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Site-resolved magnon and triplon dynamics on a programmable quantum dot spin ladder

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Pith's one-line read A germanium quantum dot ladder simulates magnon and triplon quantum walks with site-resolved readout, matching Heisenberg and XXZ spin-model simulations.

desk verdict Site-resolved magnon/triplon quantum walks in a programmable Ge quantum-dot ladder: genuinely new methodology, but the isotropic spin-model claim is softer than the data support. read the letter →

arxiv 2506.08663 v1 pith:NGURRARW submitted 2025-06-10 cond-mat.mes-hall quant-ph

Pablo Cova Fariña , Daniel Jirovec , Xin Zhang , Elizaveta Morozova , Stefan D. Oosterhout , Stefano Reale , Tzu-Kan Hsiao , Giordano Scappucci
show 2 more authors
Menno Veldhorst Lieven M. K. Vandersypen
This is my paper
classification cond-mat.mes-hallquant-ph
keywords germaniumquantumdotsmagnonwalktriplondynamicsHeisenbergspinladderXXZmodelsite-resolvedreadoutanalog-digitalsimulationdisorder-inducedlocalization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports direct, site-resolved observation of spin-excitation propagation in a 2x4 germanium quantum dot array used as a programmable quantum simulator. It combines digital spin-qubit gates for initialization and readout with analog evolution under the native spin Hamiltonian, and reconstructs quantum walk plots for single-spin excitations (magnons) and two-spin triplet excitations (triplons). The measured walks match exact-diagonalization simulations of an isotropic Heisenberg (XXX) model for magnons and an XXZ model with anisotropy parameter 0.5 for triplons. By tuning exchange couplings and single-site disorder independently, the authors show how disorder localizes the excitations and how stronger coupling restores propagation, which they position as groundwork for simulating disorder-driven phenomena such as many-body localization.

What carries the argument

The carrying mechanism is a hybrid digital-analog protocol on a 2x4 Ge/SiGe quantum dot ladder: Pauli-spin-blockade ramps and SWAP gates prepare and read out spin states at chosen sites, while in between the system evolves under its native exchange Hamiltonian. For the single-spin encoding the Hamiltonian is the isotropic Heisenberg model H0 = sum J_ij S_i dot S_j + mu_B B sum g_i S_i^z of Eq. (1), and for the singlet-triplet encoding the projected S-T- Hamiltonian of Eq. (2) realizes an XXZ interaction with $\Delta$ = 0.5. Exchange couplings J_ij are set by barrier-gate voltages, single-site disorder comes from g-factor variability or from the tunable (E_z - J_perp) terms, and SWAP-assisted readout reconstructs all single-site spin probabilities; exact-diagonalization fits of the quantum walks then serve as the benchmark that identifies the realized spin model.

What would settle it

A quantitative mismatch between measured site-resolved quantum walks and exact-diagonalization simulations that include the full J-tensor and spin-orbit terms would falsify the central claim. Concretely, repeat the magnon and triplon walks at several magnetic-field strengths and orientations: if the oscillation frequencies or beat patterns change with field orientation in ways not captured by Eqs. (1) and (2), the isotropic-Hamiltonian assumption breaks.

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Extended reading notes

Core claim

The central claim is that a gate-defined germanium quantum dot ladder can act as a programmable, site-resolved quantum simulator of spin models. The authors reconstruct quantum walks of a single magnon prepared on any site of an eight-spin 2x4 ladder, and of a single triplon propagating along a chain of singlet-triplet-encoded rungs, and show that these walks match exact-diagonalization simulations of the Heisenberg Hamiltonian for the single-spin encoding and of the projected singlet-triplet Hamiltonian, an XXZ model with $\Delta$ = 0.5, for the triplon encoding. They demonstrate per-site tunability of Heisenberg exchange couplings, independent control of single-site disorder via g-factor variability or via tunable singlet-triplet energy terms, and a localization-to-propagation transition as the ratio of exchange to disorder is varied. On the paper's own terms, this establishes that semiconductor quantum dot arrays can emulate both XXX and XXZ spin Hamiltonians with single-site resolution and programmable quench configurations.

Load-bearing premise

The analog evolution is assumed to be governed by the isotropic Heisenberg Hamiltonian of Eq. (1) and, for the singlet-triplet encoding, by Eq. (2), with scalar g-factors and no significant spin-orbit or tensorial exchange contributions; if that assumption fails, the observed walks are not faithful simulations of those spin models.

Editorial extensions

If this is right

  • The same device can be reconfigured between different Heisenberg coupling topologies, such as chains, rings, and weakly coupled pairs, making Hamiltonian quenches a routine operation without fabrication changes.
  • Because every exchange and every onsite disorder term can be set individually, the interaction-to-disorder ratio, the key control parameter for localization physics, can be swept in situ on a single sample.
  • The two encodings cover two anisotropy points, Delta = 1 and Delta = 0.5, and the projection methods used for the singlet-triplet encoding could be extended to realize other XXZ anisotropies in the same platform.
  • Single-shot readout of all pairwise triplon probabilities gives access to spin-spin correlations such as C_ij, which can witness delocalization and entanglement-related signatures without full state tomography.
  • The preparation methods extend to highly excited states such as Neel states on all eight spins, providing a route toward studying thermalization and disorder-driven dynamics in few-body but scalable arrays.

Reading between the lines

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

  • If the analog evolution remains faithful as arrays grow, the platform could cross into the many-body regime where exact diagonalization becomes intractable; a natural first probe would be a density-imbalance or entanglement-entropy measurement across the disorder-to-interaction sweep already demonstrated here.
  • The g-factor variability, usually a nuisance, is treated as a native source of disorder; this suggests a testable extension in which local g-tensor modulation creates spatially patterned disorder potentials rather than only random ones.
  • Because the singlet-triplet encoding makes both interaction and disorder terms gate-voltage tunable, the two-site phase diagram of the paper may generalize into an array-level probe of localization dynamics in dimerized spin chains.
  • The paper leaves the size of the exchange J-tensor anisotropy as an open assumption; a direct follow-up measuring the same quantum walks as a function of magnetic-field orientation would convert that assumption into a quantitative characterization.
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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

3 major / 4 minor

Summary. The manuscript reports experiments on two Ge/SiGe 2×4 quantum dot arrays in which single-spin excitations (magnons) and two-spin excitations (triplons) are prepared on chosen sites, allowed to evolve under the native exchange Hamiltonian, and read out with single-site resolution using Pauli-spin-blockade and SWAP operations. The authors reconstruct site-resolved quantum walks for several exchange topologies, including weakly coupled pairs, homogeneous and inhomogeneous 2×2 rings, an eight-site array, and a chain of three coupled singlet-triplet qubits. The data are compared to exact-diagonalization simulations of the Heisenberg (XXX) Hamiltonian of Eq. (1) and the projected singlet-triplet XXZ Hamiltonian of Eq. (2) with Δ=0.5, and the paper demonstrates the competition between exchange coupling and single-site disorder, including a two-site phase diagram in which a triplon localizes when disorder exceeds the inter-site coupling.

Significance. The raw experimental observations are significant: coherent, site-resolved propagation of magnon and triplon excitations in a gate-defined germanium quantum dot ladder, with arbitrary-site initialization, three-outcome readout, and crosstalk-mitigated exchange control. The technical toolbox developed in this work is valuable for the quantum-dot quantum-simulation community, and the deposition of raw data on Zenodo is commendable. However, the paper's stronger interpretive claim—that the data validate the isotropic Heisenberg/XXZ models as specified by Eqs. (1) and (2)—is not fully supported by the single-excitation walks, because those sectors are largely insensitive to the longitudinal and anisotropic couplings. The experimental achievement is robust, but the model-identification claim needs to be narrowed, supplemented, or explicitly qualified.

major comments (3)
  1. [Section VII / Eq. (3) / Table I] The conclusion that the quantum walks validate the isotropic Heisenberg (Δ=1) and XXZ (Δ=0.5) Hamiltonians is not supported by the single-excitation data as presented. In the single-magnon sector on the 2×2 ring, the longitudinal interaction Σ σz_i σz_j is a constant because all lattice sites have the same degree, and on the ladder it produces only a boundary potential that is indistinguishable from the site-dependent Zeeman terms. In the singlet-triplet encoding, the longitudinal part of Eq. (2) reduces, in the one-triplon sector, to a diagonal potential that is linearly dependent on the same operators as the single-site disorder terms (Ēz,i − J⊥_i)σz_i; at the experimentally calibrated homogeneous condition of Eq. (S5), this potential is absorbed into the on-site energies. The measured walks therefore constrain only the transverse hopping amplitudes and the total on-site energy differences; they are insensitive to the anisotropy parameter Δ and cannot distinguish an XXX, XXZ, or XY interaction. The statement in Section VII that 'we are able to model the quantum walk plots with an isotropic model' is thus not evidence that the exchange anisotropy is small. I request an explicit insensitivity analysis (for example, showing that simulations with Δ=0, 0.5, and 1 yield identical single-excitation walks after a redefinition of on-site energies), and either a rephrased claim that refers specifically to the transverse (XY-type) component, or an additional measurement that is sensitive to Δ (e.g., two-triplon dynamics with quantitative comparison to simulations).
  2. [Section VII / Section III] The neglect of tensorial exchange and spin-orbit spin-flip terms is acknowledged, but the experiments do not monitor or bound population leakage out of the single-excitation subspace. The readout analysis infers probabilities from the directly measured Pauli-spin-blockade outcomes plus normalization (for example, P(|↑↑⟩)=0 is assumed in the single-magnon case, and the fourth outcome is obtained by normalization), so any coherent or incoherent transfer to |↑↑⟩, |↓↓⟩, S, or T_0 during the analog evolution would be misattributed to the inferred spin-up/down probabilities. The qualitative agreement between measured and simulated oscillation patterns is suggestive but does not by itself rule out a significant leakage channel combined with renormalization. I ask the authors to provide a quantitative estimate of expected leakage during the analog evolution, for instance from the known spin-orbit anticrossing size Δ_ST and the time spent near avoided crossings, or to explicitly state that all reported probabilities are conditional on remaining in the single-excitation subspace and that this condition is not directly verified.
  3. [Section VI / Fig. 4e / Fig. S18] The claim of 'excellent agreement' between the measured triplon quantum walks and the exact-diagonalization simulation is qualitative only, because the readout visibilities differ per site: the text states that the Q3 readout fidelity is significantly lower than that of Q1 and Q2, and the visibility is not corrected. The simulation in Fig. S18 is plotted with equal per-site visibility, so the comparison validates oscillation frequencies and relative phases but not the absolute site-resolved probabilities. Please fit or independently calibrate the per-site visibilities and either overlay the corrected data on the simulation or state explicitly that the comparison is limited to relative amplitudes.
minor comments (4)
  1. [Throughout] The text renders 'SW AP' with a space in many places; this appears to be a typesetting artifact and should be corrected to 'SWAP'.
  2. [Section V / Fig. 3l] The claim that 'we can successfully prepare any single-magnon product state' is weakened by the low readout visibility for dots 7 and 8, which the authors attribute to readout visibility at the time of measurement; please qualify the statement accordingly.
  3. [Eq. (2)] The notation (σz_i − I)(σz_j − I) would benefit from a brief remark that σz is defined in the S–T− basis with eigenvalues ±1, since this mapping is not stated at the point of introduction.
  4. [Section VI / Fig. 4f] The sentence describing C13 as negative 'where the triplon is delocalized between sites 1 and 3' is imprecise; negative correlations are expected for any single-particle anticorrelation and the text should describe this more carefully.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the site-resolved quantum walk observations are direct readouts, and the Heisenberg/XXZ simulations are consistency checks with fitted exchange couplings, not parameter-free predictions.

full rationale

The paper's claimed derivation chain is not circular. The central claims—site-resolved magnon and triplon quantum walks, localization under disorder, and tunable propagation—are direct measurements reconstructed from Pauli-spin-blockade readouts (Figs. 3f-l and 4e-g). The simulations of Eqs. 1 and 2 are used after the fact to extract exchange couplings by iterating {Ji} around expected values (Supplementary XVI: 'We iterate over various interaction values {Ji} around the expected exchange configuration and compare to the measured data') and to show consistency, not to generate parameter-free predictions. The singlet-triplet Hamiltonian of Eq. 2 is imported from prior work [42] by the same group, but that mapping is a published, independently verifiable derivation, and the present paper also re-derives the homogeneous condition in Eqs. S4-S6. The authors explicitly flag the isotropic-Hamiltonian assumption: Section III states 'For holes in germanium quantum dots, this Hamiltonian is only an approximation,' and Section VII concedes that the isotropic model's success is a speculation ('we speculate that this anisotropy is either small for our particular device...'). This is a correctness and validity caveat, not a circular reduction: no output quantity is defined in terms of the claimed result, and no fitted parameter is renamed as a prediction. The qualitative oscillation topologies (e.g., the 1-5 exchange oscillation in Fig. 3f, the 2-5 ring oscillation in Fig. 3i, and triplon propagation in Fig. 4e) are read directly from the data and do not require the fitted exchange values. Therefore the derivation is self-contained with respect to its observational claims.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claims do not depend on a new theory; the Hamiltonians are stated as native to the device and the simulation parameters are either measured (Zeeman energies via EDSR) or extracted from oscillation frequencies. The listed exchange values are fitted to reproduce the same data they are used to explain, so they are free parameters with respect to the simulation comparisons, though the qualitative quantum-walk observations (Fig. 3f, 4e) stand independently. No new entities are introduced.

free parameters (5)
  • Exchange couplings for 2x2 ring with inhomogeneous couplings (Fig. 3j) = J12=11.5 MHz, J56=27.0 MHz, J15=20.0 MHz, J26=15.5 MHz
    Obtained by iterating simulation over exchange values and comparing with measured quantum walk (Supplementary XVIII-XIX).
  • Exchange couplings for weakly coupled pairs (Fig. 3h) = J12=J56=100 MHz, J15=J26=25 MHz
    Obtained by matching simulation to data in Supplementary XVII.
  • Homogeneous ring exchange (Fig. 3i) = J=21 MHz
    Tuned experimentally to equalize all couplings; value confirmed by simulation match (Supplementary XIX).
  • Parallel exchange for three-site triplon walk (Fig. 4e) = J^par = 14 MHz
    Extracted from simulation of Eq. S6 to match the measured triplon quantum walks (Supplementary XXIII, Fig. S18).
  • Effective Zeeman energies in Fig. S7 simulation = Ez,1=50 MHz, Ez,2=55 MHz
    Slightly higher than EDSR-measured values; adjusted to reproduce S-T0 oscillation pattern, attributed by authors to g-factor modulation by barrier pulses (Supplementary XIII).
assumptions (4)
  • domain assumption The isotropic Heisenberg Hamiltonian of Eq. 1 with nearest-neighbor exchange and scalar g-factors describes the spin dynamics.
    Section III; the authors explicitly note this neglects tensorial Jij and gi and spin-orbit terms, assumed negligible during analog evolution.
  • domain assumption The singlet-triplet qubit ladder is governed by the projected Hamiltonian of Eq. 2 (XXZ with Delta = 0.5) from Ref. [42].
    Section III and Supplementary Section XXIII; the mapping is adopted from the authors' earlier published work.
  • domain assumption Pauli spin blockade with diabatic, intermediate, and adiabatic ramps distinguishes the targeted two-spin states in readout.
    Section IV; relies on the separation of timescales between tunnel coupling, Zeeman difference, and the spin-orbit anticrossing.
  • domain assumption Only a single excitation is present during the magnon quantum walks, so two readout configurations suffice to reconstruct all single-spin probabilities.
    Section V: 'if only a single excitation is present in the array, only two of the three readouts are necessary'.

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Cite this review

Pith. "Pith review of Site-resolved magnon and triplon dynamics on a programmable quantum dot spin ladder." pith.science (2026). https://pith.science/paper/NGURRARW

@misc{pith2026250608663,
  author       = {Pith},
  title        = {Pith review of: Site-resolved magnon and triplon dynamics on a programmable quantum dot spin ladder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NGURRARW}},
  note         = {Machine review of arXiv:2506.08663}
}
read the original abstract

Quasi-particle dynamics in interacting systems in the presence of disorder challenges the notion of internal thermalization, but proves difficult to investigate theoretically for large particle numbers. Engineered quantum systems may offer a viable alternative, as witnessed in experimental demonstrations in a variety of physical platforms, each with its own capabilities and limitations. Semiconductor gate-defined quantum dot arrays are of particular interest since they offer both a direct mapping of their Hamiltonian to Fermi-Hubbard and Heisenberg models and the in-situ tunability of (magnetic) interactions and onsite potentials. In this work, we use an array of germanium quantum dots to simulate the dynamics of both single-spin excitations (magnons) and two-spin excitations (triplons). We develop a methodology that combines digital spin qubit operations for state preparation and readout with analog evolution under the full system Hamiltonian. Using these techniques, we can reconstruct quantum walk plots for both magnons and triplons, and for various configurations of Heisenberg exchange couplings. We furthermore explore the effect of single-site disorder and its impact on the propagation of spin excitations. The obtained results can provide a basis for simulating disorder-based solid-state phenomena such as many-body localization.

Figures

Figures reproduced from arXiv: 2506.08663 by the authors.

Figure 1
Figure 1. FIG. 1. Atomic-force microscopy images of the two germanium 2 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Pairwise initialization, readout, characterization and control of hole spins. (a) Energy diagram for a pair of spins. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Magnon propagation for the left half of the 2 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Triplon propagation in a dimerized quantum dot array. (a) Quantum circuit showing the state preparation and readout [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Reference graph

Works this paper leans on

71 extracted references · 56 canonical work pages · cited by 1 Pith paper

  1. [1]

    Feynman, R. P. Simulating physics with computers. In- ternational Journal of Theoretical Physics 21, 467–488 (1982). URL https://doi.org/10.1007/BF02650179

    doi:10.1007/bf02650179 1982

  2. [2]

    Universal Quantum Simulators

    Lloyd, S. Universal Quantum Simulators. Science 273, 1073–1078 (1996). URL https://www.science. org/doi/10.1126/science.273.5278.1073. Publisher: American Association for the Advancement of Science

    arXiv 1996

  3. [3]

    & Nori, F

    Georgescu, I., Ashhab, S. & Nori, F. Quantum simulation. Reviews of Modern Physics 86, 153– 185 (2014). URL https://link.aps.org/doi/10.1103/ RevModPhys.86.153. Publisher: American Physical So- ciety

    work page 2014

  4. [4]

    A., Altman, E., Bloch, I

    Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermaliza- tion, and entanglement. Reviews of Modern Physics 91, 021001 (2019). URL https://link.aps.org/doi/ 10.1103/RevModPhys.91.021001. Publisher: American Physical Society

    doi:10.1103/revmodphys.91.021001 2019

  5. [5]

    Schreiber, M. et al. Observation of many-body localiza- tion of interacting fermions in a quasirandom optical lat- tice. Science 349, 842–845 (2015). URL https://www. science.org/doi/10.1126/science.aaa7432. Pub- lisher: American Association for the Advancement of Sci- ence

    doi:10.1126/science.aaa7432 2015

  6. [6]

    & DeMarco, B

    Kondov, S., McGehee, W., Xu, W. & DeMarco, B. Disorder-Induced Localization in a Strongly Correlated Atomic Hubbard Gas. Physical Review Letters 114, 083002 (2015). URL https://link.aps.org/doi/10. 1103/PhysRevLett.114.083002. Publisher: American Physical Society

    work page 2015

  7. [7]

    Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nature Physics 12, 907–911 (2016). URL https://www.nature. com/articles/nphys3783. Publisher: Nature Publishing Group

    work page 2016

  8. [8]

    Choi, J.-y. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016). URL https://www.science.org/doi/10.1126/ science.aaf8834. Publisher: American Association for the Advancement of Science

    work page 2016

Show all 71 references
  1. [9]

    Roushan, P. et al. Spectroscopic signatures of localiza- tion with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017). URL https://www. science.org/doi/10.1126/science.aao1401. Pub- lisher: American Association for the Advancement of Sci- ence

    2017 doi

  2. [10]

    Xu, K. et al. Emulating Many-Body Localization with a Superconducting Quantum Processor. Physical Review Letters 120, 050507 (2018). URL https://link.aps. org/doi/10.1103/PhysRevLett.120.050507. Publisher: American Physical Society

    2018 doi

  3. [11]

    Morong, W. et al. Observation of Stark many- body localization without disorder. Nature 599, 393– 398 (2021). URL https://www.nature.com/articles/ s41586-021-03988-0 . Publisher: Nature Publishing Group

    2021

  4. [12]

    & Manucharyan, V

    Mehta, N., Kuzmin, R., Ciuti, C. & Manucharyan, V. E. Down-conversion of a single photon as a probe of many-body localization. Nature 613, 650– 655 (2023). URL https://www.nature.com/articles/ s41586-022-05615-y . Publisher: Nature Publishing Group

    2023

  5. [13]

    & Nascimb` ene, S

    Bloch, I., Dalibard, J. & Nascimb` ene, S. Quantum simu- lations with ultracold quantum gases. Nature Physics 8, 267–276 (2012). URL https://www.nature.com/ articles/nphys2259. Publisher: Nature Publishing Group

    2012

  6. [14]

    & Roos, C

    Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nature Physics 8, 277–284 (2012). URL https://www.nature.com/articles/nphys2252. Pub- lisher: Nature Publishing Group

    2012

  7. [15]

    Kaufman, A. M. & Ni, K.-K. Quantum science with opti- cal tweezer arrays of ultracold atoms and molecules. Na- ture Physics 17, 1324–1333 (2021). URL https://www. nature.com/articles/s41567-021-01357-2 . Publisher: Nature Publishing Group

    2021

  8. [16]

    L., Tarbutt, M

    Cornish, S. L., Tarbutt, M. R. & Hazzard, K. R. A. Quantum computation and quantum simula- tion with ultracold molecules. Nature Physics 20, 730– 740 (2024). URL https://www.nature.com/articles/ s41567-024-02453-9 . Publisher: Nature Publishing Group

    2024

  9. [17]

    Kjaergaard, M. et al. Superconducting Qubits: Current State of Play. Annual Review of Con- densed Matter Physics 11, 369–395 (2020). URL https://www.annualreviews.org/content/journals/ 10.1146/annurev-conmatphys-031119-050605 . Pub- lisher: Annual Reviews

    2020 doi

  10. [18]

    Choi, D.-J. et al. Colloquium: Atomic spin chains on surfaces. Reviews of Modern Physics 91, 041001 (2019). URL https://link.aps.org/doi/10.1103/ RevModPhys.91.041001. Publisher: American Physical Society. 11

    2019

  11. [19]

    Hensgens, T. et al. Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array. Nature 548, 70–73 (2017). URL https: //www.nature.com/articles/nature23022. Publisher: Nature Publishing Group

    2017

  12. [20]

    & Vandersypen, L

    Barthelemy, P. & Vandersypen, L. M. K. Quantum Dot Systems: a versatile platform for quantum sim- ulations. Annalen der Physik 525, 808–826 (2013). URL https://onlinelibrary.wiley.com/doi/abs/10. 1002/andp.201300124

    2013

  13. [21]

    Dehollain, J. P. et al. Nagaoka ferromagnetism ob- served in a quantum dot plaquette. Nature 579, 528– 533 (2020). URL https://www.nature.com/articles/ s41586-020-2051-0 . Publisher: Nature Publishing Group

    2020

  14. [22]

    Kiczynski, M. et al. Engineering topological states in atom-based semiconductor quantum dots. Nature 606, 694–699 (2022). URL https://www.nature.com/ articles/s41586-022-04706-0 . Publisher: Nature Publishing Group

    2022

  15. [23]

    Hsiao, T.-K. et al. Exciton Transport in a Germa- nium Quantum Dot Ladder. Physical Review X 14, 011048 (2024). URL https://link.aps.org/doi/10. 1103/PhysRevX.14.011048. Publisher: American Physi- cal Society

    2024

  16. [24]

    van Diepen, C. et al. Quantum Simulation of An- tiferromagnetic Heisenberg Chain with Gate-Defined Quantum Dots. Physical Review X 11, 041025 (2021). URL https://link.aps.org/doi/10.1103/ PhysRevX.11.041025. Publisher: American Physical So- ciety

    2021

  17. [25]

    Wang, C.-A. et al. Probing resonating valence bonds on a programmable germanium quantum simulator. npj Quantum Information 9, 1–8 (2023). URL https://www. nature.com/articles/s41534-023-00727-3 . Publisher: Nature Publishing Group

    2023

  18. [26]

    van Riggelen, F. et al. A two-dimensional array of single- hole quantum dots. Applied Physics Letters 118, 044002 (2021). URL https://doi.org/10.1063/5.0037330

    2021 doi

  19. [27]

    Jirovec, D. et al. A singlet-triplet hole spin qubit in planar Ge. Nature Materials 20, 1106–1112 (2021). URL https://www.nature.com/articles/ s41563-021-01022-2 . Publisher: Nature Publishing Group

    2021

  20. [28]

    Scappucci, G. et al. The germanium quantum in- formation route. Nature Reviews Materials 6, 926– 943 (2021). URL https://www.nature.com/articles/ s41578-020-00262-z . Publisher: Nature Publishing Group

    2021

  21. [29]

    Borsoi, F. et al. Shared control of a 16 semiconduc- tor quantum dot crossbar array. Nature Nanotech- nology 19, 21–27 (2024). URL https://www.nature. com/articles/s41565-023-01491-3 . Publisher: Nature Publishing Group

    2024

  22. [30]

    Wang, C.-A. et al. Operating semiconductor quantum processors with hopping spins. Science 385, 447–452 (2024). URL https://www.science.org/doi/abs/10. 1126/science.ado5915. Publisher: American Associa- tion for the Advancement of Science

    2024

  23. [31]

    John, V. et al. A two-dimensional 10-qubit array in ger- manium with robust and localised qubit control (2024). URL https://arxiv.org/abs/2412.16044v2

    2024

  24. [32]

    Hendrickx, N. W. et al. A four-qubit germa- nium quantum processor. Nature 591, 580–585 (2021). URL https://www.nature.com/articles/ s41586-021-03332-6 . Publisher: Nature Publishing Group

    2021

  25. [33]

    & Sanz, M

    Parra-Rodriguez, A., Lougovski, P., Lamata, L., Solano, E. & Sanz, M. Digital-analog quan- tum computation. Physical Review A 101, 022305 (2020). URL https://link.aps.org/doi/10.1103/ PhysRevA.101.022305. Publisher: American Physical Society

    2020

  26. [34]

    Andersen, T. I. et al. Thermalization and criticality on an analogue–digital quantum simulator. Nature 638, 79– 85 (2025). URL https://www.nature.com/articles/ s41586-024-08460-3 . Publisher: Nature Publishing Group

    2025

  27. [35]

    Jirovec, D. et al. Exchange cross-talk mitigation in dense quantum dot arrays (2025). URL http://arxiv.org/ abs/2503.23846. ArXiv:2503.23846 [cond-mat]

    2025

  28. [36]

    Fukuhara, T. et al. Microscopic observation of magnon bound states and their dynamics. Nature 502, 76– 79 (2013). URL https://www.nature.com/articles/ nature12541. Publisher: Nature Publishing Group

    2013

  29. [37]

    Jurcevic, P. et al. Quasiparticle engineering and entan- glement propagation in a quantum many-body system. Nature 511, 202–205 (2014). URL https://www.nature. com/articles/nature13461. Publisher: Nature Publish- ing Group

    2014

  30. [38]

    Yan, Z. et al. Strongly correlated quantum walks with a 12-qubit superconducting processor. Science 364, 753– 756 (2019). URL https://www.science.org/doi/10. 1126/science.aaw1611. Publisher: American Associa- tion for the Advancement of Science

    2019

  31. [39]

    & Scalapino, D

    Dagotto, E., Riera, J. & Scalapino, D. Superconduc- tivity in ladders and coupled planes. Physical Review B 45, 5744–5747 (1992). URL https://link.aps.org/ doi/10.1103/PhysRevB.45.5744. Publisher: American Physical Society

    1992 doi

  32. [40]

    Quantum Phase Transitions in Quasi- One-Dimensional Sys- tems

    Giamarchi, T. Quantum Phase Transitions in Quasi- One-Dimensional Sys- tems. In Understanding Quantum Phase Transitions (CRC Press, 2010). Num Pages: 22

    2010

  33. [41]

    Nawa, K. et al. Triplon band splitting and topologically protected edge states in the dimerized antiferromagnet. Nature Communications 10, 2096 (2019). URL https:// www.nature.com/articles/s41467-019-10091-6 . Pub- lisher: Nature Publishing Group

    2019

  34. [42]

    Zhang, X. et al. Universal control of four sin- glet–triplet qubits. Nature Nanotechnology 1–7 (2024). URL https://www.nature.com/articles/ s41565-024-01817-9 . Publisher: Nature Publishing Group

    2024

  35. [43]

    Bulaev, D. V. & Loss, D. Electric Dipole Spin Reso- nance for Heavy Holes in Quantum Dots.Physical Review Letters 98, 097202 (2007). URL https://link.aps. org/doi/10.1103/PhysRevLett.98.097202. Publisher: American Physical Society

    2007 doi

  36. [44]

    Hendrickx, N. W. et al. Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity. Nature Materials 23, 920–927 (2024). URL https://www.nature.com/articles/ s41563-024-01857-5 . Publisher: Nature Publishing Group

    2024

  37. [45]

    Froning, F. N. M. et al. Ultrafast hole spin qubit with gate-tunable spin–orbit switch functionality. Nature Nanotechnology 16, 308–312 (2021). URL https://www. nature.com/articles/s41565-020-00828-6 . Publisher: 12 Nature Publishing Group

    2021

  38. [46]

    A., Bassi, M., Schmitt, V

    Mauro, L., Rodr ´ ıguez-Mena, E. A., Bassi, M., Schmitt, V. & Niquet, Y.-M. Geometry of the dephasing sweet spots of spin-orbit qubits. Physical Review B 109, 155406 (2024). URL https://link.aps.org/doi/10. 1103/PhysRevB.109.155406. Publisher: American Phys- ical Society

    2024

  39. [47]

    & Loss, D

    Het´ enyi, B., Kloeffel, C. & Loss, D. Exchange interac- tion of hole-spin qubits in double quantum dots in highly anisotropic semiconductors. Physical Review Research 2, 033036 (2020). URL https://link.aps.org/doi/10. 1103/PhysRevResearch.2.033036. Publisher: American Physica...

    2020

  40. [48]

    Wang, C.-A. et al. Modeling of planar germanium hole qubits in electric and magnetic fields. npj Quantum In- formation 10, 1–9 (2024). URL https://www.nature. com/articles/s41534-024-00897-8 . Publisher: Nature Publishing Group

    2024

  41. [49]

    Jirovec, D. et al. Dynamics of Hole Singlet-Triplet Qubits with Large $g$-Factor Differences. Physical Re- view Letters 128, 126803 (2022). URL https://link. aps.org/doi/10.1103/PhysRevLett.128.126803. Pub- lisher: American Physical Society

    2022 doi

  42. [50]

    Harvey-Collard, P. et al. Spin-orbit Interactions for Singlet-Triplet Qubits in Silicon. Physical Review Letters 122, 217702 (2019). URL https://link.aps.org/doi/ 10.1103/PhysRevLett.122.217702. Publisher: Ameri- can Physical Society

    2019 doi

  43. [51]

    Kelly, E. G. et al. Identifying and mitigating errors in hole spin qubit readout (2025). URL http://arxiv.org/ abs/2504.06898. ArXiv:2504.06898 [cond-mat]

    2025 arXiv

  44. [52]

    G., Tokura, Y

    Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current Rectification by Pauli Exclusion in a Weakly Coupled Double Quantum Dot System. Science 297, 1313–1317 (2002). URL https://www.science.org/ doi/full/10.1126/science.1070958. Publisher: Amer- ican Association for the Adv...

    2002 doi

  45. [53]

    Engel, H.-A. et al. Measurement Efficiency and $n$- Shot Readout of Spin Qubits. Physical Review Letters 93, 106804 (2004). URL https://link.aps.org/doi/ 10.1103/PhysRevLett.93.106804. Publisher: American Physical Society

    2004 doi

  46. [54]

    Petta, J. R. et al. Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots. Science 309, 2180–2184 (2005). URL https://www.science. org/doi/10.1126/science.1116955. Publisher: Amer- ican Association for the Advancement of Science

    2005 doi

  47. [55]

    Seedhouse, A. E. et al. Pauli Blockade in Silicon Quan- tum Dots with Spin-Orbit Control. PRX Quantum 2, 010303 (2021). URL https://link.aps.org/doi/10. 1103/PRXQuantum.2.010303. Publisher: American Phys- ical Society

    2021

  48. [56]

    Lundberg, T. et al. Non-symmetric Pauli spin block- ade in a silicon double quantum dot. npj Quantum In- formation 10, 1–12 (2024). URL https://www.nature. com/articles/s41534-024-00820-1 . Publisher: Nature Publishing Group

    2024

  49. [57]

    Nurizzo, M. et al. Complete Readout of Two-Electron Spin States in a Double Quantum Dot. PRX Quantum 4, 010329 (2023). URL https://link.aps.org/doi/10. 1103/PRXQuantum.4.010329. Publisher: American Phys- ical Society

    2023

  50. [58]

    V., Bosco, S

    Meinersen, C. V., Bosco, S. & Rimbach-Russ, M. Quan- tum geometric protocols for fast high-fidelity adiabatic state transfer (2024). URL http://arxiv.org/abs/ 2409.03084. ArXiv:2409.03084 [quant-ph]

    2024

  51. [59]

    Impertro, A. et al. Local Readout and Control of Current and Kinetic Energy Operators in Opti- cal Lattices. Physical Review Letters 133, 063401 (2024). URL https://link.aps.org/doi/10.1103/ PhysRevLett.133.063401. Publisher: American Physi- cal Society

    2024

  52. [60]

    Geyer, S. et al. Anisotropic exchange interaction of two hole-spin qubits. Nature Physics 20, 1152– 1157 (2024). URL https://www.nature.com/articles/ s41567-024-02481-5 . Publisher: Nature Publishing Group

    2024

  53. [61]

    Saez-Mollejo, J. et al. Exchange anisotropies in microwave-driven singlet-triplet qubits. Nature Commu- nications 16, 3862 (2025). URL https://www.nature. com/articles/s41467-025-58969-y . Publisher: Nature Publishing Group

    2025

  54. [62]

    Jurcevic, P. et al. Spectroscopy of Interacting Quasi- particles in Trapped Ions. Physical Review Letters 115, 100501 (2015). URL https://link.aps.org/doi/10. 1103/PhysRevLett.115.100501. Publisher: American Physical Society

    2015

  55. [63]

    & Moore, J

    Serbyn, M. & Moore, J. E. Spectral statistics across the many-body localization transition. Physical Review B 93, 041424 (2016). URL https://link.aps.org/ doi/10.1103/PhysRevB.93.041424. Publisher: Ameri- can Physical Society

    2016 doi

  56. [64]

    & Huse, D

    Oganesyan, V. & Huse, D. A. Localization of interacting fermions at high temperature. Physical Review B 75, 155111 (2007). URL https://link.aps.org/doi/10. 1103/PhysRevB.75.155111. Publisher: American Physi- cal Society

    2007

  57. [65]

    Ivlev, A. S. et al. Coupled vertical double quantum dots at single-hole occupancy. Applied Physics Letters 125, 023501 (2024). URL https://doi.org/10.1063/ 5.0198274

    2024

  58. [66]

    Qiao, H. et al. Coherent Multispin Exchange Coupling in a Quantum-Dot Spin Chain. Physical Review X 10, 031006 (2020). URL https://link.aps.org/doi/10. 1103/PhysRevX.10.031006. Publisher: American Physi- cal Society

    2020

  59. [67]

    Rao, A. S. et al. Modular Autonomous Virtualiza- tion System for Two-Dimensional Semiconductor Quan- tum Dot Arrays. Physical Review X 15, 021034 (2025). URL https://link.aps.org/doi/10.1103/ PhysRevX.15.021034. Publisher: American Physical So- ciety

    2025

  60. [68]

    Hsiao, T.-K. et al. Efficient Orthogonal Control of Tunnel Couplings in a Quantum Dot Array. Physical Review Ap- plied 13, 054018 (2020). URL https://link.aps.org/ doi/10.1103/PhysRevApplied.13.054018. Publisher: American Physical Society

    2020 doi

  61. [69]

    I”, the initialization point deep in the (0,2) charge state, where a singlet is initialized after a typical waiting time of 20 µs; “O

    Lodari, M. et al. Low percolation density and charge noise with holes in germanium. Materials for Quantum Technology 1, 011002 (2021). URL https://dx.doi. org/10.1088/2633-4356/abcd82. Publisher: IOP Pub- lishing. 1 Supplemental Materials: Site-resolved magnon and triplon dyna...

    2021 doi

  62. [70]

    3j was taken

    The relative voltage value of 0 corresponds to the voltage configuration for which Fig. 3j was taken. Away from that center point, the oscillations (corresponding to the spin-up probabilities of dots 2 and 5, respectively) become less regular and show a more complex pattern. (...

  63. [71]

    phase boundary

    For the regime where both parallel exchanges are equal, which we tuned up for the measurements of Fig. 4d-e, the final interaction Hamiltonian is an XXZ Hamiltonian with an anisotropy parameter ∆ = 0 .5, which simply reads: H3Q,int = J ∥ 4 2X i=1 σx i σx i+1 + σy i σy i+1 + 1 ...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.