Snakes on a Plane: mobile, low dimensional logical qubits on a 2D surface

Adam Siegel; Armands Strikis; Balint Koczor; Hamza Jnane; Shaun Pexton; Simon Benjamin; Zhenyu Cai

REVIEW 3 major objections 5 minor 2 cited by

Snakes on a Plane: mobile, low dimensional logical qubits on a 2D surface

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Mobile logical qubits can be shuttled across a planar chip, with any scratch from a static defect detected and reversed so that defect-induced logical errors stay below ordinary circuit noise.

desk verdict A genuinely new mobile-logical-qubit architecture with a clever rollback protocol; the headline noise-tolerance claim outruns the evidence but the core idea deserves serious refereeing. read the letter →

arxiv 2501.02120 v1 pith:GHP4VRAS submitted 2025-01-03 quant-ph

Adam Siegel , Zhenyu Cai , Hamza Jnane , Balint Koczor , Shaun Pexton , Armands Strikis , Simon Benjamin This is my paper · ORCID

classification quant-ph PACS 03.67.Pp03.67.Lx

keywords logicalqubitshuttlingsiliconspinqubitssurfacecodechargenoisemonitorcomplementarygapsnakesurgerylattice

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 proposes a quantum computing architecture in which a logical qubit is a one-dimensional 'snake' of physical qubits that can be shuttled over a planar latticework of 2xN rails. Its central claim is that the danger everyone expects from shuttling—a static charge defect 'scratching' the whole logical qubit with a correlated phase error—can be neutralised: monitor qubits and the syndrome's complementary gap flag likely scratches, and a lattice-surgery procedure called snake surgery splits the snake into a static tail and a travelling head, so that on suspicion the head is measured out and the logical state is recovered intact at the tail. The combination brings the defect-induced logical error rate down to or below the normal circuit-level logical error rate of the surface code, expressed as $\int_0^\pi P(\omega)p_{\mathrm{both}}(\omega)\,d\omega \le P_L$. If correct, this makes mobile logical qubits a practical route to high connectivity, rerouting around damage, and fast transversal gates in shuttling-based devices such as silicon spin qubits.

What carries the argument

Snake surgery is the central mechanism: a logical snake is doubled in length via XX lattice surgery, then split into an entangled head and tail; the tail stays put under continuous stabilisation while only the head is shuttled, so a suspected scratch can be reversed by measuring the head in the Z basis and teleporting the logical information back to the tail. Two detectors feed the decision. Monitor qubits, one per data qubit, are prepared in $|+\rangle$, shuttled with the snake, and measured in $X$, giving a rotation-angle estimator that saturates the Cramér–Rao bound and flags angles above $\omega_{\max} = 0.3$. The complementary gap—the length difference between the shortest error strings consistent with the measured syndrome but implying opposite logical outcomes—is computed from stabiliser measurements and used to reject low-gap shuttles, which sharpens the decoder's confidence as well as detecting defects. Together they filter the defect-angle distribution so strongly that the product $P(\omega)p_{\mathrm{both}}(\omega)$ integrates below the normal logical error rate.

What would settle it

Deliberately place a known local defect on a shuttling link, run a distance-5 snake through it with the full monitor-plus-complementary-gap protocol, and compare the measured logical error rate per d stabiliser cycles with $P_L + \rho\int_0^\pi P(\omega)p_{\mathrm{both}}(\omega)\,d\omega$; exceeding this by more than simulation error falsifies Eq. (14). A more basic test is to shuttle a probe qubit past a real charge defect and perform process tomography: if the channel is not of the form $U(\omega)^{\otimes N}$ with the same rotation on every qubit, the snake surgery recovery is not exact.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the worst-case shuttling hazard—an arbitrary, sudden Z phase rotation applied to every data qubit as a snake passes a pin defect—does not cause a logical error, because it can be detected and undone. The key sequence is: grow the snake to double length with an XX lattice surgery, split it into two entangled halves, leave the tail stabilised in place, shuttle only the head, and at the end assess the route. A clean assessment lets the tail be measured out, projecting the state onto the head; a suspicious one has the head measured out, projecting the state back onto the tail. Since the assumed defect channel is entirely Z, the head measurement commutes with the corruption, so the tail is restored no matter how large the phase angle was. With one monitor qubit per data qubit and a complementary-gap post-selection rule $g \ge (d+1)/2$, the paper computes that the resulting defect-induced logical error contribution satisfies $\int_0^\pi P(\omega)p_{\mathrm{both}}(\omega)\,d\omega \le P_L$ for the distances simulated, meaning defects are no worse than the ordinary circuit noise the surface code already handles.

Load-bearing premise

The reversion step only works if a scratch is a pure Z phase rotation with the same angle on every data qubit that passes the defect; any leakage, spin-flip, orbital-excitation, or relaxation component breaks the head-measurement recovery.

Editorial extensions

If this is right

Long-range shuttling of a logical qubit becomes fault-tolerant: the error rate accumulated while moving a snake across the chip is dominated by the usual circuit-level noise, not by the defects it passes.
All-to-all connectivity at the logical level follows from free movement over the latticework; even with up to 50% of interaction edges deactivated, a spanning route remains, so defective links can be bypassed.
Logical CNOTs can be applied transversally at interaction edges, and semi-transversal batching lets the user trade speed against shuttling noise.
A singlet–triplet encoding suppresses slow g-factor-fluctuation noise during shuttling, so the remaining dominant hazard is the rare catastrophic scratch that snake surgery targets.
If the defect rate is low, a multi-headed 'hydra' snake can send heads along several routes and use the first clean arrival, or exploit the shared entanglement for quantum fan-out.

Reading between the lines

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

The pure-Z assumption is the boundary of the protocol: if real defects produce X errors, leakage, orbital excitation, or relaxation, the head measurement no longer cleanly restores the tail, so the architecture's viability hinges on device-physics measurements of the defect channel, not on the coding theory alone.
The detection scheme's cost is a 5–10% shuttle rejection rate; an adaptive threshold for the complementary gap that tracks the actual background error rate p could lower this overhead without losing sensitivity.
Because the monitor qubits use separable states and saturate the Cramér–Rao bound, entangled probe states such as squeezed Dicke states could improve angle estimation by a constant factor in regimes where state-preparation noise is low, an option the paper notes but does not adopt.
The hydra extension implies circuit-level optimisations beyond rerouting: the entangled multi-head state is a resource for quantum fan-out circuits, which could shorten depth in distillation or data-loading routines if shuttling routes are plentiful.

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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

Here's my read of the snakes paper. The core idea is genuinely new and worth engaging with: instead of the looped-pipeline static logical qubits, they make the logical qubit a 1D train ('snake') that can move across a 2D latticework. The 'snake surgery' trick—growing the snake, splitting off a head that does the risky shuttling while the tail is stabilised, then measuring out either head or tail depending on whether a defect was flagged—is clever, and the conditional-independence decomposition of the two detection filters (monitor qubits, complementary gap) is clean. The semi-transversal gate scheme is a nice practical answer to the O(d^2) shuttling cost of a fully transversal CNOT. This is a real contribution to the silicon-spin shuttling literature.

The soft spots are real but manageable. First, the central quantitative claim—Eq. (14) and the Discussion's 'any code distance'—is stated more broadly than the evidence. The protocol only reverses errors that are diagonal in the computational basis. The paper says this itself: Section III A allows for orbital excitations and spin-flip terms, and Section III C conditions the whole reversion on pure Z errors. But then Eq. (14) drops the condition. If a real defect produces even a small X component or leakage on the head, the head measurement doesn't project the tail back to the uncorrupted state. That's an unvalidated device-physics assumption. A charge defect in silicon could plausibly be mostly Z-like, but 'plausibly' is not shown, and the paper gives no experimental evidence for the common-mode pure-Z model.

Second, Eq. (14) is evaluated for d ≤ 13 with Gaussian and linear extrapolations, no error bars, and the claim that the trend 'suggests' it holds for any d. That's a reasonable conjecture, not a proven result. The honest fix is to release the simulation code/data, add error bars, or rescope the claim to the simulated distances.

The paper is nevertheless a solid architecture proposal. The authors are explicit about most assumptions, the QEC simulations are standard MWPM, and the defect-tolerance logic is internally coherent once you accept the pure-Z model. The mismatch between that caveat and the headline claim is what needs fixing.

Who is this for? Anyone working on shuttling-based silicon architectures or defect-tolerant layout designs. It deserves a serious referee. I'd send it out, and ask for code/data and a more careful statement of the pure-Z scope.

Referee Report

3 major / 5 minor

Summary. The paper proposes an architecture, 'snakes on a plane', in which logical qubits are 1D strings of data qubits that shuttle across a planar latticework of 2×N filaments. The authors argue that silicon-spin qubits support fast high-fidelity shuttling, and that the architecture provides all-to-all logical connectivity, damage-tolerant routing, and efficient transversal gates. To protect against static charge defects that 'scratch' a passing logical qubit, they introduce a detection-and-reversal protocol ('snake surgery'): monitor qubits and a complementary-gap filter infer whether a defect was encountered, and if so, a head-tail split is measured out so that the logical information returns to a stationary tail. They claim that, for purely Z-type scratches of arbitrary strength, the defect-induced logical error rate is bounded by the normal circuit-level logical error rate, expressed as Eq. (14), and that this holds 'for any code distance'. They support this with QEC simulations up to distance 13 under circuit-level noise, Gaussian and linear-log extrapolations, and a Cramér-Rao-optimal monitor-qubit metrology analysis. The paper also develops a semi-transversal CNOT protocol and discusses percolation-based connectivity in the presence of defective links.

Significance. If the central claims hold, the paper makes a substantial architectural contribution: it offers a concrete, experimentally grounded route to mobile logical qubits in silicon spin devices, with an appealing combination of logical-level connectivity, damage tolerance, and efficient gates. The QEC simulations are standard and the monitor-qubit analysis is a genuine strength: the estimation strategy saturates the Cramér-Rao bound, and the robustness analysis against dephasing and readout noise is explicit. The independent surface-code threshold calculation for defect-induced dephasing is a useful quantitative anchor. However, the strongest quantitative claim—Eq. (14) and the 'any code distance' statement—is limited by two load-bearing issues: the pure-Z assumption on the scratch channel, which is acknowledged but not validated physically, and the reliance on low-distance simulations with extrapolations and no reported error bars. The significance is therefore conditional: the architecture and protocols are valuable, but the headline defect-tolerance claim needs qualification or further support.

major comments (3)

[§III.C, §III.F, Eq. (14)] The central quantitative claim, Eq. (14), is stated without the condition under which snake surgery provably works. The recovery step measures the head in the Z basis, and this only commutes with errors that are diagonal in the computational basis. Section III.A itself notes that a sudden scratch 'could lead to orbital excitations, and thus to dephasing due to the difference in g-factor between the orbital states,' and Section III.C explicitly conditions the reversion on 'provided they are pure Z errors.' The Discussion repeats this caveat, yet Eq. (14) and the surrounding text in Section III.F do not carry it, and the Discussion asserts tolerance 'for any code distance' without qualification. If a real defect produces any X-type error, leakage, non-unitary relaxation, or a phase that is not identical on every shuttled qubit, the head measurement does not project the tail back to the uncorrupted state, and the defect-induced term in Eq. (12) is underestimated. This is not an algebraic error in the protocol, but it is a load-bearing physical assumption that must either be justified by a device-physics model or explicitly carried through every quantitative claim, including Eq. (14).
[§III.F, Figs. 13–14, Eq. (14)] The claim that Eq. (14) holds 'for any code distance' is an extrapolation from simulations up to d=13. The left panel of Fig. 13 uses Gaussian extrapolation for the tails of pgap(ω), and the right panel uses linear regressions (in log scale) for P(ω); Fig. 14 is then computed from these extrapolations. No error bars or confidence intervals are reported for the extrapolated curves or for the integrals in Eq. (14). The observation that the ratio decreases with d is suggestive, but it is not a proof of the asymptotic statement. I ask the authors to either soften the 'any code distance' claim to a statement about the simulated range with extrapolation, or to provide a rigorous argument (or substantially larger-distance data with quantified extrapolation error) that the inequality persists for all d.
[§III.D, Appendix F, Eq. (13)] The monitor-qubit detection scheme assumes that the scratch channel is a single common-mode Z rotation applied identically to every monitor qubit and data qubit that passes the defect. The paper does not analyze the case where the magnitude or sign of ω varies across the shuttled qubits, or where the phase is accompanied by a small stochastic Z component. Such spatial variation would affect both the monitor distribution pmon(ω) and the logical error probability P(ω), and the conditional-independence factorization in Eq. (13) would need to be re-examined because the same physical defect would then couple the two detection channels in a more complex way. I request that the authors state the common-mode assumption explicitly and discuss how spatial variation would modify the claimed bound.

minor comments (5)

[Abstract and §III.E] The abstract uses 'complimentary gap'; this should be 'complementary gap' to match the terminology in Section III.E.
[Introduction, §II] The introduction contains 'flexility' where 'flexibility' is intended, and the caption of Fig. 1 contains 'SW AP' with an internal space; these should be corrected.
[§III.C, Eq. (7)] In Step 2, the notation 'XLXL' is used without first defining XL for the doubled snake; please clarify whether this is the logical X operator on the full 2d×d code and how the sign of the measurement outcome enters Eq. (7).
[§III.D and Appendix F] In the estimator description below Eq. (F20), 'arctan2' is used without specifying the branch or the convention for ω∈[−π,π]; please state the branch so the estimator is unambiguous.
[Fig. 13 caption] The left panel lists distances d=3,7,11,15 while the right panel plots data for distances that are not enumerated in the caption; please list the distances and symbols used in the right panel.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the defect-tolerance estimate Eq. (14) is assembled from independent Monte Carlo simulations, an explicit estimator derivation, and a justified conditional-independence factorization, rather than reducing to its own inputs.

full rationale

The paper's central derivation chain is not circular. Snake surgery (Section III C) is a direct quantum-information identity: because the assumed defect channel D_phi is diagonal in the Z basis, measuring the head in the Z basis commutes with it, so the tail is restored by construction; this is an algebraic fact, not a fitted result. The monitor-qubit performance is derived from explicit binomial likelihood functions in Appendix F, including Cramer-Rao bounds and a stated noise model, and the complementary-gap post-selection and P(omega) are obtained from surface-code Monte Carlo simulations described in Appendices D, E, and G. Equation (13) is justified by the stated non-entanglement of monitor qubits with data and ancilla qubits, giving conditional independence given omega. Equation (14) is then a computed integral of independently simulated factors; the target P_L is the ordinary circuit-level logical error rate, not a parameter fitted to force the inequality. The paper does rely on the authors' prior 2xN-array work [8] for the underlying layout and shuttling noise assumptions, and it explicitly assumes pure-Z defect errors, but these are architectural and physical assumptions rather than circular reductions of the claimed result. The extrapolation to 'any code distance' is an extrapolation, not a self-justification, and the pure-Z caveat is repeatedly stated rather than hidden.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

No new physical entities are proposed; 'snakes', 'head/tail', and 'hydra' are organizational labels for logical qubits and their split parts. The 'pin defect' is an assumed environmental object, not a new theoretical entity. The ledger focuses on the modeling assumptions and chosen parameters that the central claim rests on.

free parameters (7)

omega_max (tolerable defect angle) = 0.3 rad = omega_th/2; omega_th = 0.62 from threshold simulation
Maximum phase rotation a snake can tolerate without a sharp logical error increase; set from the authors' surface-code threshold simulation (Appendix E), controls the monitor-qubit rejection threshold and the false-negative calculation.
omega_hat_max (monitor detection threshold) = 0.075 rad = omega_max/4
Detection threshold for monitor qubits; chosen to give about 5% false-positive rate (Appendix F); affects pmon and the 5-10% restart overhead.
gmin (complementary-gap threshold) = (d+1)/2
Complementary-gap selection rule; chosen so that fewer than 5% of defect-free links are rejected under p=0.1% circuit noise (Appendix G).
lambda (monitor noise strength) = 0.2% (0.1% dephasing plus 0.1% readout)
Assumed monitor-qubit noise level; enters the estimator distributions pmon and the claimed near-saturation of the Cramer-Rao bound.
p (circuit-level noise) = 0.1% per operation
Circuit-level depolarizing noise for gates, initialization, and measurement; controls threshold omega_th, P(omega), and the target logical error rate P_L; taken from silicon spin gate demonstrations.
rho (defect rate) = not fixed; assumed much smaller than 5-10%
Variable in the final error-rate formula; the proof that rerouting does not accumulate errors requires rho small enough that false positives dominate (Section III F).
N_monitor = d^2 (one monitor qubit per data qubit)
Design choice; for d=30, N=900 gives false-negative probability P_m = 1.4e-8 in the monitor-qubit task (Appendix F).

assumptions (8)

ad hoc to paper Defect-induced scratches are pure Z phase rotations applied to every data qubit and monitor qubit that passes near the defect; there are no X errors, leakage, or orbital excitations.
Section III A and III C: snake surgery works 'provided they are pure Z errors'; no microscopic derivation is given.
domain assumption Defect rate rho is low enough that at most one defect occurs per shuttling event and most defect declarations are false positives.
Section III F: 'we did assume a low rate of defects, such that two defects would not occur during the same shuttling event'; used to separate P(log|R1) from undetected-defect terms in Appendix H.
domain assumption Monitor qubits see the same phase channel as data qubits at the same location, so their measurements reveal the Z rotation that the snake experienced.
Implicit in Section III D: monitor qubits are interlaced with data qubits and modeled by the same channel Phi; if the defect field differs on the monitor track, detection fails.
domain assumption The Ornstein-Uhlenbeck sheet model of Ref. [47] describes the slowly fluctuating magnetic-field landscape during shuttling.
Section III B adopts the model 'for the sake of simplicity' and leaves charge noise and valley effects for future work; the ST-vs-LD comparison and dephasing estimates rest on it.
standard math A coherent Z rotation of angle omega can be twirled into a dephasing channel with rate q = sin^2(omega/2).
Used in Appendix E to turn arbitrary phase defects into the dephasing channel simulated for threshold and P(omega); relies on randomized compiling [51].
domain assumption Shuttling noise on long, defect-free paths is negligible compared with gate noise.
Carried from Ref. [8] and used throughout (Appendix D); the head is shuttled for O(d^2) increments without stabilizer measurements, so this assumption is load-bearing.
domain assumption The monitor-qubit and complementary-gap detection outcomes are conditionally independent given the defect angle omega.
Used in Eq. (13) to factor pboth(omega)=pmon(omega)pgap(omega); plausible because monitors are never entangled with data qubits, but the data errors and monitor outcomes both derive from the same omega and could share device noise.
standard math Lattice surgery operations for snake growth and splitting are fault-tolerant and have the same logical error rate as d rounds of static surface-code stabilizer measurement.
The paper invokes lattice surgery [48] for Steps 1-2 of snake surgery; this is standard QEC theory, not proven in the paper.

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Cite this review

Pith. "Pith review of Snakes on a Plane: mobile, low dimensional logical qubits on a 2D surface." pith.science (2026). https://pith.science/paper/GHP4VRAS

@misc{pith2026250102120,
  author       = {Pith},
  title        = {Pith review of: Snakes on a Plane: mobile, low dimensional logical qubits on a 2D surface},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GHP4VRAS}},
  note         = {Machine review of arXiv:2501.02120}
}

read the original abstract

Recent demonstrations indicate that silicon-spin QPUs will be able to shuttle physical qubits rapidly and with high fidelity - a desirable feature for maximising logical connectivity, supporting new codes, and routing around damage. However it may seem that shuttling at the logical level is unwise: static defects in the device may 'scratch' a logical qubit as it passes, causing correlated errors to which the code is highly vulnerable. Here we explore an architecture where logical qubits are 1D strings ('snakes') which can be moved freely over a planar latticework. Possible scratch events are inferred via monitor qubits and the complimentary gap; if deemed a risk, remarkably the shuttle process can be undone in a way that negates any corruption. Interaction between logical snakes is facilitated by a semi-transversal method. We obtain encouraging estimates for the tolerable levels of shuttling-related imperfections.

Figures

Figures reproduced from arXiv: 2501.02120 by the authors.

**Figure 1.** FIG. 1. Two paradigms for fault tolerant QC in a 2D latticework, exploiting shuttling of physical along linear arrays (black [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** FIG. 2. Representation of the 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Two-way mapping for the rotated surface code. Left: [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (17 more)

**Figure 4.** Figure 4: FIG. 4. An example layout for the snakes on a plane architecture. Each edge is a 2 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Stabiliser measurements while shuttling a snake. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. Representation of a junction. Red arrows show the [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 8.** Figure 8: FIG. 8. Dephasing error as a function of the shuttling speed [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

**Figure 9.** Figure 9: FIG. 9. Snake surgery protocol. During long shuttles, snakes [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 10.** Figure 10: FIG. 10. Detailed steps of the snake surgery protocol. ( [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

**Figure 11.** Figure 11: FIG. 11. Schematic representation of the monitor-qubit-based [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]

**Figure 12.** Figure 12: FIG. 12. Performance of the monitor qubits for the two tasks detailed in the main text. [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

**Figure 13.** Figure 13: FIG. 13. Performance of the complementary-gap-based detection scheme for various code distances [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]

**Figure 14.** Figure 14: FIG. 14. Probability that a defect of angle [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]

**Figure 15.** Figure 15: FIG. 15. Implementation of a Hadamard gate via gate tele [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]

**Figure 16.** Figure 16: FIG. 16. Semi-transversal [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]

**Figure 17.** Figure 17: FIG. 17. Hexagonal lattice using three-way junctions. [PITH_FULL_IMAGE:figures/full_fig_p020_17.png]

**Figure 18.** Figure 18: FIG. 18. Rectangular lattice using four-way junctions. [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]

**Figure 21.** Figure 21: FIG. 21. Defect-induced error threshold. Ancilla and data [PITH_FULL_IMAGE:figures/full_fig_p022_21.png]

**Figure 22.** Figure 22: FIG. 22. Probability of a false positive, [PITH_FULL_IMAGE:figures/full_fig_p024_22.png]

**Figure 23.** Figure 23: FIG. 23. Rejection rate corresponding to the selection rule [PITH_FULL_IMAGE:figures/full_fig_p025_23.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A route to damage tolerance exceeding $10\%$ in shuttling-equipped quantum processors
quant-ph 2026-07 conditional novelty 6.0 of 10

Shuttling-based spin-qubit surface codes retain roughly half their effective code distance at 10% hardware damage, so oversizing by ~2x can compensate.
Spin-orbit-enabled realization of arbitrary two-qubit gates on moving spins
cond-mat.mes-hall 2025-08 unverdicted novelty 5.0 of 10

Spin-orbit coupling during shuttling of two spin qubits can realize any two-qubit gate in one step.

Reference graph

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In such a scenario the channel Φ(·) = U (·)U † is unitary and acts on each qubit as a Z rotation gate by an unknown angle as U = e−iωZ/2

Parameter estimation task A dominant source of error in spin qubits is the fluctua- tion of the internal Rabi frequency of the qubits by a vari- able amount ω via the Hamiltonian as H = ωZ/2, where Z is the Pauli Z operator. In such a scenario the channel Φ(·) = U (·)U † is un...
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The first one is detecting with maximum probability if a defect occurred, regard- less of the value of its angle

T ask (i): defect detection After explaining the generalities of monitor qubits, we can now delve into the implementation of the two tasks monitor qubits are utilised for. The first one is detecting with maximum probability if a defect occurred, regard- less of the value of it...
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the precise evalua- tion of the angle ω

T ask (ii): estimating large rotation angles We now focus on task ( ii), i.e. the precise evalua- tion of the angle ω. For this purpose, we devise an es- timator that can accurately approximate ω in the full range ( −π, π), such that we are optimally sensitive to the angles 0 ...
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For this reason, we estimate resource requirements for esti- mating whether the purity of the shuttled qubits remains nearly pure

T est non-unitarity by estimating purity Unitary rotations can be estimated and then corrected by inverse rotations, however, significant non-unitary noise above threshold can potentially be detrimental. For this reason, we estimate resource requirements for esti- mating wheth...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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Task (i): defect detection For task (i), we first define ωmax as the maximum value of ω a logical snake can tolerate when it is shuttled near a defect, without inducing a dramatic increase of the log- ical error rate. We set ωmax = ωth/2, where ωth = 9% is the error correction threshold for such a scenario (as- suming circuit-level noise of strength p = 0...

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