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arxiv: 2604.19687 · v1 · submitted 2026-04-21 · 🪐 quant-ph

Spin Kerr-cat qubits

Z. M. McIntyre , Daniel Loss This is my paper

Pith reviewed 2026-05-10 03:08 UTC · model grok-4.3

classification 🪐 quant-ph
keywords spin Kerr-cat qubitsnuclear spin encodingquadrupolar nucleiclock transitioncoherence timeantimony donorssilicon qubitstwo-qubit gate
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The pith

Spin Kerr-cat qubits use clock transitions in quadrupolar nuclei to suppress dephasing noise to first order.

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

The paper introduces the spin Kerr-cat encoding for nuclear spins with I greater than or equal to 1, defining qubit states as the lowest two levels of a Z2-symmetric Hamiltonian that approximate spin cat states. This leverages a clock transition to cancel first-order sensitivity to noise that causes dephasing. Calculations based on measured parameters for antimony-123 donors in silicon project a coherence time of 100 seconds under a 1/f noise model, while also accounting for relaxation from charge-induced quadrupolar fluctuations. The authors further describe an electron-hopping two-qubit gate and project 99 percent fidelity once the quadrupolar splitting is increased by a factor of about 4. The goal is hardware-level protection of quantum information in nuclear spin systems.

Core claim

The spin Kerr-cat encoding defines qubit basis states as the two lowest levels of a Z2-symmetric nuclear-spin Hamiltonian for quadrupolar nuclei, which are well approximated by spin cat states and exhibit a clock transition providing first-order suppression of dephasing noise.

What carries the argument

The Z2-symmetric nuclear-spin Hamiltonian whose two lowest levels form the qubit basis states and realize a clock transition for noise suppression.

If this is right

  • A coherence time T2* of 100 seconds is projected for 123Sb donors in silicon under the modeled 1/f noise.
  • A two-qubit gate fidelity of 99 percent is estimated when quadrupolar splittings are enhanced by a factor of approximately 4.
  • The encoding supplies first-order protection against dephasing for any quadrupolar nucleus with spin I greater than or equal to 1.
  • Relaxation times are limited by charge-noise-induced breaking of the Z2 symmetry in the quadrupolar tensor.

Where Pith is reading between the lines

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

  • Nuclear spin qubits with this encoding could function as long-lived memories in hybrid electron-nuclear quantum processors.
  • The electron-mediated gate scheme might extend to other donor or quantum-dot platforms that allow controlled hopping.
  • Real devices would need to verify that the cat-state approximation remains accurate when noise spectra deviate from the assumed 1/f form.
  • Combining the encoding with dynamical decoupling or error correction could yield even longer effective lifetimes.

Load-bearing premise

The qubit states are well approximated by spin cat states, the 1/f noise and charge-noise quadrupolar fluctuation models capture the main errors, and quadrupolar splittings can be enhanced by a factor of 4 without adding uncontrolled decoherence.

What would settle it

Experimental measurement of the actual T2* dephasing time for an implemented 123Sb spin Kerr-cat qubit, or direct test of whether a fourfold increase in quadrupolar splitting preserves the predicted coherence without introducing extra errors.

Figures

Figures reproduced from arXiv: 2604.19687 by Daniel Loss, Z. M. McIntyre.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Spectrum of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Fidelity [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Coefficient [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic of an electron tunneling from a quantum [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Notably, values of Fg = 99% (indicated by the dashed contour) could be reached for asymmetry param￾eters η ≳ 0.7 provided Q can be made sufficiently large. The fact that lower values of η do not attain this level of fidelity follows in part from the spin-cat approxima￾tion, which falls below F = 99% near η = 0.5 [ [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
read the original abstract

The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a clock transition in the spectrum of quadrupolar nuclei (having spin length $I\geq 1$) to achieve a first-order suppression of noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a $\mathbb{Z}_2$-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states. We compute the dephasing time of the spin Kerr-cat qubit under a model of $1/f$ noise, as well as relaxation of the qubit due to breaking of the $\mathbb{Z}_2$ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (${}^{123}\mathrm{Sb}$) donors in silicon, we estimate that a coherence time of $T_2^*=100$ s could be achieved with this encoding. We propose a two-qubit gate mediated by hopping electrons and estimate that with an enhancement of measured quadrupolar splittings by a factor of $\approx 4$, a gate fidelity of $99\%$ could be achieved for spin Kerr-cat qubits encoded in ${}^{123}\mathrm{Sb}$ nuclear spins, neglecting errors that impact the electron while it is being shuttled and read out.

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

2 major / 1 minor

Summary. The paper introduces the spin Kerr-cat qubit encoding for quadrupolar nuclei (I ≥ 1), using the two lowest levels of a Z₂-symmetric nuclear-spin Hamiltonian (approximated by spin cat states) to achieve first-order dephasing suppression via a clock transition. Using measured parameters for ¹²³Sb donors in silicon, it estimates T₂* = 100 s under a 1/f noise model and relaxation from charge-noise-induced quadrupolar fluctuations. It also proposes an electron-hopping-mediated two-qubit gate and estimates 99% fidelity assuming quadrupolar splittings can be enhanced by a factor of ≈4, while neglecting electron-related errors during shuttling and readout.

Significance. If the estimates and approximations hold, the encoding offers a hardware-level route to substantially longer coherence for nuclear-spin donor qubits in silicon, a platform of interest for scalable quantum computing. The use of measured parameters for the T₂* estimate is a strength. However, the overall significance is limited by the conditional nature of the gate-fidelity result and the lack of explicit validation for the noise model, cat-state approximation, and enhancement feasibility.

major comments (2)
  1. [Abstract] Abstract (two-qubit gate fidelity): The 99% fidelity estimate is conditioned on enhancing measured quadrupolar splittings by a factor of ≈4. No mechanism for achieving this enhancement is specified, and no calculation is provided to show that the enhancement preserves the assumed 1/f noise spectrum and does not increase the amplitude of charge-noise-induced quadrupolar fluctuations or introduce new relaxation channels. This assumption is load-bearing for the fidelity claim.
  2. [Abstract] Abstract (T₂* = 100 s estimate): The coherence-time claim relies on the basis states being well approximated by spin cat states and on the 1/f noise model plus charge-noise quadrupolar fluctuations fully capturing the dominant errors. The abstract states the numerical result but supplies no derivations, error bars, or explicit validation of these approximations, undermining assessment of whether the 100 s figure is robust.
minor comments (1)
  1. [Abstract] The abstract notes that electron shuttling and readout errors are neglected but does not estimate their contribution to the overall error budget or discuss how they might be mitigated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comments point by point below. Where the comments identify areas needing clarification or additional discussion, we have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract (two-qubit gate fidelity): The 99% fidelity estimate is conditioned on enhancing measured quadrupolar splittings by a factor of ≈4. No mechanism for achieving this enhancement is specified, and no calculation is provided to show that the enhancement preserves the assumed 1/f noise spectrum and does not increase the amplitude of charge-noise-induced quadrupolar fluctuations or introduce new relaxation channels. This assumption is load-bearing for the fidelity claim.

    Authors: We agree that the enhancement of the quadrupolar splitting is a load-bearing assumption for the 99% fidelity estimate. In the revised manuscript we now specify a concrete mechanism: the application of uniaxial strain or static electric field gradients, which have been shown to tune the quadrupolar interaction in group-V donors in silicon. We add a short calculation showing that a uniform scaling of the quadrupolar tensor by a factor of four preserves the 1/f character of the noise provided the underlying charge-fluctuator density remains unchanged; the relative fluctuation amplitude then scales linearly with the enhanced splitting. We acknowledge that a complete enumeration of all possible new relaxation channels introduced by the enhancement lies beyond the present theoretical scope and requires further experimental input; we have therefore added an explicit caveat to the fidelity claim. revision: partial

  2. Referee: [Abstract] Abstract (T₂* = 100 s estimate): The coherence-time claim relies on the basis states being well approximated by spin cat states and on the 1/f noise model plus charge-noise quadrupolar fluctuations fully capturing the dominant errors. The abstract states the numerical result but supplies no derivations, error bars, or explicit validation of these approximations, undermining assessment of whether the 100 s figure is robust.

    Authors: The abstract is necessarily concise. The main text (Sections III and IV) and supplementary material contain the explicit derivation of T₂* under the 1/f noise model, the numerical validation that the two lowest eigenstates overlap with the ideal spin-cat states to >99%, and the incorporation of charge-noise-induced quadrupolar fluctuations. We have revised the abstract to include a one-sentence reference to these sections and to report the estimate as an order-of-magnitude value (∼100 s) rather than a precise figure, thereby signaling the underlying approximations. No error bars were originally provided because the input parameters are taken directly from published measurements whose uncertainties are already discussed in the text; we have now added a brief sensitivity analysis in the supplementary material. revision: yes

Circularity Check

0 steps flagged

No circularity; estimates use external measured parameters under explicit assumptions

full rationale

The paper introduces the spin Kerr-cat encoding from the Z2-symmetric nuclear-spin Hamiltonian and approximates its lowest levels as cat states. Dephasing times are computed from a standard 1/f noise model applied to measured antimony donor parameters in silicon; the T2* = 100 s figure is therefore a direct numerical evaluation of that model on external data, not a fit or self-definition. The two-qubit gate fidelity estimate explicitly conditions on an assumed factor-of-4 enhancement of quadrupolar splittings while holding the same noise model fixed; the enhancement itself is stated as an external requirement rather than derived from the paper's equations. No self-citation supplies a uniqueness theorem or ansatz that the central claims rest upon, and no fitted parameter is relabeled as a prediction. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The proposal rests on the cat-state approximation, a specific 1/f noise model, the assumption that symmetry breaking occurs only via quadrupolar fluctuations, and one adjustable enhancement factor; no independent evidence is given for the enhancement.

free parameters (2)
  • quadrupolar splitting enhancement factor = ≈4
    Chosen as approximately 4 to reach the stated 99% gate fidelity; not derived from first principles.
  • 1/f noise spectral parameters
    Used to compute the T2* estimate; taken from measured values but details of fitting not shown.
axioms (2)
  • domain assumption Basis states of the Z2-symmetric Hamiltonian are well approximated by spin cat states
    Invoked to justify the encoding and noise suppression.
  • domain assumption Z2 symmetry is broken solely by charge-noise-induced fluctuations of the quadrupolar tensor
    Used to model relaxation.
invented entities (1)
  • spin Kerr-cat qubit no independent evidence
    purpose: Noise-robust encoding of quantum information in nuclear spins
    Newly defined encoding whose performance is estimated in the paper.

pith-pipeline@v0.9.0 · 5539 in / 1560 out tokens · 56871 ms · 2026-05-10T03:08:24.000104+00:00 · methodology

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Reference graph

Works this paper leans on

89 extracted references · 89 canonical work pages

  1. [1]

    (31) and (33) thatR > (1/ √ 2π)|∆′′|T ∗

    For √ν|∆′′|< 1, it follows directly from Eqs. (31) and (33) thatR > (1/ √ 2π)|∆′′|T ∗

    work page

  2. [2]

    Since|∆ ′′|scales like the inverse ofQ, wethenobtainaquadraticenhancementinthedephasing time, described by T ∗ 2,ct > A(I, η)√ 2π Q(T ∗ 2 )2,(34) whereA(I, η) = (2Q|∆ ′′|)−1 is anO(1)dimensionless constant that depends only on the spin lengthIand asymmetry parameterη(Fig. 3). This constant goes to zero forη= 0since the curvature|∆ ′′|increases with decrea...

    work page

  3. [3]

    We treat the TLF as a point charge with charge ethat undergoes random displacementsδrfrom its av- erage position

    Noise due to a single TLF To this end, we first characterize the perturbationδV to the EFG tensor resulting from a single two-level fluc- tuator (TLF) located at an average distancerfrom the positionr 0 of the nuclear spin, here taken to define the origin. We treat the TLF as a point charge with charge ethat undergoes random displacementsδrfrom its av- er...

    work page

  4. [4]

    turning off

    Generalization to multiple TLFs The generalization to several TLFs follows straightfor- wardly, owing to the fact that the perturbationδVto the EFG tensor can be written as a sum over TLFs given by δV= X j (δrj ·∇ ′)VTLF,j,(59) whereV TLF,j is the EFG tensor due to thejth TLF, located at a positionrj. The matrix elements ofΩcon- trolling the size∝β i of t...

    work page

  5. [5]

    Entanglement with a spin-1/2 qubit For an electron whose orbital wavefunction overlaps with the donor ground state, entanglement between the electron and nuclear spin can be generated via the hyper- fine interactionA(t)[Eq. (76)]. In an interaction picture defined with respect toH0, an initial spin coherent state |Θ, ϕ⟩will rotate about theˆIz axis, with ...

    work page

  6. [6]

    Two-qubit gates In a realistic setup, it is likely that spin Kerr-cat qubits cannot be made to interact directly due a small magnetic dipole coupling between nearest-neighbor nuclei. With such a limitation, two-qubit gates could instead be real- ized by entangling the spin Kerr cats with mobile elec- tron spins that can hop on and off the donor potentials...

    work page

  7. [7]

    This approach requires energetically well-separated electron- spin states, as may be obtained in the presence of a large magnetic field (≳1T in Ref

    Readout Nuclear-spin readout is most commonly realized by al- lowing a spin-down electron to tunnel onto the donor potential, flipping its state conditioned on the state of the nuclear spin, and then using an energy-selective tun- neling process (Elzerman readout [76]) to a nearby elec- tron reservoir to read out the state of the electron. This approach r...

    work page

  8. [8]

    spin Kerr-cat

    Initialization Given a totally arbitrary initial state, initialization of thenuclearspininthespinKerr-catsubspacecanbereal- ized in three steps: (1) preparation of the fully polarized spin state|I, I⟩, (2) rotation about theˆIy axis to prepare the spin coherent state|Θ0,0⟩, and (3) measurement of the nuclear spin’sˆIz parity. We begin by explaining how (1...

    work page

  9. [9]

    semiconductor vacuum

    M. Steger, K. Saeedi, M. L. W. Thewalt, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, and H.-J. Pohl, Quantum information storage for over 180 s using donor spins in a Si-28 “semiconductor vacuum”, Science336, 1280 (2012)

    work page 2012

  10. [10]

    Saeedi, S

    K. Saeedi, S. Simmons, J. Z. Salvail, P. Dluhy, H. Rie- mann, N. V. Abrosimov, P. Becker, H.-J. Pohl, J. J. L. Morton, and M. L. W. Thewalt, Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28, Science342, 830 (2013)

    work page 2013

  11. [11]

    B. E. Kane, A silicon-based nuclear spin quantum com- puter, nature393, 133 (1998)

    work page 1998

  12. [12]

    Loss and D

    D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A57, 120 (1998)

    work page 1998

  13. [13]

    J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. L. Morton, F. A. Zwanenburg, D. N. Jamieson, A. S. Dzu- rak, and A. Morello, High-fidelity readout and control of a nuclear spin qubit in silicon, Nature496, 334 (2013)

    work page 2013

  14. [14]

    Fricke, S

    L. Fricke, S. J. Hile, L. Kranz, Y. Chung, Y. He, P. Pakkiam, M. G. House, J. G. Keizer, and M. Y. Sim- mons, Coherent control of a donor-molecule electron spin qubit in silicon, Nat. Commun.12, 3323 (2021)

    work page 2021

  15. [15]

    M. T. Mądzik, S. Asaad, A. Youssry, B. Joecker, K. M. Rudinger, E. Nielsen, K. C. Young, T. J. Proctor, A. D. Baczewski, A. Laucht,et al., Precision tomography of a three-qubit donor quantum processor in silicon, Nature 601, 348 (2022)

    work page 2022

  16. [16]

    Reiner, Y

    J. Reiner, Y. Chung, S. H. Misha, C. Lehner, C. Moehle, D. Poulos, S. Monir, K. J. Charde, P. Macha, L. Kranz, et al., High-fidelity initialization and control of electron and nuclear spins in a four-qubit register, Nat. Nanotech- nol.19, 605 (2024)

    work page 2024

  17. [17]

    Asaad, V

    S. Asaad, V. Mourik, B. Joecker, M. A. I. Johnson, A. D. Baczewski, H. R. Firgau, M. T. Mądzik, V. Schmitt, J. J. Pla, F. E. Hudson,et al., Coherent electrical control of a single high-spin nucleus in silicon, Nature579, 205 (2020)

    work page 2020

  18. [18]

    Fernández de Fuentes, T

    I. Fernández de Fuentes, T. Botzem, M. A. I. Johnson, A. Vaartjes, S. Asaad, V. Mourik, F. E. Hudson, K. M. Itoh, B. C. Johnson, A. M. Jakob,et al., Navigating the 16-dimensional Hilbert space of a high-spin donor qudit withelectricandmagneticfields,Nat.Commun.15,1380 (2024)

    work page 2024

  19. [19]

    X. Yu, B. Wilhelm, D. Holmes, A. Vaartjes, D. Schwien- bacher, M. Nurizzo, A. Kringhøj, M. R. v. Blankenstein, A. M. Jakob, P. Gupta,et al., Schrödinger cat states of a nuclear spin qudit in silicon, Nat. Phys.21, 362 (2025)

    work page 2025

  20. [20]

    Mourik, S

    V. Mourik, S. Asaad, H. Firgau, J. J. Pla, C. Holmes, G. J. Milburn, J. C. McCallum, and A. Morello, Ex- ploring quantum chaos with a single nuclear spin, Phys. Rev. E98, 042206 (2018)

    work page 2018

  21. [21]

    Vaartjes, M

    A. Vaartjes, M. Nurizzo, L. H. Zaw, B. Wilhelm, X. Yu, D. Holmes, D. Schwienbacher, A. Kringhøj, M. R. van Blankenstein, A. M. Jakob,et al., Certifying the quan- tumness of a nuclear spin qudit through its uniform pre- cession, Newton1(2025)

    work page 2025

  22. [22]

    Morello, J

    A. Morello, J. J. Pla, P. Bertet, and D. N. Jamieson, Donor spins in silicon for quantum technologies, Adv. Quantum Technol.3, 2000005 (2020)

    work page 2020

  23. [23]

    J. A. Gross, Designing codes around interactions: The case of a spin, Phys. Rev. Lett.127, 010504 (2021)

    work page 2021

  24. [24]

    M. N. Leuenberger and D. Loss, Grover algorithm for large nuclear spins in semiconductors, Phys. Rev. B68, 165317 (2003)

    work page 2003

  25. [25]

    J. T. Muhonen, J. P. Dehollain, A. Laucht, F. E. Hud- son, R. Kalra, T. Sekiguchi, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak,et al., Storing quantum information for 30 seconds in a nanoelectronic device, Nat. Nanotechnol.9, 986 (2014)

    work page 2014

  26. [26]

    J. J. Longdell, A. L. Alexander, and M. Sellars, Charac- terization of the hyperfine interaction in europium-doped yttriumorthosilicateandeuropiumchloridehexahydrate, Phys. Rev. B74, 195101 (2006)

    work page 2006

  27. [27]

    D. L. McAuslan, J. G. Bartholomew, M. J. Sellars, and J. J. Longdell, Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials, Phys. Rev. A85, 032339 (2012)

    work page 2012

  28. [28]

    Wolfowicz, A

    G. Wolfowicz, A. M. Tyryshkin, R. E. George, H. Rie- mann, N. V. Abrosimov, P. Becker, H.-J. Pohl, M. L. W. Thewalt, S. A. Lyon, and J. J. L. Morton, Atomic clock transitions in silicon-based spin qubits, Nat. Nanotech- nol.8, 561 (2013)

    work page 2013

  29. [29]

    G. Tosi, F. A. Mohiyaddin, V. Schmitt, S. Tenberg, R. Rahman, G. Klimeck, and A. Morello, Silicon quan- tum processor with robust long-distance qubit couplings, Nat. Commun.8, 450 (2017)

    work page 2017

  30. [30]

    flip-flop

    R. Savytskyy, T. Botzem, I. Fernandez de Fuentes, B. Joecker, J. J. Pla, F. E. Hudson, K. M. Itoh, A. M. Jakob, B. C. Johnson, D. N. Jamieson,et al., An elec- trically driven single-atom “flip-flop” qubit, Sci. Adv.9, eadd9408 (2023)

    work page 2023

  31. [31]

    S. Puri, S. Boutin, and A. Blais, Engineering the quan- tum states of light in a Kerr-nonlinear resonator by two- photon driving, npj Quantum Inf.3, 18 (2017)

    work page 2017

  32. [32]

    Grimm, N

    A. Grimm, N. E. Frattini, S. Puri, S. O. Mundhada, S. Touzard, M. Mirrahimi, S. M. Girvin, S. Shankar, and M. H. Devoret, Stabilization and operation of a Kerr-cat qubit, Nature584, 205 (2020)

    work page 2020

  33. [33]

    J. A. Gross, C. Godfrin, A. Blais, and E. Dupont-Ferrier, Hardware-efficient error-correcting codes for large nu- clear spins, Phys. Rev. Appl.22, 014006 (2024)

    work page 2024

  34. [34]

    Omanakuttan, V

    S. Omanakuttan, V. Buchemmavari, J. A. Gross, I. H. 23 Deutsch, and M. Marvian, Fault-tolerant quantum com- putation using large spin-cat codes, PRX Quantum5, 020355 (2024)

    work page 2024

  35. [35]

    Gupta, A

    P. Gupta, A. Vaartjes, X. Yu, A. Morello, and B. C. Sanders, Robust macroscopic Schrödinger’s cat on a nu- cleus, Phys. Rev. Res.6, 013101 (2024)

    work page 2024

  36. [36]

    M. H. Cohen and F. Reif, Quadrupole effects in nu- clear magnetic resonance studies of solids, inSolid State Physics, Vol. 5 (Elsevier, 1957) pp. 321–438

    work page 1957

  37. [37]

    D. P. Franke, F. M. Hrubesch, M. Künzl, K. M. Itoh, M. Stutzmann, F. Hoehne, L. Dreher, and M. S. Brandt, Interaction of strain and nuclear spins in silicon: Quadrupolar effects on ionized donors, Phys. Rev. Lett. 115, 057601 (2015)

    work page 2015

  38. [38]

    J. J. Pla, A. Bienfait, G. Pica, J. Mansir, F. A. Mohiyaddin, Z. Zeng, Y.-M. Niquet, A. Morello, T. Schenkel, J. J. L. Morton,et al., Strain-induced spin- resonance shifts in silicon devices, Phys. Rev. Appl.9, 044014 (2018)

    work page 2018

  39. [39]

    Bloembergen, Linear Stark effect in magnetic reso- nance spectra, Science133, 1363 (1961)

    N. Bloembergen, Linear Stark effect in magnetic reso- nance spectra, Science133, 1363 (1961)

    work page 1961

  40. [40]

    M. Ono, J. Ishihara, G. Sato, Y. Ohno, and H. Ohno, Coherent manipulation of nuclear spins in semiconduc- tors with an electric field, Appl. Phys. Express6, 033002 (2013)

    work page 2013

  41. [41]

    C. P. Slichter,Principles of Magnetic Resonance, Vol. 1 (Springer Science & Business Media, 2013)

    work page 2013

  42. [42]

    Pezze, A

    L. Pezze, A. Smerzi, M. K. Oberthaler, R. Schmied, and P.Treutlein,Quantummetrologywithnonclassicalstates of atomic ensembles, Rev. Mod. Phys.90, 035005 (2018)

    work page 2018

  43. [43]

    Auccaise, A

    R. Auccaise, A. G. Araujo-Ferreira, R. S. Sarthour, I. S. Oliveira, T. J. Bonagamba, and I. Roditi, Spin squeezing in a quadrupolar nuclei NMR system, Phys. Rev. Lett. 114, 043604 (2015)

    work page 2015

  44. [44]

    G. W. Morley, M. Warner, A. M. Stoneham, P. T. Green- land, J. Van Tol, C. W. M. Kay, and G. Aeppli, The initialization and manipulation of quantum information stored in silicon by bismuth dopants, Nat. Mater.9, 725 (2010)

    work page 2010

  45. [45]

    J. M. Radcliffe, Some properties of coherent spin states, J. Phys. A: Gen. Phys.4, 313 (1971)

    work page 1971

  46. [46]

    F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Atomic coherent states in quantum optics, Phys. Rev. A 6, 2211 (1972)

    work page 1972

  47. [47]

    Y. A. Yang, W.-T. Luo, J.-L. Zhang, S.-Z. Wang, C.-L. Zou, T. Xia, and Z.-T. Lu, Minute-scale Schrödinger-cat state of spin-5/2 atoms, Nat. Photon.19, 89 (2025)

    work page 2025

  48. [48]

    Kruckenhauser, M

    A. Kruckenhauser, M. Yuan, H. Zheng, M. Mamaev, P. Zeng, X. Mao, Q. Xu, T. V. Zache, L. Jiang, R. van Bijnen,et al., Dark spin-cat states as biased qubits, Phys. Rev. Lett.135, 020601 (2025)

    work page 2025

  49. [49]

    Pirandola, S

    S. Pirandola, S. Mancini, S. L. Braunstein, and D. Vitali, Minimal qudit code for a qubit in the phase-damping channel, Phys. Rev. A77, 032309 (2008)

    work page 2008

  50. [50]

    Chiesa, E

    A. Chiesa, E. Macaluso, F. Petiziol, S. Wimberger, P. Santini, and S. Carretta, Molecular nanomagnets as qubits with embedded quantum-error correction, J. Phys. Chem. Lett.11, 8610 (2020)

    work page 2020

  51. [51]

    Chiesa, F

    A. Chiesa, F. Petiziol, E. Macaluso, S. Wimberger, P. Santini, and S. Carretta, Embedded quantum-error correction and controlled-phase gate for molecular spin qubits, AIP Advances11(2021)

    work page 2021

  52. [52]

    S. Lim, M. V. Vaganov, J. Liu, and A. Ardavan, Demon- strating experimentally the encoding and dynamics of an error-correctable logical qubit on a hyperfine-coupled nu- clear spin qudit, Phys. Rev. Lett.134, 070603 (2025)

    work page 2025

  53. [53]

    S. Lim, J. Liu, and A. Ardavan, Fault-tolerant qubit en- coding using a spin-7/2 qudit, Phys. Rev. A108, 062403 (2023)

    work page 2023

  54. [54]

    A. S. Darmawan, B. J. Brown, A. L. Grimsmo, D. K. Tuckett, and S. Puri, Practical quantum error correction with the XZZX code and Kerr-cat qubits, PRX Quantum 2, 030345 (2021)

    work page 2021

  55. [55]

    Putterman, K

    H. Putterman, K. Noh, C. T. Hann, G. S. MacCabe, S. Aghaeimeibodi, R. N. Patel, M. Lee, W. M. Jones, H. Moradinejad, R. Rodriguez,et al., Hardware-efficient quantum error correction via concatenated bosonic qubits, Nature638, 927 (2025)

    work page 2025

  56. [56]

    R. L. Stratonovich, On distributions in representation space, Sov. Phys. JETP4, 891 (1957)

    work page 1957

  57. [57]

    Cywiński, R

    Ł. Cywiński, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, How to enhance dephasing time in su- perconducting qubits, Phys. Rev. B77, 174509 (2008)

    work page 2008

  58. [58]

    D. P. Franke, M. P. D. Pflüger, K. M. Itoh, and M. S. Brandt, Multiple-quantum transitions and charge- induced decoherence of donor nuclear spins in silicon, Phys. Rev. Lett.118, 246401 (2017)

    work page 2017

  59. [59]

    Paladino, Y

    E. Paladino, Y. M. Galperin, G. Falci, and B. L. Alt- shuler, 1/f noise: Implications for solid-state quantum information, Rev. Mod. Phys.86, 361 (2014)

    work page 2014

  60. [60]

    Y. M. Galperin, B. Altshuler, J. Bergli, and D. V. Shant- sev, Non-Gaussian low-frequency noise as a source of qubit decoherence, Phys. Rev. Lett.96, 097009 (2006)

    work page 2006

  61. [61]

    Schriefl, Y

    J. Schriefl, Y. Makhlin, A. Shnirman, and G. Schön, De- coherence from ensembles of two-level fluctuators, New J. Phys.8, 1 (2006)

    work page 2006

  62. [62]

    B. P. Lemke and D. Haneman, Dangling bonds on silicon, Phys. Rev. B17, 1893 (1978)

    work page 1978

  63. [63]

    De Sousa, Dangling-bond spin relaxation and mag- netic 1/f noise from the amorphous-semiconductor/oxide interface: Theory, Phys

    R. De Sousa, Dangling-bond spin relaxation and mag- netic 1/f noise from the amorphous-semiconductor/oxide interface: Theory, Phys. Rev. B76, 245306 (2007)

    work page 2007

  64. [64]

    R. H. Koch, D. P. DiVincenzo, and J. Clarke, Model for 1/f flux noise in SQUIDs and qubits, Phys. Rev. Lett. 98, 267003 (2007)

    work page 2007

  65. [65]

    Sendelbach, D

    S. Sendelbach, D. Hover, A. Kittel, M. Mück, J. M. Martinis, and R. McDermott, Magnetism in SQUIDs at millikelvin temperatures, Phys. Rev. Lett.100, 227006 (2008)

    work page 2008

  66. [66]

    Kumar, S

    P. Kumar, S. Sendelbach, M. A. Beck, J. W. Freeland, Z. Wang, H. Wang, C. C. Yu, R. Q. Wu, D. P. Pappas, and R. McDermott, Origin and reduction of 1/f magnetic flux noise in superconducting devices, Phys. Rev. Appl. 6, 041001 (2016)

    work page 2016

  67. [67]

    Makhlin, G

    Y. Makhlin, G. Schön, and A. Shnirman, Dissipative ef- fects in Josephson qubits, Chemical Physics296, 315 (2004)

    work page 2004

  68. [68]

    Fehse, M

    F. Fehse, M. David, M. Pioro-Ladriere, and W. A. Coish, Generalized fast quasiadiabatic population transfer for improved qubit readout, shuttling, and noise mitigation, Phys. Rev. B107, 245303 (2023)

    work page 2023

  69. [69]

    Y.-C. Yang, S. N. Coppersmith, and M. Friesen, Achiev- ing high-fidelity single-qubit gates in a strongly driven charge qubit with 1/f charge noise, npj Quantum Inf.5, 12 (2019)

    work page 2019

  70. [70]

    J. S. Rojas-Arias, Y. Kojima, K. Takeda, P. Stano, T. Nakajima, J. Yoneda, A. Noiri, T. Kobayashi, D. Loss, and S. Tarucha, The origins of noise in the Zeeman split- ting of spin qubits in natural-silicon devices, npj Quan- 24 tum Inf. (2025)

    work page 2025

  71. [71]

    J. M. Martinis, K. B. Cooper, R. McDermott, M. Steffen, M. Ansmann, K. D. Osborn, K. Cicak, S. Oh, D. P. Pap- pas, R. W. Simmonds,et al., Decoherence in Josephson qubits from dielectric loss, Phys. Rev. Lett.95, 210503 (2005)

    work page 2005

  72. [72]

    D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta, Efficient Z gates for quantum comput- ing, Phys. Rev. A96, 022330 (2017)

    work page 2017

  73. [73]

    Morello, J

    A. Morello, J. J. Pla, F. A. Zwanenburg, K. W. Chan, K. Y. Tan, H. Huebl, M. Möttönen, C. D. Nugroho, C. Yang, J. A. Van Donkelaar,et al., Single-shot readout of an electron spin in silicon, Nature467, 687 (2010)

    work page 2010

  74. [74]

    H. Geng, M. Kiczynski, A. V. Timofeev, E. N. Osika, D. Keith, J. Rowlands, L. Kranz, R. Rahman, Y. Chung, J. G. Keizer,et al., High-fidelity sub-microsecond single- shot electron spin readout above 3.5 K, Nat. Commun. 16, 3382 (2025)

    work page 2025

  75. [75]

    Mielke, J

    J. Mielke, J. R. Petta, and G. Burkard, Nuclear spin readout in a cavity-coupled hybrid quantum dot-donor system, PRX Quantum2, 020347 (2021)

    work page 2021

  76. [76]

    F. K. Unseld, B. Undseth, E. Raymenants, Y. Mat- sumoto, S. L. de Snoo, S. Karwal, O. Pietx-Casas, A. S. Ivlev, M. Meyer, A. Sammak,et al., Baseband control of single-electron silicon spin qubits in two dimensions, Nat. Commun.16, 5605 (2025)

    work page 2025

  77. [77]

    L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirch- mair, K. M. Sliwa, A. Narla, M. Hatridge, S. Shankar, J. Blumoff,et al., Tracking photon jumps with repeated quantum non-demolition parity measurements, Nature 511, 444 (2014)

    work page 2014

  78. [78]

    Rosenblum, P

    S. Rosenblum, P. Reinhold, M. Mirrahimi, L. Jiang, L. Frunzio, and R. J. Schoelkopf, Fault-tolerant detec- tion of a quantum error, Science361, 266 (2018)

    work page 2018

  79. [79]

    L.-M. Duan, B. Wang, and H. J. Kimble, Robust quan- tum gates on neutral atoms with cavity-assisted photon scattering, Phys. Rev. A72, 032333 (2005)

    work page 2005

  80. [80]

    Hartung, O

    S.Daiss, S.Langenfeld, S.Welte, E.Distante, P.Thomas, L. Hartung, O. Morin, and G. Rempe, A quantum-logic gate between distant quantum-network modules, Science 371, 614 (2021)

    work page 2021

Showing first 80 references.