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arxiv: 2604.11145 · v1 · submitted 2026-04-13 · 🪐 quant-ph · physics.atom-ph· physics.optics

Autonomous Quantum Error Correction of Spin-Oscillator Hybrid Qubits

Sungjoo Cho , Ju-yeon Gyhm , Hyukjoon Kwon , Hyunseok Jeong This is my paper

Pith reviewed 2026-05-10 15:51 UTC · model grok-4.3

classification 🪐 quant-ph physics.atom-phphysics.optics
keywords autonomous quantum error correctionspin-oscillator hybrid qubitsengineered Lindbladianmeasurement-free stabilizationdissipation engineeringtrapped ionscode space attractornoise-biased qubits
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The pith

Engineered dissipation turns the code space into a stable attractor for spin-oscillator hybrid qubits.

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

The paper proposes a measurement-free autonomous quantum error correction scheme for a hybrid qubit formed by a spin coupled to an oscillator. It engineers a Lindbladian that couples the storage mode to a rapidly cooled bath, making the logical code space an attractive steady-state subspace. This is done through a controlled beam-splitter interaction combined with spin-dependent displacement. A reader would care because the method avoids active syndrome measurements and feedforward control while using couplings already demonstrated in trapped-ion experiments, offering a simpler path to hardware-efficient protected qubits.

Core claim

The central claim is that an engineered Lindbladian, realized by coupling the storage mode to a rapidly cooled bath through controlled beam-splitter and spin-dependent displacement interactions, renders the code space an attractive steady-state subspace. This continuous-variable–discrete-variable hybrid construction preserves the hardware efficiency of dissipation engineering while simplifying the required system-bath coupling and remaining compatible with simple logical gates.

What carries the argument

Engineered Lindbladian created by controlled beam-splitter and spin-dependent displacement interactions that couple the hybrid system to a cooled bath.

If this is right

  • The scheme enables noise-biased logical qubits without repeated syndrome measurements or feedforward.
  • It is compatible with simple logical gates on the hybrid system.
  • The approach leverages primitives already shown in trapped-ion systems.
  • It offers hardware efficiency comparable to conventional dissipation engineering but with simpler couplings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could lower experimental overhead in near-term quantum processors by removing the need for fast classical control loops.
  • Similar bath-coupling constructions might apply to other hybrid systems, such as superconducting circuits with mechanical resonators.
  • Testing the steady-state fidelity under realistic noise in current ion traps would provide a direct check on whether the attractor property survives.

Load-bearing premise

The controlled beam-splitter and spin-dependent displacement couplings can be realized with high precision and without introducing uncontrolled decoherence.

What would settle it

Applying the proposed couplings in a trapped-ion platform and finding that the system fails to relax into the code space or that logical error rates do not decrease would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.11145 by Hyukjoon Kwon, Hyunseok Jeong, Ju-yeon Gyhm, Sungjoo Cho.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Probability decay rate Γ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Logical (a) bit error rates and (b) phase error rates o [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The error probabilities per single error correction [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) QCRB of the probe state [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Approximate Markov diagram of states up to excita [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We propose a novel measurement-free scheme for stabilizing a spin-oscillator hybrid qubit via autonomous quantum error correction. The engineered Lindbladian renders the code space into an attractive steady-state subspace, realized by coupling the storage mode to a rapidly cooled bath through a controlled beam-splitter and spin-dependent displacement interactions. The continuous variable-discrete variable hybrid approach to autonomous quantum error correction preserves the hardware efficiency of conventional dissipation engineering while simplifying the required system-bath coupling. The construction is compatible with simple logical gates and leverages primitives already demonstrated in experimental platforms, such as trapped-ion systems, suggesting a practical route to hardware-efficient, noise-biased logical qubits without repeated syndrome measurements and feedforward.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a measurement-free autonomous quantum error correction scheme for spin-oscillator hybrid qubits. An engineered Lindbladian is constructed by coupling the storage oscillator to a rapidly cooled bath via a controlled beam-splitter interaction and spin-dependent displacement terms; the resulting dissipators are asserted to render the logical code space an attractive steady-state subspace. The approach is presented as hardware-efficient, compatible with simple logical gates, and realizable with demonstrated primitives in trapped-ion platforms.

Significance. If the effective master equation and its spectral properties hold, the construction would offer a practical, measurement-free route to noise-biased logical qubits that preserves the hardware simplicity of dissipation engineering while avoiding repeated syndrome extraction. The use of standard quantum-optics primitives and compatibility with existing experimental platforms constitute genuine strengths of the proposal.

major comments (3)
  1. [Abstract, §2] Abstract and §2: The central claim that the controlled beam-splitter plus spin-dependent displacement interactions produce dissipators whose unique attractive steady state is exactly the code space is not supported by any explicit derivation of the Lindblad operators, adiabatic elimination, or Born-Markov steps. Without these, it is impossible to verify that the generator has the required kernel and spectral gap.
  2. [§3] §3: The attractiveness of the code space is asserted to follow from the engineered Lindbladian, yet no proof or numerical diagonalization of the resulting superoperator is provided to confirm uniqueness of the steady state or absence of leakage fixed points under realistic parameter regimes.
  3. [§4] §4: The discussion of experimental feasibility in trapped-ion systems assumes that the required system-bath couplings can be realized with sufficient precision and without introducing uncontrolled decoherence channels; no quantitative error-budget analysis or fidelity estimates under finite cooling rates are given.
minor comments (2)
  1. [§1] Notation for the hybrid qubit encoding and the precise definition of the code space should be introduced earlier and used consistently throughout.
  2. [Figure 1] Figure 1 caption and axis labels would benefit from explicit indication of which subspaces are being stabilized.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the proposal's potential strengths. We address each major comment below and will revise the manuscript accordingly to provide the requested details and analyses.

read point-by-point responses

  1. Referee: [Abstract, §2] Abstract and §2: The central claim that the controlled beam-splitter plus spin-dependent displacement interactions produce dissipators whose unique attractive steady state is exactly the code space is not supported by any explicit derivation of the Lindblad operators, adiabatic elimination, or Born-Markov steps. Without these, it is impossible to verify that the generator has the required kernel and spectral gap.

    Authors: We thank the referee for highlighting this point. Section 2 of the manuscript derives the effective Lindbladian by starting from the system-bath Hamiltonian with the controlled beam-splitter interaction and spin-dependent displacement couplings, followed by the Born-Markov approximation and adiabatic elimination of the rapidly cooled bath. The resulting dissipators are constructed to have the code space as their kernel. To make this fully explicit and verifiable, we will expand the derivation in §2 with intermediate steps and add a dedicated appendix detailing the adiabatic elimination procedure, including the explicit form of the Lindblad operators and a discussion of the spectral properties of the generator. revision: yes

  2. Referee: [§3] §3: The attractiveness of the code space is asserted to follow from the engineered Lindbladian, yet no proof or numerical diagonalization of the resulting superoperator is provided to confirm uniqueness of the steady state or absence of leakage fixed points under realistic parameter regimes.

    Authors: We agree that explicit confirmation of uniqueness and the spectral gap is essential for rigor. In the revised version, we will include a proof that the engineered dissipators have the code space as their unique attractive steady-state subspace, leveraging the structure of the jump operators. We will also add numerical results obtained by diagonalizing the Liouvillian superoperator on truncated Hilbert spaces (up to relevant photon numbers) to demonstrate the absence of other fixed points and the presence of a finite gap for realistic parameter values. revision: yes

  3. Referee: [§4] §4: The discussion of experimental feasibility in trapped-ion systems assumes that the required system-bath couplings can be realized with sufficient precision and without introducing uncontrolled decoherence channels; no quantitative error-budget analysis or fidelity estimates under finite cooling rates are given.

    Authors: We acknowledge that a quantitative error analysis strengthens the experimental discussion. In the revision of §4, we will incorporate an error-budget analysis that estimates logical error rates as a function of finite cooling rates, coupling strengths, and typical trapped-ion parameters. This will include fidelity estimates for the stabilized code space and a discussion of potential additional decoherence channels together with mitigation strategies based on demonstrated experimental capabilities. revision: yes

Circularity Check

0 steps flagged

No circularity: constructive proposal grounded in standard primitives

full rationale

The paper advances a constructive scheme that engineers a specific Lindbladian via controlled beam-splitter and spin-dependent displacement couplings to a cooled bath. The attractiveness of the code space as steady state follows from the form of the resulting dissipators under standard Born-Markov and adiabatic-elimination steps, not from any self-definition, parameter fitting to the target result, or load-bearing self-citation. The derivation invokes only externally demonstrated quantum-optics interactions and does not rename or smuggle prior results by the same authors. The central claim therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the feasibility of engineering the stated couplings in real hardware without extra noise; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The storage mode can be coupled to a rapidly cooled bath through controlled beam-splitter and spin-dependent displacement interactions without significant additional noise.
    Invoked to realize the attractive steady-state subspace; stated as compatible with demonstrated trapped-ion primitives.

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Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages · 1 internal anchor

  1. [1]

    A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010)

    work page 2010

  2. [2]

    P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995)

    work page 1995

  3. [3]

    Demonstration of logical qubits and repeated error correction with better-than-physical error rates

    A. Paetznick et al. , Demonstration of logical qubits and repeated error correction with better-than-physical erro r rates, 2024, arXiv:2404.02280 [quant-ph]

    work page internal anchor Pith review arXiv 2024

  4. [4]

    Putterman et al

    H. Putterman et al. , Hardware-efficient quantum error correction via concatenated bosonic qubits, Nature 638, 927 (2025)

    work page 2025

  5. [5]

    Acharya et al

    R. Acharya et al. , Quantum error correction below the surface code threshold, Nature 638, 920 (2025)

    work page 2025

  6. [6]

    Bluvstein et al

    D. Bluvstein et al. , Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

    work page 2024

  7. [7]

    H¨ affner, C

    H. H¨ affner, C. F. Roos, and R. Blatt, Quantum comput- ing with trapped ions, Physics Reports 469, 155 (2008)

    work page 2008

  8. [8]

    Kjaergaard et al

    M. Kjaergaard et al. , Superconducting Qubits: Cur- rent State of Play, Annual Review of Condensed Matter Physics 11, 369 (2020)

    work page 2020

  9. [9]

    A. d. iOlius, P. Fuentes, R. Or´ us, P. M. Crespo, and J. E. Martinez, Decoding algorithms for surface codes, Quantum 8, 1498 (2024)

    work page 2024

  10. [10]

    J. P. Paz and W. H. Zurek, Continuous error correction, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 355 (1998)

    work page 1998

  11. [11]

    Leghtas et al

    Z. Leghtas et al. , Hardware-efficient autonomous quan- tum memory protection, Phys. Rev. Lett. 111, 120501 (2013)

    work page 2013

  12. [12]

    J. F. Poyatos, J. I. Cirac, and P. Zoller, Quantum reser- voir engineering with laser cooled trapped ions, Phys. Rev. Lett. 77, 4728 (1996)

    work page 1996

  13. [13]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quan- tum computation and quantum-state engineering driven by dissipation, Nature Physics 5, 633 (2009)

    work page 2009

  14. [14]

    P. M. Harrington, E. J. Mueller, and K. W. Murch, Engi- neered dissipation for quantum information science, Na- ture Reviews Physics 4, 660 (2022)

    work page 2022

  15. [15]

    Sarovar and G

    M. Sarovar and G. J. Milburn, Continuous quantum error correction by cooling, Phys. Rev. A 72, 012306 (2005)

    work page 2005

  16. [16]

    Reiter, A

    F. Reiter, A. S. Sørensen, P. Zoller, and C. A. Muschik, 6 Dissipative quantum error correction and application to quantum sensing with trapped ions, Nature Communica- tions 8, 1822 (2017)

    work page 2017

  17. [17]

    Pastawski, L

    F. Pastawski, L. Clemente, and J. I. Cirac, Quantum memories based on engineered dissipation, Phys. Rev. A 83, 012304 (2011)

    work page 2011

  18. [18]

    H. Kwon, R. Mukherjee, and M. S. Kim, Reversing lind- blad dynamics via continuous petz recovery map, Phys. Rev. Lett. 128, 020403 (2022)

    work page 2022

  19. [19]

    Mirrahimi et al

    M. Mirrahimi et al. , Dynamically protected cat-qubits: a new paradigm for universal quantum computation, New J. Phys. 16, 045014 (2014)

    work page 2014

  20. [20]

    Lescanne et al

    R. Lescanne et al. , Exponential suppression of bit-flips in a qubit encoded in an oscillator, Nature Physics 16, 509 (2020)

    work page 2020

  21. [21]

    Putterman et al

    H. Putterman et al. , Preserving phase coherence and lin- earity in cat qubits with exponential bit-flip suppression, Phys. Rev. X 15, 011070 (2025)

    work page 2025

  22. [22]

    Xu et al

    Q. Xu et al. , Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits, npj Quantum Inf 9, 1 (2023)

    work page 2023

  23. [23]

    Gottesman, A

    D. Gottesman, A. Kitaev, and J. Preskill, Encoding a qubit in an oscillator, Physical Review A 64, 012310 (2001)

    work page 2001

  24. [24]

    Campagne-Ibarcq et al

    P. Campagne-Ibarcq et al. , Quantum error correction of a qubit encoded in grid states of an oscillator, Nature 584, 368 (2020)

    work page 2020

  25. [25]

    de Neeve, T.-L

    B. de Neeve, T.-L. Nguyen, T. Behrle, and J. P. Home, Error correction of a logical grid state qubit by dissipativ e pumping, Nature Physics 18, 296 (2022)

    work page 2022

  26. [26]

    Guillaud and M

    J. Guillaud and M. Mirrahimi, Repetition cat qubits for fault-tolerant quantum computation, Phys. Rev. X 9, 041053 (2019)

    work page 2019

  27. [27]

    Chamberland et al

    C. Chamberland et al. , Building a Fault-Tolerant Quan- tum Computer Using Concatenated Cat Codes, PRX Quantum 3, 010329 (2022)

    work page 2022

  28. [28]

    Niset, J

    J. Niset, J. Fiur´ aˇ sek, and N. J. Cerf, No-go theorem for gaussian quantum error correction, Phys. Rev. Lett. 102, 120501 (2009)

    work page 2009

  29. [29]

    H. C. J. Gan, G. Maslennikov, K.-W. Tseng, C. Nguyen, and D. Matsukevich, Hybrid quantum computing with conditional beam splitter gate in trapped ion system, Phys. Rev. Lett. 124, 170502 (2020)

    work page 2020

  30. [30]

    Jeon et al

    H. Jeon et al. , Two-mode bosonic state tomography with single-shot joint-parity measurement of a trapped ion, PRX Quantum 6, 040352 (2025)

    work page 2025

  31. [31]

    D. J. Wineland et al. , Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl. Inst. Stand. Technol 103, 259 (1998)

    work page 1998

  32. [32]

    Wallraff et al

    A. Wallraff et al. , Strong coupling of a single photon to a superconducting qubit using circuit quantum electrody- namics, Nature 431, 162 (2004)

    work page 2004

  33. [33]

    Lee and H

    S.-W. Lee and H. Jeong, Near-deterministic quantum teleportation and resource-efficient quantum computa- tion using linear optics and hybrid qubits, Phys. Rev. A 87, 022326 (2013)

    work page 2013

  34. [34]

    U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, Hybrid discrete- and continuous- variable quantum information, Nature Physics 11, 713 (2015)

    work page 2015

  35. [35]

    van Loock, Optical hybrid approaches to quantum information, Laser & Photonics Reviews 5, 167 (2011)

    P. van Loock, Optical hybrid approaches to quantum information, Laser & Photonics Reviews 5, 167 (2011)

    work page 2011

  36. [36]

    Lee et al

    J. Lee et al. , Photonic hybrid quantum computing, New- ton 2, 100359 (2026)

    work page 2026

  37. [37]

    Bose and H

    S. Bose and H. Jeong, Quantum teleportation of hy- brid qubits and single-photon qubits using Gaussian re- sources, Physical Review A 105 (2022)

    work page 2022

  38. [38]

    S. Bose, J. Singh, A. Cabello, and H. Jeong, Long- distance entanglement sharing using hybrid states of dis- crete and continuous variables, Physical Review Applied 21 (2024)

    work page 2024

  39. [39]

    Omkar, Y

    S. Omkar, Y. S. Teo, and H. Jeong, Resource-efficient topological fault-tolerant quantum computation with hy- brid entanglement of light, Phys. Rev. Lett. 125, 060501 (2020)

    work page 2020

  40. [40]

    Lee et al

    J. Lee et al. , Fault-Tolerant Quantum Computation by Hybrid Qubits with Bosonic Cat Code and Single Pho- tons, PRX Quantum 5 (2024)

    work page 2024

  41. [41]

    Vlastakis et al., Characterizing entanglement of an ar- tificial atom and a cavity cat state with Bell’s inequality, Nature Communications 6, 8970 (2015)

    B. Vlastakis et al., Characterizing entanglement of an ar- tificial atom and a cavity cat state with Bell’s inequality, Nature Communications 6, 8970 (2015)

    work page 2015

  42. [42]

    P. C. Haljan, K.-A. Brickman, L. Deslauriers, P. J. Lee, and C. Monroe, Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion, Phys. Rev. Lett. 94, 153602 (2005)

    work page 2005

  43. [43]

    K. G. Johnson, J. D. Wong-Campos, B. Neyenhuis, J. Mizrahi, and C. Monroe, Ultrafast creation of large Schr¨ odinger cat states of an atom, Nature Communica- tions 8, 697 (2017)

    work page 2017

  44. [44]

    Touzard et al

    S. Touzard et al. , Gated conditional displacement read- out of superconducting qubits, Phys. Rev. Lett. 122, 080502 (2019)

    work page 2019

  45. [45]

    Brownnutt, M

    M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, Ion- trap measurements of electric-field noise near surfaces, Rev. Mod. Phys. 87, 1419 (2015)

    work page 2015

  46. [46]

    Dalibard, Y

    J. Dalibard, Y. Castin, and K. Mølmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett. 68, 580 (1992)

    work page 1992

  47. [47]

    Poulin, Stabilizer formalism for operator quantum error correction, Phys

    D. Poulin, Stabilizer formalism for operator quantum error correction, Phys. Rev. Lett. 95, 230504 (2005)

    work page 2005

  48. [48]

    Reiter and A

    F. Reiter and A. S. Sørensen, Effective operator formal- ism for open quantum systems, Physical Review A 85, 032111 (2012)

    work page 2012

  49. [49]

    Q. Wu, Y. Shi, and J. Zhang, Continuous raman sideband cooling beyond the lamb-dicke regime in a trapped ion chain, Phys. Rev. Res. 5, 023022 (2023)

    work page 2023

  50. [50]

    Feng et al

    L. Feng et al. , Efficient ground-state cooling of large trapped-ion chains with an electromagnetically-induced- transparency tripod scheme, Phys. Rev. Lett. 125, 053001 (2020)

    work page 2020

  51. [51]

    Steinbach, J

    J. Steinbach, J. Twamley, and P. L. Knight, Engineering two-mode interactions in ion traps, Phys. Rev. A 56, 4815 (1997)

    work page 1997

  52. [52]

    Frattini, Three-wave Mixing in Superconducting Cir- cuits: Stabilizing Cats with SNAILs, Yale Graduate School of Arts and Sciences Dissertations (2021)

    N. Frattini, Three-wave Mixing in Superconducting Cir- cuits: Stabilizing Cats with SNAILs, Yale Graduate School of Arts and Sciences Dissertations (2021)

    work page 2021

  53. [53]

    R. W. Heeres et al. , Cavity state manipulation using photon-number selective phase gates, Phys. Rev. Lett. 115, 137002 (2015)

    work page 2015

  54. [54]

    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, 060504 (2016)

    work page 2016

  55. [55]

    C. W. Helstrom, Minimum mean-squared error of esti- mates in quantum statistics, Physics Letters A 25, 101 (1967)

    work page 1967

  56. [56]

    K. A. Gilmore et al. , Quantum-enhanced sensing of displacements and electric fields with two-dimensional 7 trapped-ion crystals, Science 373, 673 (2021)

    work page 2021

  57. [57]

    Hempel et al

    C. Hempel et al. , Entanglement-enhanced detection of single-photon scattering events, Nature Photonics 7, 630 (2013)

    work page 2013

  58. [58]

    Van Damme et al

    J. Van Damme et al. , Advanced CMOS manufacturing of superconducting qubits on 300 mm wafers, Nature 634, 74 (2024)

    work page 2024

  59. [59]

    Sivak et al

    V. Sivak et al. , Kerr-free three-wave mixing in supercon- ducting quantum circuits, Phys. Rev. Appl. 11, 054060 (2019). APPENDIX A. METROLOGICAL SETUP We consider a particular Ramsey-type displacement sensing scenario using a spin-oscillator state [ 56, 57]. The displacement parameter β is estimated by the spin-y measurement on the final state |ψ⟩f , the ...

    work page 2019