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REVIEW 4 major objections 5 minor 28 references

Entanglement teleportation along a regenerating hamster-wheel graph state

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper shows that a two-qubit graph state can be teleported around a ring of qubits again and again, because every measured qubit is reset and re-entangled, so the teleportation distance is no longer capped by the number of physical…

desk verdict A solid, honestly reported demonstration of cyclic graph-state teleportation beyond the device qubit count; the main unquantified risk is the effect of mid-circuit readout errors on the feedforward corrections. read the letter →

arxiv 2411.13060 v3 pith:WZGBPYKT submitted 2024-11-20 quant-ph

Haiyue Kang , John F. Kam , Gary J. Mooney , Lloyd C. L. Hollenberg This is my paper · ORCID
classification quant-ph MSC 81P6881P40 PACS 03.67.-a03.67.Mn
keywords quantumteleportationgraphstatesmeasurement-basedcomputationdynamiccircuitsqubitreuseentanglementnegativityreadouterrormitigationion-trapcomputer
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 claims that quantum teleportation can be made reusable: instead of sending a two-qubit entangled state once along a chain and losing the used qubits, the authors reset and re-entangle every measured qubit, turning a line into a regenerating ring they call a hamster wheel. With this scheme, the teleported state can hop around the ring many times, exceeding the total number of qubits in the hardware. On a 20-qubit ion-trap computer the two-qubit graph state remained entangled after 56 hops, three full revolutions, with a negativity of $0.291 \pm 0.018$, about 58% of the maximum, and the emulator showed entanglement surviving 100 hops. The significance is that teleportation depth becomes a matter of accumulated noise and correction quality rather than device size, which speaks directly to measurement-based quantum computing, where computation proceeds by measuring an entangled resource state.

What carries the argument

The central object is the regenerating ring graph state, a path graph whose measured vertices are reset to $|0\rangle$, restored to $|+\rangle$, and re-entangled with the current receiver via controlled-Z gates so the path reforms in a new cycle. The identity that carries the argument is the accumulated byproduct operator $U_m = H^m Z^{\oplus_{\text{odd}} s_i} X^{\oplus_{\text{even}} s_i}$ on the moving qubit, whose correction requires only the XOR of measurement outcomes, computed by the discriminator. This reduces the correction to a fixed-depth dynamic circuit of at most three gates, independent of hop count, and explains why dynamic correction and post-selection perform almost identically.

What would settle it

A concrete test: inject a known readout error model into the emulator's mid-circuit measurements, for example flip each outcome with probability $p$, and measure the negativity after 56 hops; if a modest $p$ destroys the entanglement, then the demonstrated hop depth rests on unverified mid-circuit readout fidelity.

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Extended reading notes

Core claim

Starting from a two-qubit graph state $|\phi(P_2)\rangle_{0,1}$ entangled with a line of qubits prepared in $|+\rangle$ and linked by controlled-Z gates, the authors teleport the second qubit around the ring by measuring successive qubits in the Pauli-X basis. Each hop leaves the teleported state changed by a local unitary $H^m Z^{s_1\oplus s_3\oplus\cdots} X^{s_2\oplus s_4\oplus\cdots}$ whose exponents are the parities of the measurement outcomes from odd and even hops. After measuring all ring qubits except the axis and receiver, they reset the measured qubits and re-entangle them with the receiver, allowing further hops around the same ring. The local transformation is undone either by a byproduct operator applied through a dynamic circuit conditioned on the mid-circuit outcomes, or by post-selecting on the four possible outcome classes. Using quantum state tomography with readout error mitigation, they report negativity $0.291\pm0.018$ and fidelity $0.791\pm0.018$ after 56 hops on the real device, and negativity $0.224\pm0.009$ after 100 hops on the emulator, showing that entanglement is preserved across more hops than the device has qubits.

Load-bearing premise

Every mid-circuit measurement that decides a correction gate must return the correct classical bit; a single wrong bit applies the wrong correction and leaves an uncorrected error on the teleported state.

Editorial extensions

If this is right

  • Teleportation distance is no longer bounded by the number of physical qubits; any sufficiently low-noise device can in principle teleport a state arbitrarily far by cycling the ring.
  • Dynamic-circuit correction and post-selection give nearly the same entanglement, so the choice between them can be made on latency and shot budget rather than quality.
  • The slow, roughly linear decay of negativity with hops on the emulator implies that noise, not the protocol's structure, sets the hop limit; improving gate fidelity and mid-circuit readout directly extends the reachable depth.
  • The agreement between emulator and real device across the tested range supports using the emulator to predict performance at greater depths, such as beyond 100 hops.
  • The protocol is a direct resource for measurement-based quantum computation, since teleportation along a graph state by X-basis measurements is the basic operation of that model.

Reading between the lines

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

  • If mid-circuit readout errors are the dominant uncorrected error source, as the paper's own mitigation scheme suggests because readout error mitigation is applied only to the final two qubits, then improving intermediate measurement fidelity should raise the hop ceiling more than improving two-qubit gates.
  • The ring-reuse idea could be generalized from a two-qubit graph state to multi-qubit encoded states or to a continuous stream of Bell pairs, effectively converting a fixed hardware register into a renewable entanglement resource for quantum repeaters.
  • The same cycling could implement logical gates by choosing measurement bases adaptively, turning the hamster wheel into a universal measurement-based quantum computing fabric whose depth is limited only by noise.
  • A direct test would be to run the scheme with randomized mid-circuit readout errors injected in the emulator and compare the negativity decay, quantifying how much of the observed decay comes from intermediate measurements rather than two-qubit gates.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a cyclic quantum teleportation protocol, the 'quantum hamster wheel', in which a two-qubit graph state is teleported repeatedly around a ring of qubits by measuring intermediate qubits, resetting them, and re-entangling them for further hops. The protocol is tested on the 20-qubit Quantinuum H1-1 processor and its noise-model emulator, with dynamic-circuit feedforward correction of the byproduct operators. The authors report a real-machine negativity of 0.291 ± 0.018 after 56 hops and an emulator negativity of 0.224 ± 0.009 after 100 hops, and interpret these results as demonstrating entanglement preservation beyond the number of available qubits. The mathematical framework (Eqs. 3-5) is standard stabilizer teleportation and is presented clearly.

Significance. If the experimental claims are fully supported, the paper would provide a concrete demonstration of a reusable, measurement-based teleportation resource that exceeds the physical qubit count of the device, which is a useful step toward measurement-based quantum computation. Strengths of the paper include the clean formulation of the byproduct operator, the use of both dynamic-circuit and post-selection implementations, the availability of source code, and the explicit acknowledgment of several experimental limitations. However, the central quantitative claims rest on experimental data whose error bars omit a potentially dominant error source: uncalibrated mid-circuit readout errors in the dynamic-circuit feedforward. The emulator results also contain a discontinuity from a change in noise-model parameters. These issues must be addressed before the headline numbers can be taken at face value.

major comments (4)
  1. [Results / Figure 3 caption] The dynamic-circuit results are vulnerable to mid-circuit readout errors that are neither calibrated nor mitigated. The Figure 3 caption explicitly states that REM is applied only to the two qubits of the final teleported state, yet the feedforward correction in Eqs. (4)-(5) depends on all mid-circuit measurement outcomes. A single erroneous outcome flips the discriminator parity and applies the wrong byproduct operator, leaving an uncorrected Pauli error on the teleported state. The reported error bars, obtained by bootstrapping the final QST counts, account only for shot noise and exclude this feedforward error channel. The authors should report the device's mid-circuit readout fidelity and either fold it into the uncertainty estimate or provide a real-machine comparison between dynamic circuits and post-selection at the same hop counts to bound the feedforward penalty.
  2. [Eq. (8)] The normalization of the post-selection density matrix is unclear or incorrect as written. If the sum runs over all 2^m measurement outcome strings s, the prefactor 1/2^{m-2} gives a trace of 4 rather than 1. If the sum is intended to run only over outcomes within one discriminator class, that class contains 2^{m-2} strings and the prefactor is correct, but the text does not state this restriction. Since the post-selection negativity and fidelity values are presented as evidence in Figure 3, the definition of the averaged state must be made precise and correct.
  3. [Results / Figure 3] The real-machine data consist of a single trial per hop count (9, 18, and 56 hops), and the error bars are obtained by bootstrapping the 1000-shot QST measurement within that single trial. This quantifies only within-run statistical fluctuations, not run-to-run reproducibility or calibration drift. The claim '0.291 ± 0.018 after 56 hops' should therefore be presented as a single-run result, and at least one repeated run at a given hop count would be needed to assess the reliability of the reported error bars.
  4. [Results / Figure 3 and Discussion] The emulator data show a clear discontinuity at 76 hops, which the authors attribute to a change in noise-model parameters due to a time gap between experiments. The 100-hop negativity of 0.224 ± 0.009 is obtained after this parameter change and lies on a different noise baseline than the earlier hop counts. Consequently, the statement that 'the actual limit of the number of hops ... is far beyond 100' is not supported by a consistent noise-model trend. The authors should either rerun the emulator with a single calibration across all hop counts or explicitly limit the extrapolation claim.
minor comments (5)
  1. [Abstract and Discussion] The abstract says 56 hops is 'three complete revolutions around the hamster wheel,' but with a ring of 19 qubits, three full revolutions would be 57 hops; the equivalence to 56 hops should be explained or corrected.
  2. [Eq. (7)] The fidelity formula contains an unusual notational artifact, '− − − − − →', and the condition 'tr(σ)=1' is used in a confusing way; this should be rewritten cleanly.
  3. [Figure 3 caption] The caption states both that 'All results are mitigated with REM' and that 'REM is applied to only the two qubits of the final teleported state' for the dynamic-circuit approach; this apparent contradiction should be clarified in the main text.
  4. [Figure 4] The y-axis of panel (b) is labeled 'Negativity' but the panel shows fidelity; this should be corrected to 'Fidelity'.
  5. [Data Availability Statement] The text says the code is available in the GitHub repository [29], but the Data Availability Statement says data are available from the corresponding author upon reasonable request; these statements should be reconciled.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the byproduct correction is re-derived from graph-state evolution and all headline quantities are measured, not fitted.

full rationale

The paper's derivation chain is self-contained. The initial state is defined in Eq. (3) as a path graph state built from |+> states and CZ gates, and Eq. (4) is derived (not assumed) by propagating the X-basis measurement outcomes through the graph state; the byproduct operator then follows from this formula. The quantities reported as evidence — negativity 0.291±0.018 at 56 hops and fidelity 0.791±0.018 — are reconstructed from QST measurements on the device with REM, not obtained by plugging fitted parameters back into the model. The emulator data uses a vendor-supplied H1-1 noise model, which is an external input rather than a parameter fit to the paper's own results. Self-citations [6,19-21] supply the earlier protocol and the standard Peres-Horodecki entanglement criterion; [6] is cited for the overall approach and discriminator, but the present paper re-derives the teleportation transformation and checks it against graph-state mathematics, so the self-citation is not load-bearing. No uniqueness theorem from the authors is invoked to force the choice of protocol. The concern that mid-circuit readout errors are unmitigated affects the validity/robustness of the dynamic-circuit results, but it is not a circularity: it is an unquantified noise channel, not an input reused as an output. The central claim therefore does not reduce to its own assumptions.

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

No free parameters were fitted by the authors to produce the central result; the derivation uses standard graph-state formalism and the reported negativity/fidelity are measurements. The H1-1 emulator uses vendor-calibrated noise parameters from the Quantinuum product data sheet, which are external inputs rather than author-fitted values, so they are not counted here.

assumptions (5)
  • standard math X-basis measurement on a qubit of a line graph state teleports the logical information one step along the line, accumulating a Hadamard and Pauli corrections (Raussendorf et al., Ref. [15]; Jozsa, Ref. [13]).
    Invoked in the protocol description and in Eq. (4) for the byproduct operator; this is the standard wire-teleportation property of cluster states.
  • domain assumption Reset gates return measured qubits to a pure |0> state with no residual correlation to the teleported state, so the graph state can be regenerated exactly for the next cycle.
    Used in Step 3 of Figure 1 and in the protocol: 'we reset all measured qubits and re-entangle the teleported two-qubit state with them.' If reset is imperfect, the regenerated graph state would carry noise not captured by the model.
  • domain assumption Mid-circuit measurement outcomes used for feedforward are reliable classical bits; a wrong outcome would apply the wrong byproduct operator and corrupt the teleported state.
    Assumed throughout the dynamic-circuit approach; REM is applied only to the final two qubits (Figure 3 caption), so intermediate readout errors are not mitigated or characterized.
  • domain assumption The Quantinuum H1-1 device and its emulator implement CZ gates, X-basis measurements, resets, and feedforward with fidelities consistent with the product data sheet (Ref. [16]).
    The emulator results (e.g., 0.224 at 100 hops) and the inference that the real device can exceed 100 hops depend on this vendor-provided noise model.
  • standard math Negativity N > 0 is a necessary and sufficient entanglement criterion for two-qubit states, and fidelity against a pure target is tr(ρσ).
    Used in the 'Teleportation quality witnesses' section to justify interpreting the measured negativity as entanglement.

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Pith. "Pith review of Entanglement teleportation along a regenerating hamster-wheel graph state." pith.science (2026). https://pith.science/paper/WZGBPYKT

@misc{pith2026241113060,
  author       = {Pith},
  title        = {Pith review of: Entanglement teleportation along a regenerating hamster-wheel graph state},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WZGBPYKT}},
  note         = {Machine review of arXiv:2411.13060}
}
abstract

We scheme an efficient and reusable approach to quantum teleportation that allows cyclic teleportation of a two-qubit graph state around a quantum hamster wheel -- a ring of qubits entangled as a one-dimensional line prepared on the 20-qubit Quantinuum H1-1 ion-trap quantum processor. The qubits on the ring are periodically measured and reused to achieve a teleportation depth that exceeds the total number of available qubits in the quantum processor. Using the outcomes measured during teleportation, we calculate and apply byproduct operators through dynamic circuits to correct local transformations induced on the teleported state. We evaluate the quality of teleportation by tracing the preserved entanglement and fidelity of the teleported two-qubit graph state from its density matrix. In the real-machine experiments, we demonstrate that 58% of the teleported state's entanglement is sustained with a measured two-qubit negativity of $0.291\pm0.018$ after three complete revolutions around the hamster wheel, or equivalently, after hopping across 56 qubits. On the machine-specific noisy emulator, we found that the teleported state after 100 hops still sustained 45% of its entanglement. By performing teleportation along a regenerating graph state, our work is a step forward in demonstrating the feasibility of measurement-based quantum computation.

Figures

Figures reproduced from arXiv: 2411.13060 by the authors.

Figure 1
Figure 1. FIG. 1. The evolution of a general quantum hamster wheel consisting of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Overall workflow of the quantum hamster wheel. Initially, the two-qubit graph state [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Polar plots of the teleported two-qubit graph state showing [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The same [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 14 canonical work pages

  1. [1]

    C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky- Rosen channels, Phys. Rev. Lett.70, 1895 (1993)

    1993

  2. [2]

    Bouwmeester, J.-W

    D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. We- infurter, and A. Zeilinger, Experimental quantum tele- portation, Nature 390, 575 (1997)

    1997

  3. [3]

    Y.-H. Kim, S. P. Kulik, and Y. Shih, Quantum telepor- tation of a polarization state with a complete Bell state measurement, Phys. Rev. Lett.86, 1370 (2001)

    work page 2001

  4. [4]

    Olmschenk, D

    S. Olmschenk, D. Matsukevich, P. Maunz, D. Hayes, L.- M. Duan, and C. Monroe, Quantum teleportation be- tween distant matter qubits, Science323, 486 (2009)

    work page 2009

  5. [5]

    Hermans, M

    S. Hermans, M. Pompili, H. Beukers, S. Baier, J. Borre- gaard, and R. Hanson, Qubit teleportation between non- neighbouring nodes in a quantum network, Nature605, 663 (2022)

    2022

  6. [6]

    H. Kang, J. F. Kam, G. J. Mooney, and L. C. Hollenberg, Teleporting two-qubit entanglement across 19 qubits on a superconducting quantum computer, Phys. Rev. Applied 23, 014057 (2025)

    work page 2025

  7. [7]

    C. H. Bennett and S. J. Wiesner, Communication via one-and two-particle operators on Einstein-Podolsky- Rosen states, Phys. Rev. Lett.69, 2881 (1992)

    work page 1992

  8. [9]

    Yokoyama, R

    S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphat- phong, T. Kaji, S. Suzuki, J.-i. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, Ultra-large-scale continuous-variable cluster states multiplexed in the time domain, Nature Photonics7, 982 (2013)

    2013

Show all 28 references
  1. [10]

    Beverland, V

    M. Beverland, V. Kliuchnikov, and E. Schoute, Surface code compilation via edge-disjoint paths, PRX Quantum 3, 020342 (2022)

    2022

  2. [11]

    Bäumer, V

    E. Bäumer, V. Tripathi, D. S. Wang, P. Rall, E. H. Chen, S. Majumder, A. Seif, and Z. K. Minev, Efficient long- range entanglement using dynamic circuits, PRX Quan- tum 5, 030339 (2024)

    2024

  3. [12]

    S. Bose, V. Vedral, and P. L. Knight, Multiparticle gen- eralization of entanglement swapping, Phys. Rev. A57, 822 (1998)

    1998

  4. [13]

    Jozsa, An introduction to measurement based quan- tum computation, NATO Science Series, III: Computer and Systems Sciences

    R. Jozsa, An introduction to measurement based quan- tum computation, NATO Science Series, III: Computer and Systems Sciences. Quantum Information Processing- From Theory to Experiment199, 137 (2006)

    2006

  5. [14]

    Van den Nest, Measurement-based quantum compu- tation, Nature Physics5, 19 (2009)

    H.J.Briegel, D.E.Browne, W.Dür, R.Raussendorf,and M. Van den Nest, Measurement-based quantum compu- tation, Nature Physics5, 19 (2009)

    2009

  6. [15]

    Raussendorf, D

    R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A68, 022312 (2003)

    2003

  7. [16]

    Quantinuum system model H1 product data sheet

  8. [17]

    Wang, X.-T

    K. Wang, X.-T. Yu, S.-L. Lu, and Y.-X. Gong, Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation, Phys. Rev. A89, 022329 (2014)

    2014

  9. [18]

    Shapourian, K

    H. Shapourian, K. Shiozaki, and S. Ryu, Partial time- reversal transformation and entanglement negativity in fermionic systems, Phys. Rev. B95, 165101 (2017)

    2017

  10. [19]

    J. F. Kam, H. Kang, C. D. Hill, G. J. Mooney, and L. C. Hollenberg, Characterization of entanglement on superconducting quantum computers of up to 414 qubits, Phys. Rev. Res.6, 033155 (2024)

    2024

  11. [20]

    G. J. Mooney, G. A. White, C. D. Hill, and L. C. Hollen- berg, Whole-device entanglement in a 65-qubit supercon- ducting quantum computer, Advanced Quantum Tech- nologies 4, 2100061 (2021)

    2021

  12. [21]

    G. J. Mooney, C. D. Hill, and L. C. Hollenberg, Entangle- ment in a 20-qubit superconducting quantum computer, Scientific reports 9, 13465 (2019)

    2019

  13. [22]

    Jozsa, Fidelity for mixed quantum states, Journal of modern optics 41, 2315 (1994)

    R. Jozsa, Fidelity for mixed quantum states, Journal of modern optics 41, 2315 (1994)

    1994

  14. [23]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information (Cambridge University Press, 2022)

    2022

  15. [24]

    P. D. Nation, H. Kang, N. Sundaresan, and J. M. Gambetta, Scalable mitigation of measurement errors on quantum computers, PRX Quantum2, 040326 (2021)

    2021

  16. [25]

    Michelot, A finite algorithm for finding the projection of a point onto the canonical simplex ofRn, Journal of Optimization Theory and Applications50, 195 (1986)

    C. Michelot, A finite algorithm for finding the projection of a point onto the canonical simplex ofRn, Journal of Optimization Theory and Applications50, 195 (1986)

    1986

  17. [26]

    B. Yang, R. Raymond, and S. Uno, Efficient quantum readout-error mitigation for sparse measurement out- comes of near-term quantum devices, Phys. Rev. A106, 012423 (2022)

    2022

  18. [27]

    G. J. Mooney, G. A. White, C. D. Hill, and L. C. Hollenberg, Generation and verification of 27-qubit Greenberger-Horne-Zeilinger states in a superconducting quantum computer, Journal of Physics Communications 5, 095004 (2021)

    2021

  19. [28]

    J. A. Smolin, J. M. Gambetta, and G. Smith, Efficient method for computing the maximum-likelihood quantum 7 state from measurements with additive Gaussian noise, Phys. Rev. Lett.108, 070502 (2012)

    2012

  20. [29]

    Kang and J

    H. Kang and J. F. Kam, teleportation_code_IBM, https://github.com/KangHaiYue/Quantum_hamster_ wheel (2024). END MA TTER We include two supplementary plots which describe the same information as in Figure 3 but plotted in regular axes layout. (a) Negativity 0 5 10 15 20 25 30 3...

    2024

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