefore not yet established.

major comments (3)
  1. [Section V, Eq. (12), Appendix A] Eq. (12) is stated as an upper bound, but it is not an upper bound for the paper's own d=5 simulation. At the pseudothreshold of Fig. 2(a), taking p ≈ 1.3e-5 with pg=pi=pc=p and full parallelism k=d(d-1)=20 (so t ≈ 9 and p~c = 2(k-1)p = 38p), Eq. (12) gives pL ≈ 0.015[(p + 4.5p + 1.3*38p)/0.013]^3 ≈ 2.5e-6, whereas Fig. 2(a) reports pL ≈ 1.3e-5 at the same point. The formula under-predicts the simulated logical error rate by about a factor of five. This originates from the fact that Appendix A fits Eq. (12) to the depolarizing-crosstalk model of Fig. 6, while the main-text simulations use the XX Pauli crosstalk channel of Sec. II B. Consequently the extrapolations to d=17 and d=41 in Fig. 5(d), and the claim that pL < 1e-10 is reachable, are not currently supported.
  2. [Appendix A, Fig. 7] The exponent (d+1)/2 in Eq. (12) is extracted from slopes near threshold, but the paper itself notes in Appendix A that the asymptotic scaling of the crosstalk contribution is pL ~ pc^{⌈d/4⌉}. The target pL < 1e-10 is far below threshold, where the near-threshold exponent is not the relevant one. Since the bracket in Eq. (12) is below one in the extrapolated regime, replacing the crosstalk exponent with the asymptotic ⌈d/4⌉ value changes the required code distances; at minimum, the authors should justify the larger exponent for the deep-sub-threshold regime or present a conservative bound using the asymptotic exponent for the crosstalk term.
  3. [Sec. II B] The conversion of coherent crosstalk e^{i ε_ij X_i X_j} into a stochastic XX error with probability pc = ε_ij^2 relies on randomized compiling, but no explicit twirling circuit is given and no estimate of the residual coherent component is provided. This assumption is load-bearing: the d=5 necessity, the pL ~ p^2 scaling, and Eq. (12) all use a stochastic Pauli channel. A direct simulation with a coherent crosstalk rotation, or an explicit randomized-compiling sequence with finite sampling, is needed to confirm that the conclusions survive partial or imperfect twirling.
minor comments (4)
  1. [Sec. III] The notation 'J25, 1, 5K' in the text appears to be a rendering error for [[5,1,5]]; please correct the typesetting.
  2. [Fig. 5 and Sec. V] Fig. 5(b) reports an average crosstalk pc ≈ 1.1e-5, but the scaling curves in Fig. 5(d) are computed with pc = 1e-5; the rounding should be stated explicitly in the caption or text.
  3. [Abstract and Sec. III] The statement that a distance-5 code is 'necessary' should be qualified as necessary for the rotated surface code under MWPM decoding with this crosstalk model; the evidence does not establish impossibility for all distance-3 codes or all decoders.
  4. [Fig. 5(d)] The caption should state explicitly that both curves are predictions from Eq. (12) for d > 5 and are not direct simulations at those distances.

Circularity Check

1 steps flagged · score 6.0 of 10

Eq. (12) is a fit to the paper's own simulation data; the d=41 / d=17 below-10^-10 predictions are that fitted curve extrapolated, making the large-distance scaling claim circular.

  1. fitted input called prediction [Appendix A, applied in Sec. V Eq. (12) and Fig. 5(d)]
    "Based on the above numerical results, now we can fit pL = A(˜pc/pth)(d+1)/2 where A ≈ 0.01, pth ≈ 0.01. Similarly, for the two-qubit entangling gate with a depolarizing error pg, we perform numerical simulation (not shown) and fit pL = B(pg/p′th)(d+1)/2 where B ≈ 0.015 and p′th ≈ 0.013."

    Appendix A obtains the prefactor, threshold, and (d+1)/2 exponent by fitting the same Stim simulations shown in Figs. 6 and 7, plus an unshown gate-error simulation. The main text then promotes this combined fit to Eq. (12), labels it an upper bound, and evaluates it at d=41 and d=17 to conclude pL<10^-10 with hundreds-to-thousands of ions. The large-distance 'prediction' is therefore the fitted scaling law evaluated at larger d—a compact summary of the input simulation data—rather than an independent derivation. The paper itself notes the true asymptotic small-p exponent is ⌈d/4⌉, not (d+1)/2, so the extrapolated exponent is a near-threshold fit value and using it far below threshold is a fitted input, not a derived bound.

full rationale

The central distance-5 claim is not circular: it is supported by direct Stim simulation (Fig. 2) and by the standard surface-code distance argument that a weight-2 crosstalk error cannot be corrected by d=3 but can be corrected by d=5. The randomized-compiling reduction from coherent to Pauli XX crosstalk is an explicit modeling assumption with external citations, not a self-referential derivation. No load-bearing self-citation chain or imported uniqueness theorem is present: self-citations such as [55], [59], and [61] supply standard formulas or data but do not force the paper's conclusions. The circular element is confined to the scaling analysis: Eq. (12) is fit to the paper's own small-distance simulations and then used as a predictive 'bound' for large distances, so the claimed 10^-10 rates at d=41 and d=17 reduce to the fitted curve rather than to an independent first-principles scaling law. This is a partial circularity in the long-term scaling sub-claim, while the main threshold/break-even results remain independent numerical findings.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central quantitative predictions rest on a small number of fitted constants and explicit modeling assumptions. The distance-5 necessity itself is well grounded in direct simulation, but the large-distance scaling and resource estimates depend on the parameters and axioms listed here.

free parameters (6)
  • Crosstalk error rate pc = 1.1e-5 (simulated), then set to 1e-5 in calculations
    Estimated from sampled amplitude and frequency noise in EASE pulse sequences; used as the crosstalk probability per ion pair.
  • Gate infidelity pg = 1e-3 or 3e-3 in examples
    Assumed target gate infidelity in the numerical examples, not fitted to a specific experiment.
  • Physical coherence time T = 5e4 or 1e5 gate times
    Assumed coherence time in the scaling examples.
  • Crosstalk scaling constants A and p_th = A=0.01, p_th=0.01
    Obtained by fitting pL = A(p_tilde_c/p_th)^((d+1)/2) to the authors' Stim simulations; used to predict large-d behavior.
  • Gate-error scaling constants B and p'_th = B=0.015, p'_th=0.013
    Obtained by fitting to numerical simulations (listed as not shown in Appendix A).
  • Spatial crosstalk power law constants = C=0.015, alpha=5.87 in pc = C(r/a)^-alpha
    Fit to simulated crosstalk in the fast-gate regime; used to estimate p_tilde_c for sublattice parallelization.
assumptions (5)
  • domain assumption Crosstalk errors can be converted from coherent to incoherent Pauli errors by randomized compiling.
    Used in Sec. II B to justify modeling crosstalk as a two-qubit Pauli XX error with probability pc. If randomization is imperfect, the distance-5 conclusion could be affected.
  • domain assumption Residual spin-phonon entanglement acts as independent single-qubit dephasing.
    Eq. (10) assumes the alpha_jk are random with independent magnitudes and directions, reducing a joint multi-qubit dephasing to per-qubit errors; otherwise the noise may not be correctable by distance-5.
  • domain assumption The depolarizing channel approximates the XX crosstalk for scaling predictions.
    Appendix A switches from the Pauli XX model to a two-qubit depolarizing channel for the scaling analysis, assuming the error structure does not change the scaling exponents.
  • ad hoc to paper The fitted logical error formula holds beyond simulated code distances.
    Eq. (12) is used to predict d up to 41 from simulations for d up to 21, without a proof that the fitted form is valid in that range.
  • domain assumption Crosstalk is spatially uniform in the slow-gate regime for large crystals.
    Sec. V assumes the crosstalk pc measured on a d=5 lattice applies to all ion pairs in a much larger crystal, based on a sound-wave propagation argument.

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Cite this review

Pith. "Pith review of Performance Analysis for Crosstalk Errors between Parallel Entangling Gates in Trapped Ion Quantum Error Correction." pith.science (2026). https://pith.science/paper/L7DO5GVA

@misc{pith2026250109554,
  author       = {Pith},
  title        = {Pith review of: Performance Analysis for Crosstalk Errors between Parallel Entangling Gates in Trapped Ion Quantum Error Correction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L7DO5GVA}},
  note         = {Machine review of arXiv:2501.09554}
}
abstract

The ability to execute a large number of quantum gates in parallel is a fundamental requirement for quantum error correction, allowing an error threshold to exist under the finite coherence time of physical qubits. Recently, two-dimensional ion crystals have been demonstrated as a plausible approach to scale up the qubit number in a trapped ion quantum computer. However, although the long-range Coulomb interaction between the ions enables their strong connectivity, it also complicates the design of parallel gates and leads to intrinsic crosstalk errors. Here we examine the effects of crosstalk errors on a rotated surface code. We show that, instead of the distance-3 code considered in previous works, a distance-5 code is necessary to correct the two-qubit crosstalk error. We numerically calculate the logical error rates and coherence times under various crosstalk errors, gate infidelities and coherence times of the physical qubits, and we optimize the parallelism level according to the competition between different error sources. We show that a break-even point can be reached under realistic parameters. We further analyze the spatial dependence of the crosstalk, and discuss the scaling of the logical error rate versus the code distance for the long-term goal of a logical error rate below $10^{-10}$.

Figures

Figures reproduced from arXiv: 2501.09554 by the authors.

Figure 1
Figure 1. (a). Apart from the d 2 data qubits, it further uses d 2 − 1 ancilla qubits to extract the error syndrome from the X-type and Z-type stabilizers. These stabilizers are indicated by the red (green) plaquettes in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Logical error rates of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The logical error rate for the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The logical coherence time [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Scalability of ion trap quantum error correction un [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The logical error rate [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. We plot the slope of the curves in Fig. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

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Works this paper leans on

75 extracted references · 52 canonical work pages

  1. [1]

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges, Applied Physics Reviews 6, 021314 (2019)

    2019

  2. [2]

    Crain, C

    S. Crain, C. Cahall, G. Vrijsen, E. E. Wollman, M. D. Shaw, V. B. Verma, S. W. Nam, and J. Kim, High-speed low-crosstalk detection of a 171yb+ qubit using super- conducting nanowire single photon detectors, Communi- cations Physics 2, 97 (2019)

    work page 2019

  3. [3]

    Roman, A

    C. Roman, A. Ransford, M. Ip, and W. C. Campbell, Coherent control for qubit state readout, New Journal of Physics 22, 073038 (2020)

    work page 2020

  4. [4]

    C. L. Edmunds, T. R. Tan, A. R. Milne, A. Singh, M. J. Biercuk, and C. Hempel, Scalable hyperfine qubit state detection via electron shelving in the 2D5/2 and 2F7/2 manifolds in 171yb+, Phys. Rev. A 104, 012606 (2021)

    work page 2021

  5. [5]

    F. A. An, A. Ransford, A. Schaffer, L. R. Sletten, J. Gae- bler, J. Hostetter, and G. Vittorini, High fidelity state preparation and measurement of ion hyperfine qubits with i >1 2 , Phys. Rev. Lett. 129, 130501 (2022)

    work page 2022

  6. [6]

    T. P. Harty, D. T. C. Allcock, C. J. Ballance, L. Guidoni, H. A. Janacek, N. M. Linke, D. N. Stacey, and D. M. Lu- cas, High-fidelity preparation, gates, memory, and read- out of a trapped-ion quantum bit, Phys. Rev. Lett. 113, 220501 (2014)

    2014

  7. [7]

    M. C. Smith, A. D. Leu, K. Miyanishi, M. F. Gely, and D. M. Lucas, Single-qubit gates with errors at the 10 −7 level, arXiv:2412.04421 (2024)

    arXiv 2024

  8. [8]

    C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, High-fidelity quantum logic gates us- ing trapped-ion hyperfine qubits, Phys. Rev. Lett. 117, 13 060504 (2016)

    work page 2016

Show all 75 references
  1. [9]

    J. P. Gaebler, T. R. Tan, Y. Lin, Y. Wan, R. Bowler, A. C. Keith, S. Glancy, K. Coakley, E. Knill, D. Leibfried, and D. J. Wineland, High-fidelity universal gate set for 9Be + ion qubits, Phys. Rev. Lett. 117, 060505 (2016)

    2016

  2. [10]

    C. R. Clark, H. N. Tinkey, B. C. Sawyer, A. M. Meier, K. A. Burkhardt, C. M. Seck, C. M. Shappert, N. D. Guise, C. E. Volin, S. D. Fallek, H. T. Hayden, W. G. Rel- lergert, and K. R. Brown, High-fidelity bell-state prepa- ration with 40ca+ optical qubits, Phys. Rev. Lett. 127,...

    2021

  3. [11]

    C. M. L¨ oschnauer, J. M. Toba, A. C. Hughes, S. A. King, M. A. Weber, R. Srinivas, R. Matt, R. Nour- shargh, D. T. C. Allcock, C. J. Ballance, C. Matthiesen, M. Malinowski, and T. P. Harty, Scalable, high- fidelity all-electronic control of trapped-ion qubits, arXiv:2407.07694 (2024)

    2024

  4. [12]

    J.-S. Chen, E. Nielsen, M. Ebert, V. Inlek, K. Wright, V. Chaplin, A. Maksymov, E. P´ aez, A. Poudel, P. Maunz, and J. Gamble, Benchmarking a trapped-ion quantum computer with 30 qubits, Quantum 8, 1516 (2024)

    2024

  5. [13]

    Postler, S

    L. Postler, S. Heu βen, I. Pogorelov, M. Rispler, T. Feld- ker, M. Meth, C. D. Marciniak, R. Stricker, M. Ring- bauer, R. Blatt, P. Schindler, M. M¨ uller, and T. Monz, Demonstration of fault-tolerant universal quantum gate operations, Nature 605, 675 (2022)

    2022

  6. [14]

    S. A. Moses, C. H. Baldwin, M. S. Allman, R. An- cona, L. Ascarrunz, C. Barnes, J. Bartolotta, B. Bjork, P. Blanchard, M. Bohn, J. G. Bohnet, N. C. Brown, N. Q. Burdick, W. C. Burton, S. L. Campbell, J. P. Campora, C. Carron, J. Chambers, J. W. Chan, Y. H. Chen, A. Chernoguzov...

    2023

  7. [15]

    DeCross, R

    M. DeCross, R. Haghshenas, M. Liu, E. Rinaldi, J. Gray, Y. Alexeev, C. H. Baldwin, J. P. Bartolotta, M. Bohn, E. Chertkov, J. Cline, J. Colina, D. DelVento, J. M. Dreiling, C. Foltz, J. P. Gaebler, T. M. Gatterman, C. N. Gilbreth, J. Giles, D. Gresh, A. Hall, A. Hankin, A. Han...

    2024 arXiv

  8. [16]

    D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, Experimental issues in coherent quantum-state manipulation of trapped atomic ions, Journal of research of the National Institute of Stan- dards and Technology 103, 259 (1998)

    1998

  9. [17]

    Kielpinski, C

    D. Kielpinski, C. Monroe, and D. J. Wineland, Architec- ture for a large-scale ion-trap quantum computer, Nature 417, 709 (2002)

    2002

  10. [18]

    R. J. Hughes, D. F. V. James, E. H. Knill, R. Laflamme, and A. G. Petschek, Decoherence bounds on quantum computation with trapped ions, Phys. Rev. Lett.77, 3240 (1996)

    1996

  11. [19]

    Clark, Proceedings of the 1st International Conference on Experimental Implementation of Quantum Computa- tion: Sydney, Australia, 16-19 January 2001 (Rinton Press, 2001)

    R. Clark, Proceedings of the 1st International Conference on Experimental Implementation of Quantum Computa- tion: Sydney, Australia, 16-19 January 2001 (Rinton Press, 2001)

    2001

  12. [20]

    Szymanski, R

    B. Szymanski, R. Dubessy, B. Dubost, S. Guibal, J.- P. Likforman, and L. Guidoni, Large two dimensional Coulomb crystals in a radio frequency surface ion trap, Applied Physics Letters 100, 171110 (2012)

    2012

  13. [21]

    Y. Wang, M. Qiao, Z. Cai, K. Zhang, N. Jin, P. Wang, W. Chen, C. Luan, B. Du, H. Wang, Y. Song, D. Yum, and K. Kim, Coherently manipulated 2d ion crystal in a monolithic paul trap, Advanced Quantum Technologies 3, 2000068 (2020)

    2020

  14. [22]

    Y. Xie, J. Cui, M. D’Onofrio, A. J. Rasmusson, S. W. Howell, and P. Richerme, An open-endcap blade trap for radial-2d ion crystals, Quantum Science and Technology 6, 044009 (2021)

    2021

  15. [23]

    A. Kato, A. Goel, R. Lee, Z. Ye, S. Karki, J. J. Liu, A. Nomerotski, and B. B. Blinov, Two-tone doppler cooling of radial two-dimensional crystals in a radio- frequency ion trap, Phys. Rev. A 105, 023101 (2022)

    2022

  16. [24]

    Kiesenhofer, H

    D. Kiesenhofer, H. Hainzer, A. Zhdanov, P. C. Holz, M. Bock, T. Ollikainen, and C. F. Roos, Controlling two-dimensional coulomb crystals of more than 100 ions in a monolithic radio-frequency trap, PRX Quantum 4, 020317 (2023)

    2023

  17. [25]

    M. Qiao, Z. Cai, Y. Wang, B. Du, N. Jin, W. Chen, P. Wang, C. Luan, E. Gao, X. Sun, H. Tian, J. Zhang, and K. Kim, Tunable quantum simulation of spin models with a two-dimensional ion crystal, Nature Physics 20, 623 (2024)

    2024

  18. [26]

    Guo, Y.-K

    S.-A. Guo, Y.-K. Wu, J. Ye, L. Zhang, W.-Q. Lian, R. Yao, Y. Wang, R.-Y. Yan, Y.-J. Yi, Y.-L. Xu, B.- W. Li, Y.-H. Hou, Y.-Z. Xu, W.-X. Guo, C. Zhang, B.-X. Qi, Z.-C. Zhou, L. He, and L.-M. Duan, A site- resolved two-dimensional quantum simulator with hun- dreds of trapped ion...

    2024

  19. [27]

    Hou, Y.-J

    Y.-H. Hou, Y.-J. Yi, Y.-K. Wu, Y.-Y. Chen, L. Zhang, Y. Wang, Y.-L. Xu, C. Zhang, Q.-X. Mei, H.-X. Yang, J.- Y. Ma, S.-A. Guo, J. Ye, B.-X. Qi, Z.-C. Zhou, P.-Y. Hou, and L.-M. Duan, Individually addressed entangling gates in a two-dimensional ion crystal, Nature Communication...

    2024

  20. [28]

    Figgatt, A

    C. Figgatt, A. Ostrander, N. M. Linke, K. A. Landsman, D. Zhu, D. Maslov, and C. Monroe, Parallel entangling operations on a universal ion-trap quantum computer, Nature 572, 368 (2019)

    2019

  21. [29]

    Y. Lu, S. Zhang, K. Zhang, W. Chen, Y. Shen, J. Zhang, J.-N. Zhang, and K. Kim, Global entangling gates on arbitrary ion qubits, Nature 572, 363 (2019)

    2019

  22. [30]

    Nielsen and I

    M. Nielsen and I. Chuang, Quantum Computation and 14 Quantum Information (Cambridge University Press, 2000)

    2000

  23. [31]

    Grzesiak, R

    N. Grzesiak, R. Bl¨ umel, K. Wright, K. M. Beck, N. C. Pisenti, M. Li, V. Chaplin, J. M. Amini, S. Debnath, J.- S. Chen, and Y. Nam, Efficient arbitrary simultaneously entangling gates on a trapped-ion quantum computer, Nature Communications 11, 2963 (2020)

    2020

  24. [32]

    Olsacher, L

    T. Olsacher, L. Postler, P. Schindler, T. Monz, P. Zoller, and L. M. Sieberer, Scalable and parallel tweezer gates for quantum computing with long ion strings, PRX Quan- tum 1, 020316 (2020)

    2020

  25. [33]

    Cheng, S.-C

    L. Cheng, S.-C. Liu, L.-Y. Peng, and Q. Gong, Crosstalk suppression of parallel gates for fault-tolerant quantum computation with trapped ions via optical tweezers, Phys. Rev. Appl. 22, 034021 (2024)

    2024

  26. [34]

    Cheng, S.-C

    L. Cheng, S.-C. Liu, G.-Z. Yao, Y.-X. Wang, L.-Y. Peng, and Q. Gong, High-quality parallel entangling gates in long mixed-species ion chains, Phys. Rev. A 108, 042603 (2023)

    2023

  27. [35]

    fast gate

    or simply spin echoes [31, 38]. In comparison, as we will show, in our case the crosstalk errors are long-range two-qubit errors, necessitating the use of distance-5 QEC codes rather than the commonly used distance-3 codes for a pseudothreshold to exist. The paper is organized...

  28. [36]

    Shen, Z.-X

    C. Shen, Z.-X. Gong, and L.-M. Duan, Individual ad- dressing in quantum computation through spatial refo- cusing, Phys. Rev. A 88, 052325 (2013)

    2013

  29. [37]

    D. M. Debroy, M. Li, S. Huang, and K. R. Brown, Log- ical performance of 9 qubit compass codes in ion traps with crosstalk errors, Quantum Science and Technology 5, 034002 (2020)

    2020

  30. [38]

    Parrado-Rodr ´ ıguez, C

    P. Parrado-Rodr ´ ıguez, C. Ryan-Anderson, A. Bermudez, and M. M¨ uller, Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions, Quantum 5, 487 (2021)

    2021

  31. [39]

    C. Fang, Y. Wang, S. Huang, K. R. Brown, and J. Kim, Crosstalk suppression in individually addressed two- qubit gates in a trapped-ion quantum computer, Phys. Rev. Lett. 129, 240504 (2022)

    2022

  32. [40]

    M. N. H. Chow, C. G. Yale, A. D. Burch, M. Ivory, D. S. Lobser, M. C. Revelle, and S. M. Clark, First-order crosstalk mitigation in parallel quantum gates driven with multi-photon transitions, Applied Physics Letters 124, 044002 (2024)

    2024

  33. [41]

    Flannery, R

    J. Flannery, R. Matt, L. Huber, K. Wang, C. Axline, R. Oswald, and J. P. Home, Physical coherent cancella- tion of optical addressing crosstalk in a trapped-ion ex- periment, arXiv:2406.06775 (2024)

    2024 arXiv

  34. [42]

    S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052 (1998)

    1998 arXiv

  35. [43]

    Bombin and M

    H. Bombin and M. A. Martin-Delgado, Optimal resources for topological two-dimensional stabilizer codes: Com- parative study, Phys. Rev. A 76, 012305 (2007)

    2007

  36. [44]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012)

    2012

  37. [45]

    Acharya, D

    R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa,...

    2024

  38. [46]

    Edmonds, Paths, trees, and flowers, Canadian Journal of Mathematics 17, 449–467 (1965)

    J. Edmonds, Paths, trees, and flowers, Canadian Journal of Mathematics 17, 449–467 (1965)

    1965

  39. [47]

    Edmonds, Maximum matching and a polyhedron with 0, 1-vertices, Journal of research of the National Bureau of Standards 69B, 125 (1965)

    J. Edmonds, Maximum matching and a polyhedron with 0, 1-vertices, Journal of research of the National Bureau of Standards 69B, 125 (1965)

    1965

  40. [48]

    Gidney, Stim: a fast stabilizer circuit simulator, Quan- tum 5, 497 (2021)

    C. Gidney, Stim: a fast stabilizer circuit simulator, Quan- tum 5, 497 (2021)

    2021

  41. [49]

    Sørensen and K

    A. Sørensen and K. Mølmer, Quantum computation with ions in thermal motion, Phys. Rev. Lett. 82, 1971 (1999)

    1999

  42. [50]

    Mølmer and A

    K. Mølmer and A. Sørensen, Multiparticle entanglement of hot trapped ions, Phys. Rev. Lett. 82, 1835 (1999)

    1999

  43. [51]

    Milburn, S

    G. Milburn, S. Schneider, and D. James, Ion trap quan- tum computing with warm ions, Fortschritte der Physik 48, 801 (2000)

    2000

  44. [52]

    Leibfried, B

    D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Bar- rett, J. Britton, W. M. Itano, B. Jelenkovi´ c, C. Langer, 15 T. Rosenband, and D. J. Wineland, Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate, Nature 422, 412 (2003)

    2003

  45. [53]

    Monroe, and L.-M

    Shi-Liang Zhu, C. Monroe, and L.-M. Duan, Arbitrary- speed quantum gates within large ion crystals through minimum control of laser beams, Europhys. Lett. 73, 485 (2006)

    2006

  46. [54]

    T. J. Green and M. J. Biercuk, Phase-modulated decou- pling and error suppression in qubit-oscillator systems, Phys. Rev. Lett. 114, 120502 (2015)

    2015

  47. [55]

    P. H. Leung and K. R. Brown, Entangling an arbitrary pair of qubits in a long ion crystal, Phys. Rev. A 98, 032318 (2018)

    2018

  48. [56]

    Wu, S.-T

    Y. Wu, S.-T. Wang, and L.-M. Duan, Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear paul trap, Phys. Rev. A 97, 062325 (2018)

    2018

  49. [57]

    O. Kern, G. Alber, and D. L. Shepelyansky, Quantum er- ror correction of coherent errors by randomization, The European Physical Journal D - Atomic, Molecular, Op- tical and Plasma Physics 32, 153 (2005)

    2005

  50. [58]

    J. J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Phys. Rev. A 94, 052325 (2016)

    2016

  51. [59]

    Tomita and K

    Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014)

    2014

  52. [60]

    Wu, Data used in ”Performance Analysis for Crosstalk Errors between Parallel Entangling Gates in Trapped Ion Quantum Error Correction” (2025), https://doi.org/m9.figshare.28218161

    Y. Wu, Data used in ”Performance Analysis for Crosstalk Errors between Parallel Entangling Gates in Trapped Ion Quantum Error Correction” (2025), https://doi.org/m9.figshare.28218161

    2025

  53. [61]

    K. A. Landsman, Y. Wu, P. H. Leung, D. Zhu, N. M. Linke, K. R. Brown, L. Duan, and C. Monroe, Two-qubit entangling gates within arbitrarily long chains of trapped ions, Phys. Rev. A 100, 022332 (2019)

    2019

  54. [62]

    Wu and L.-M

    Y.-K. Wu and L.-M. Duan, A two-dimensional architec- ture for fast large-scale trapped-ion quantum computing, Chinese Physics Letters 37, 070302 (2020)

    2020

  55. [63]

    J. J. Garc ´ ıa-Ripoll, P. Zoller, and J. I. Cirac, Speed op- timized two-qubit gates with laser coherent control tech- niques for ion trap quantum computing, Phys. Rev. Lett. 91, 157901 (2003)

    2003

  56. [64]

    Duan, Scaling ion trap quantum computation through fast quantum gates, Phys

    L.-M. Duan, Scaling ion trap quantum computation through fast quantum gates, Phys. Rev. Lett. 93, 100502 (2004)

    2004

  57. [65]

    J. D. Wong-Campos, S. A. Moses, K. G. Johnson, and C. Monroe, Demonstration of two-atom entangle- ment with ultrafast optical pulses, Phys. Rev. Lett. 119, 230501 (2017)

    2017

  58. [66]

    A. K. Ratcliffe, R. L. Taylor, J. J. Hope, and A. R. R. Carvalho, Scaling trapped ion quantum computers using fast gates and microtraps, Phys. Rev. Lett. 120, 220501 (2018)

    2018

  59. [67]

    Wang, C.-Y

    P. Wang, C.-Y. Luan, M. Qiao, M. Um, J. Zhang, Y. Wang, X. Yuan, M. Gu, J. Zhang, and K. Kim, Single ion qubit with estimated coherence time exceeding one hour, Nature communications 12, 233 (2021)

    2021

  60. [68]

    Yao, W.-Q

    R. Yao, W.-Q. Lian, Y.-K. Wu, G.-X. Wang, B.-W. Li, Q.-X. Mei, B.-X. Qi, L. Yao, Z.-C. Zhou, L. He, and L.-M. Duan, Experimental realization of a multiqubit quantum memory in a 218-ion chain, Phys. Rev. A 106, 062617 (2022)

    2022

  61. [69]

    Y. Wang, S. Crain, C. Fang, B. Zhang, S. Huang, Q. Liang, P. H. Leung, K. R. Brown, and J. Kim, High- fidelity two-qubit gates using a microelectromechanical- system-based beam steering system for individual qubit addressing, Phys. Rev. Lett. 125, 150505 (2020)

    2020

  62. [70]

    M. Kang, Y. Wang, C. Fang, B. Zhang, O. Khosra- vani, J. Kim, and K. R. Brown, Designing filter functions of frequency-modulated pulses for high-fidelity two-qubit gates in ion chains, Phys. Rev. Appl. 19, 014014 (2023)

    2023

  63. [71]

    Pogorelov, T

    I. Pogorelov, T. Feldker, C. D. Marciniak, L. Postler, G. Jacob, O. Krieglsteiner, V. Podlesnic, M. Meth, V. Negnevitsky, M. Stadler, B. H¨ ofer, C. W¨ achter, K. Lakhmanskiy, R. Blatt, P. Schindler, and T. Monz, Compact ion-trap quantum computing demonstrator, PRX Quantum 2, ...

    2021

  64. [72]

    P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, and C. Monroe, Phase control of trapped ion quantum gates, Journal of Optics B: Quantum and Semiclassical Optics 7, S371 (2005)

    2005

  65. [73]

    Gottesman, Fault-tolerant quantum computation with constant overhead, Quantum Info

    D. Gottesman, Fault-tolerant quantum computation with constant overhead, Quantum Info. Comput. 14, 1338–1372 (2014)

    2014

  66. [74]

    N. P. Breuckmann and J. N. Eberhardt, Quantum low- density parity-check codes, PRX Quantum 2, 040101 (2021)

    2021

  67. [75]

    A. G. Fowler, Analytic asymptotic performance of topo- logical codes, Phys. Rev. A 87, 040301 (2013)

    2013

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