Pith. sign in

REVIEW 3 major objections 4 minor 52 references

On a four-qubit silicon spin device, a sequential Monte Carlo particle filter turns each single-shot bit into a real-time Hamiltonian update, cutting per-update measurements from 100 to 1 and roughly doubling coherence time.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 14:57 UTC pith:FQNIH7DJ

load-bearing objection The hardware-level SMC feedback on four spin qubits, including active exchange-coupling stabilization, is a genuine first — but the headline SMC-vs-BE comparison is unfair because SMC starts from an EDSR-calibrated prior that BE is not given. the 3 major comments →

arxiv 2607.26480 v1 pith:FQNIH7DJ submitted 2026-07-29 quant-ph

Feedback stabilization of multi-qubit Hamiltonian parameters enabled by single-shot measurement-based sequential Monte Carlo

Hyeongyu Jang , Jaemin Park , Younguk Song , Jinwoong Kim , Hanseo Sohn , Lucas E. A. Stehouwer , Davide Degli Esposti , Giordano Scappucci
show 1 more author
Dohun Kim
This is my paper
classification quant-ph
keywords sequential Monte Carloparticle filterspin qubitsfeedback controlHamiltonian parameter estimationsingle-shot measurementexchange couplingcoherence time
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims that a sequential Monte Carlo (SMC) particle filter running on an FPGA can turn every single-shot bit of a spin-qubit measurement into an update of the qubit's Hamiltonian parameters, replacing the 80–100 averaged shots conventionally needed for Bayesian frequency estimation. On a four-qubit silicon/silicon-germanium device, the filter simultaneously tracks the resonance frequencies of all four qubits; active feedback on the microwave drive cuts frequency fluctuations by roughly half and raises coherence times by about 1.5 to 1.9 times compared with Bayesian feedback. The same filter estimates the exchange coupling J between a pair of qubits from two bits per update, locks it to its 3.8 MHz target, reduces two-qubit phase drift by about 80–88%, and lifts CNOT calibration visibility from 76% to 89%. The deeper claim is that estimation error falls as 1/N_particles, so extra classical computation can substitute for repeated quantum measurement, shifting the feedback bottleneck from measurement latency to FPGA resources.

Core claim

The central claim is that a recursive particle filter — particles propagated by an Ornstein-Uhlenbeck state model and reweighted by the binary Ramsey-outcome likelihood — produces a posterior mean accurate enough to drive real-time feedback after a single shot, not after the ~100 shots used by a Bayesian estimator. On the four-qubit device this makes the per-update measurement count one bit for individual qubit frequencies and two bits for an exchange coupling, gives an approximately twofold coherence-time improvement over Bayesian feedback for all four qubits, and, for the first time in semiconductor spin qubits, stabilizes a two-qubit coupling in closed loop. The paper reports that the res

What carries the argument

The carrying object is the sequential Monte Carlo particle filter, implemented on an FPGA with 2^12 particles. Each particle is a hypothesized frequency that diffuses according to an Ornstein-Uhlenbeck process; after a single Ramsey shot, each particle is reweighted by the likelihood of the observed bit, and the weighted mean becomes the new frequency estimate. For the two-qubit parameter, two interleaved Ramsey probes produce two bits that update f_CROT and f_zCROT, whose difference is J. The mechanism that makes the framework work is the O(1/N_particles) convergence of the weighted-particle approximation to the true posterior: increasing the particle count reduces estimation error, so clas

Load-bearing premise

The central claim depends on the SMC filter being seeded with an informative prior from an EDSR calibration that costs more than 10^4 measurements (S0, Fig. 1d), while the Bayesian comparison starts from a uniform prior (Fig. 1f), and on the noise-model parameters D and tau_c being tuned against the same two-qubit CPhase data (Fig. 4f) they are then used to explain; remove that prior information or that in-sample tuning and the one-shot speedup and reported error suppression

What would settle it

Repeat the single-qubit comparison with SMC initialized from a flat prior, or add the more than 10^4 EDSR shots to the SMC measurement budget; separately freeze D and tau_c to values extracted from noise data taken before the CPhase feedback run. If the coherence-time doubling or the reduction of sigma_phi from 0.35/0.42 rad to 0.04/0.08 rad disappears, the one-shot advantage is inherited from prior calibration and in-sample model tuning.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Per-update measurement count drops from about 100 to 1 for qubit frequencies, so feedback can run at roughly two orders of magnitude higher rate; estimation cycle times are 300 microseconds per qubit and 1 millisecond for the pair.
  • With simultaneous feedback on all four qubits, frequency fluctuation standard deviations fall by 48–70%, and coherence times increase from 3.78–6.54 microseconds to 7.13–10.05 microseconds, roughly doubling the Bayesian-feedback values.
  • Two-bit estimation stabilizes the exchange coupling: J fluctuation drops about 27%, CPhase phase drift is held near 0.04–0.08 rad, and the phase-noise error falls from 0.072 to 0.002.
  • CNOT calibration becomes reproducible: mean visibility rises from 76.2% ± 8.9% to 88.7% ± 0.9%, largely eliminating stochastic calibration failure between consecutive runs.
  • Because estimation error scales as O(1/N_particles), adding or parallelizing FPGA particles should improve tracking further without any additional quantum measurements.

Where Pith is reading between the lines

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

  • Inference: if the EDSR-seeded prior were replaced by an uninformative prior, the one-shot advantage would shrink or vanish; the honest comparison would count the more than 10^4 EDSR shots as initialization cost.
  • Inference: the same filter could be applied to any binary-outcome parameter drift — tunnel couplings, charge noise, flux noise in other qubit platforms — wherever the likelihood P(m|parameter) is known, making this a general calibration primitive rather than a spin-qubit-specific trick.
  • Inference: because D and tau_c are tuned on the same CPhase data used to evaluate feedback, a hold-out test with parameters fixed a priori is needed to separate true suppression from in-sample fitting; the reported sigma_phi values may be optimistic.
  • Inference: the O(1/N_particles) convergence suggests a resource trade-off — classical FPGA memory and parallelism can substitute for quantum measurement averaging, so for large arrays the main scaling bottleneck may be classical control hardware, not per-qubit readout.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports an FPGA-implemented sequential Monte Carlo (SMC) particle filter for real-time estimation and feedback stabilization of Hamiltonian parameters in a four-qubit 28Si/SiGe quantum dot device. The authors claim that a single binary Ramsey outcome (one bit) per update is sufficient to estimate qubit resonance frequencies, replacing a Bayesian estimation (BE) baseline that uses Nshot = 100, thereby increasing the feedback rate by two orders of magnitude and roughly doubling coherence times. They further extend the method to estimate the exchange coupling J from two bits per update, and demonstrate stabilized CPhase/CNOT operation with substantially reduced phase drift. The experimental data include Ramsey traces, power spectral densities, CPhase oscillations, and visibility measurements.

Significance. If the central claims hold, this is a valuable experimental advance: it would be the first demonstration of active stabilization of a two-qubit exchange parameter in semiconductor spin qubits, and it would show that a standard particle-filtering algorithm, running in real time, can dramatically reduce the quantum-measurement overhead for frequency calibration. The paper is generally clearly written, and the authors provide useful details on the state-space model, FPGA implementation, simulation cross-checks, and raw-data handling. However, the headline quantitative claims depend on two comparisons that are not currently fair: the SMC filter starts with an EDSR-calibrated informative prior while the BE baseline starts from a uniform prior, and the OU model parameters D and tau_c are tuned with the same CPhase metric used to report the error suppression. These issues are fixable, but they must be addressed before the stated improvements can be accepted at face value.

major comments (3)
  1. [S0, Fig. 1d-f] The headline comparison between SMC and BE is asymmetric. S0 sets the initial mean mu0 to the EDSR-spectroscopy frequencies with Sigma0 = 200 kHz, while the BE baseline is initialized with a uniform prior (Fig. 1f). The text explicitly states that EDSR spectroscopy requires more than 10^4 measurements per qubit, and these measurements are not counted in the SMC cost. With a 200-kHz prior, one Ramsey bit refines a frequency that is already known; BE from a uniform prior must first locate the resonance. Therefore the claimed reduction from Nshot = 100 to Nshot = 1 and the two-orders-of-magnitude feedback-rate improvement conflate the SMC recursion with the prior information. The authors should either initialize both methods with the same prior, or add an SMC run from an uninformative prior, or amortize the EDSR calibration cost into the SMC overhead. Without such a comparison, the central
  2. [Fig. 4f; Methods 'Nonlinear state-space model'; Supplementary Data Table 2] The two-qubit error-suppression result is partly in-sample. The text states: 'sigma_phi is evaluated to optimize the SMC model parameters, namely the diffusion coefficient D and noise correlation time tau_c' (Fig. 4f). The same sigma_phi is then used to quantify the reduction in phase drift (88% and 81% suppression) and the corresponding error rate of 0.002. Because D and tau_c are tuned against the same metric used for the reported improvement, the quoted suppression may be optimistic. The authors should provide a cross-validation procedure (e.g., estimating D and tau_c on a calibration segment and evaluating sigma_phi on an independent segment), or show that the results are insensitive to the chosen parameter values. This is essential for the two-qubit stabilization claim.
  3. [Fig. 1c; Methods 'Qubit initialization'] The claim that each update uses 'one bit of data from a single-shot measurement' is misleading as stated. The adaptive initialization protocol compares the spin parity measured before qubit manipulation (mi) with that measured after manipulation (mf), so each processed binary outcome m actually requires two parity readouts. If the authors consider the processed XOR as the 'one bit', this should be stated explicitly, and the physical measurement overhead should be acknowledged. The same issue applies to the 'two bits' for the two-qubit J estimation. This does not necessarily invalidate the SMC-vs-BE comparison if BE uses the same initialization, but it affects the absolute claim of minimized quantum-measurement overhead.
minor comments (4)
  1. [Fig. 3e] The abstract's 'approximately twofold increase in coherence time' is not directly evident from the reported no-feedback values: for Q1-Q4 the ratios are about 1.46, 1.43, 1.89, and 1.54. Please report the BE-feedback T2* values explicitly and specify the comparison basis for the twofold claim.
  2. [References] References 12 and 47 are dated 2026 and lack complete page numbers; please update or verify these citations. Also, the arXiv identifier in the header is not standard for published work; please confirm the correct preprint identifier.
  3. [Data availability] The data availability statement says data are available 'upon request'. Given the emphasis on reproducible methodology, I encourage the authors to deposit the raw experimental data and the SMC/FPGA code in a public repository.
  4. [Supplementary Note 3] The derivation of the 1/Nptl variance assumes independent and identically distributed samples, whereas particle-filter samples are correlated. The authors cite rigorous convergence results, but the intermediate argument in Supplementary Note 3 is heuristic and should be labeled as such.

Circularity Check

0 steps flagged

No significant circularity: the SMC feedback results are measured experimental outputs, not derivations that reduce to their inputs.

full rationale

The paper is an experimental demonstration of SMC-based feedback, not a derivation in which a predicted quantity is defined in terms of the fitted input. The SMC update equations (S0–S3, Eqs. 1–4) are standard Bayesian filtering; the initial mean μ0 from EDSR and Σ0=200 kHz are explicitly stated warm-start conditions, and the EDSR cost (>10^4 measurements) is disclosed in the text. The BE comparison starts from a uniform prior, which makes the Nshot=1 vs 100 comparison asymmetrical and limits the strength of the headline feedback-rate improvement, but this is a cost-accounting and prior-design issue rather than a circular step: the reported T2*, PSD cutoffs, σ(J), σ_φ, and CNOT visibility are measured closed-loop quantities, not identities implied by the prior. Similarly, D and τ_c are fitted from experimental data and optimized against σ_φ (Fig. 4f, Methods); this is transparent in-sample tuning of control-model parameters, not a fitted parameter being relabeled as an independent prediction, and the suppression percentages are experimental outcomes with the chosen parameters. Self-citations (Refs 5, 7) supply external baseline values and are not used as a uniqueness theorem or as the load-bearing justification for the SMC framework, which is standard and independently referenced (Refs 28–29). No equation in the paper reduces to its own input by construction, so there is no qualifying circular step.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central demonstration rests on a standard Bayesian filtering setup plus a device-specific OU noise model. The load-bearing inputs the paper adds beyond standard math are an informative EDSR prior, calibrated Ramsey-likelihood constants, and per-parameter D and tau_c values tuned from the same experiments whose performance they are used to report. No new physical entities are introduced.

free parameters (5)
  • D (diffusion coefficient) per qubit/parameter = 60 kHz^2/ms (fQ1-fQ4); 70 (fCROT); 75 (fzCROT)
    OU noise strength in Eq. (2); determined from experimental data and optimized to minimize sigma_phi in Fig. 4f; listed in Supp Data Table 2.
  • tau_c (noise correlation time) per qubit/parameter = 150 ms (fQ); 100 ms (fCROT/fzCROT)
    Mean-reversion timescale in Eqs. (2)-(3); system-dependent and tuned in Fig. 4f.
  • Initial particle variance Sigma0 = 200 kHz
    Set by hand in S0; controls the initial spread of the particle cloud and affects early convergence.
  • Initial mean mu0 from EDSR spectra = qubit-specific, not tabulated
    S0 initializes the filter at EDSR-measured frequencies; the one-shot claim depends on this informative prior, and its calibration cost is excluded from the reported feedback rate.
  • Ramsey likelihood constants alpha, beta, theta
    Enter Eq. (4) for the single-shot likelihood; alpha is the rotation-axis parameter, beta the visibility, theta the initial phase. Calibrated from the Ramsey/readout setup; no values or uncertainties are reported.
axioms (6)
  • domain assumption The unknown qubit frequency follows the Ornstein-Uhlenbeck process in Eqs. (2)-(3) with constant D and tau_c.
    Used in the SMC prediction step; if the real noise is non-stationary or not OU, the predicted particle distributions and estimates are biased.
  • domain assumption Single-shot Ramsey outcome probabilities are given exactly by Eq. (4) with calibrated alpha, beta, theta.
    Weight updates use this likelihood; unmodeled readout errors or non-sinusoidal fringes would distort the posterior.
  • domain assumption Noise is quasi-static within each 280 us cycle and diffuses between cycles.
    Assumed in Supp Note 3 to simulate BE and SMC; supports the interpretation of the Nshot optimum in Fig. 2a.
  • ad hoc to paper The initial mean mu0 from EDSR spectra with Sigma0 = 200 kHz constitutes an adequate prior for one-shot SMC.
    S0. The headline one-bit performance depends on this prior; the EDSR calibration itself costs more than 10^4 measurements and is not counted in the Nshot comparison.
  • domain assumption CPhase phase fluctuations are Gaussian, so epsilon = 1 - exp(-sigma_phi^2 / 2).
    Supp Note 6. Converts measured sigma_phi into the quoted 0.2% phase-noise error rate.
  • domain assumption The Q12 exchange Hamiltonian and transition frequencies in Supp Note 4 Eqs. (3)-(5) describe the device.
    Standard silicon spin-qubit model used to interpret J = fCROT - fzCROT and the CNOT phase calibration.

pith-pipeline@v1.3.0-daily-deepseek · 18195 in / 17958 out tokens · 202611 ms · 2026-08-01T14:57:11.486029+00:00 · methodology

0 comments
read the original abstract

Fast measurement, signal processing, and accurate estimation of Hamiltonian parameters are essential for feedback control in quantum-classical interface circuitry. However, existing frequentist and Bayesian inference methods typically require a large number of measurements to achieve the accuracy needed to mitigate qubit decoherence. Consequently, feedback control of semiconductor qubits has largely been limited to single-qubit frequency stabilization, whereas two-qubit parameter stabilization remains experimentally unexplored. Here, we demonstrate a real-time feedback framework based on sequential Monte Carlo estimation using one bit of data from a single-shot measurement. Using a four-qubit semiconductor quantum dot device, we rapidly estimate individual qubit frequencies, yielding an approximately twofold increase in coherence time compared with a conventional Bayesian strategy. Moreover, sequential two-qubit parameter estimation using two bits of data enables stabilization of qubit-qubit coupling, allowing both quasi-static frequency drift and exchange-interaction noise to be estimated and suppressed. By shortening the time required for precise parameter estimation, these results demonstrate the importance of the synergistic development of classical and quantum electronics for building robust and scalable quantum technologies in fluctuating environments.

Figures

Figures reproduced from arXiv: 2607.26480 by Davide Degli Esposti, Dohun Kim, Giordano Scappucci, Hanseo Sohn, Hyeongyu Jang, Jaemin Park, Jinwoong Kim, Lucas E. A. Stehouwer, Younguk Song.

Figure 1
Figure 1. Figure 1: Device, circuit, and estimation framework. a. False-colored scanning electron microscopy image of the 28Si/SiGe device. Purple, green, and blue denote the first, second, and third metallic gate layers, respectively. Quantum dots located between sensor dots SD1 and SD2 are defined by screening gates (purple), plunger gates (blue, P1–P4), and barrier gates (green, B0–B4). b. Histogram of radiofrequency-demod… view at source ↗
Figure 2
Figure 2. Figure 2: Analysis of estimation methods. a. Quasi-static variances for each of the four qubits as a function of the number of measurements and the estimation time. The data are fitted to exp(-A × Nshot) × B, yielding A = 0.008, 0.005, 0.004, and 0.012 and B = 2,302, 2,539, 4,669, and 3,102 kHz2 for Q1–Q4, respectively. The fitted curves are not shown for clarity. Gray triangles indicate the mean squared error (MSE)… view at source ↗
Figure 4
Figure 4. Figure 4: Exchange-coupling feedback. a. Experimental sequence comprising the zero￾controlled-rotation frequency (fzCROT) probe, controlled-rotation frequency (fCROT) probe, and corrected controlled-NOT (CNOT) operation used for the experiments shown in panels d–g. The gray dashed box indicates an optional  pulse. b. Schematic blocks representing the feedback-initialization protocol. c. Example time traces of the e… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

52 extracted references

  1. [2]

    Yang, C. H. et al. Silicon qubit fidelities approaching incoherent noise limits via pulse engineering. Nat. Electron. 2, 151–158 (2019)

    2019

  2. [4]

    Nakajima, T. et al. Coherence of a Driven Electron Spin Qubit Actively Decoupled from Quasistatic Noise. Phys. Rev. X 10, 011060 (2020)

    2020

  3. [5]

    Kim, J. et al. Approaching Ideal Visibility in Singlet -Triplet Qubit Operations Using Energy -Selective Tunneling-Based Hamiltonian Estimation. Phys. Rev. Lett. 129, 040501 (2022)

    2022

  4. [6]

    Berritta, F. et al. Real-time two-axis control of a spin qubit. Nat. Commun. 15, 1676 (2024)

    2024

  5. [8]

    Steinacker, P. et al. Industry-compatible silicon spin-qubit unit cells exceeding 99% fidelity. Nature 646, 81– 87 (2025)

    2025

  6. [9]

    Acosta, V . M. et al. Dynamic Stabilization of the Optical Resonances of Single Nitrogen-Vacancy Centers in Diamond. Phys. Rev. Lett. 108, 206401 (2012)

    2012

  7. [10]

    Johnson, K. G. et al. Active stabilization of ion trap radiofrequency potentials. Rev. Sci. Instrum. 87, 053110 (2016)

    2016

  8. [11]

    Vepsäläinen, A. et al. Improving qubit coherence using closed-loop feedback. Nat. Commun. 13, 1932 (2022)

    1932

  9. [12]

    Real-Time Adaptive Tracking of Fluctuating Relaxation Rates in Superconducting Qubits

    Berritta, F. Real-Time Adaptive Tracking of Fluctuating Relaxation Rates in Superconducting Qubits. Phys. Rev. X 16, (2026)

    2026

  10. [13]

    Quantum Computing in the NISQ era and beyond

    Preskill, J. Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018)

    2018

  11. [14]

    Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)

    1995

  12. [15]

    Kitaev, A. Yu. Fault-tolerant quantum computation by anyons. Annals of Physics 303, 2–30 (2003)

    2003

  13. [16]

    Fowler, A. G. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A 86, (2012)

    2012

  14. [17]

    Fedele, F. et al. Simultaneous Operations in a Two -Dimensional Array of Singlet -Triplet Qubits. PRX Quantum 2, 040306 (2021)

    2021

  15. [18]

    Lawrie, W. I. L. et al. Simultaneous single-qubit driving of semiconductor spin qubits at the fault -tolerant threshold. Nat. Commun. 14, 3617 (2023)

    2023

  16. [19]

    Undseth, B. et al. Nonlinear Response and Crosstalk of Electrically Driven Silicon Spin Qubits. Phys. Rev. Appl. 19, 044078 (2023)

    2023

  17. [20]

    M., Hazard, T

    Zajac, D. M., Hazard, T. M., Mi, X., Nielsen, E. & Petta, J. R. Scalable Gate Archi tecture for a One - Dimensional Array of Semiconductor Spin Qubits. Phys. Rev. Appl. 6, 054013 (2016)

    2016

  18. [21]

    Borsoi, F. et al. Shared control of a 16 semiconductor quantum dot crossbar array. Nat. Nanotechnol. 19, 21– 27 (2024)

    2024

  19. [23]

    Reiner, J. et al. High-fidelity initialization and control of electron and nuclear spins in a four -qubit register. Nat. Nanotechnol. 19, 605–611 (2024)

    2024

  20. [24]

    Sergeevich, A., Chandran, A., Combes, J., Bartlett, S. D. & Wiseman, H. M. Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis. Phys. Rev. A 84, 052315 (2011)

    2011

  21. [26]

    Yoneda, J. et al. Noise-correlation spectrum for a pair of spin qubits in silicon. Nat. Phys. 19, 1793–1798 (2023)

    2023

  22. [27]

    Dumoulin Stuyck, N. et al. Silicon spin qubit noise characterization usin g real-time feedback protocols and wavelet analysis. Appl. Phys. Lett. 124, 114003 (2024)

    2024

  23. [28]

    & Andrieu, C

    Doucet, A., Godsill, S. & Andrieu, C. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing 10, 197–208 (2000)

    2000

  24. [30]

    & Hodgkiss, W

    Yardim, C., Gerstoft, P. & Hodgkiss, W. S. Tracking Refractivity from Clutter Using Kalman and Particle Filters. IEEE Transactions on Antennas and Propagation 56, 1058–1070 (2008)

    2008

  25. [31]

    Hajieghrary, H., Tomás, A. F. & Hsieh, M. A. An information theoretic source seeking strategy for plume tracking in 3D turbulent fields. in 2015 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR) 1–8 (2015). doi:10.1109/SSRR.2015.7442994

    arXiv 2015

  26. [32]

    Amor, N., Rasool, G., Bouaynaya, N. C. & Shterenberg, R. Constrained particle filtering for movement identification in forearm prosthesis. Signal Processing 161, 25–35 (2019)

    2019

  27. [33]

    Rathinam, M. & Yu, M. Stochastic filtering of reaction networks partially observed in time snapshots. Journal of Computational Physics 515, 113265 (2024)

    2024

  28. [34]

    Chase, B. A. & Geremia, J. M. Single-shot parameter estimation via continuous quantum measurement. Phys. Rev. A 79, 022314 (2009)

    2009

  29. [36]

    Degli Esposti, D. et al. Wafer-scale low-disorder 2DEG in 28Si/SiGe without an epitaxial Si cap. Appl. Phys. Lett. 120, 184003 (2022)

    2022

  30. [37]

    J., Wahlgren, P., Kozhevnikov, A

    Schoelkopf, R. J., Wahlgren, P., Kozhevnikov, A. A., Delsing, P. & Prober, D. E. The Radio -Frequency Single-Electron Transistor (RF -SET): A Fast and Ultrasensitive Electrometer. Science 280, 1238–1242 (1998)

    1998

  31. [38]

    J., Marcus, C

    Reilly, D. J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Fast single -charge sensing with a rf quantum point contact. Appl. Phys. Lett. 91, 162101 (2007)

    2007

  32. [41]

    Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633–637 (2018)

    2018

  33. [42]

    Pioro-Ladrière, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776–779 (2008)

    2008

  34. [43]

    Kotecha, J. H. & Djuric, P. M. Gaussian particle filtering. IEEE Transactions on Signal Processing 51, 2592– 2601 (2003)

    2003

  35. [44]

    Uhlenbeck, G. E. On the Theory of the Brownian Motion. Phys. Rev. 36, 823–841 (1930)

    1930

  36. [46]

    & Djurić, P

    Elvira, V ., Míguez, J. & Djurić, P. M. Adapting the Number of Particles in Sequential Monte Carlo Methods Through an Online Scheme for Convergence Assessment. IEEE Transactions on Signal Processing 65, 1781– 1794 (2017)

    2017

  37. [47]

    Rojas-Arias, J. S. et al. Inferring Charge-Noise Source Locations from Correlations in Spin Qubits. Phys. Rev. Lett. 136, 027001 (2026)

    2026

  38. [48]

    Martinis, J. M. & Geller, M. R. Fast adiabatic qubit gates using only σz control. Phys. Rev. A 90, 022307 (2014)

    2014

  39. [49]

    Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022). Acknowledgments This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (Ministry of Science and ICT (MSIT)) (RS -2023-00283291), RS - 2024-00413957, SRC Center for Quantum Coherence in Conde...

    2022

  40. [50]

    Seedhouse, A. E. et al. Pauli Blockade in Silicon Quantum Dots with Spin -Orbit Control. PRX Quantum 2, 010303 (2021)

    2021

  41. [51]

    Niegemann, D. J. et al. Parity and Singlet-Triplet High-Fidelity Readout in a Silicon Double Quantum Dot at 0.5 K. PRX Quantum 3, 040335 (2022)

    2022

  42. [52]

    Philips, S. G. J. et al. Universal control of a six -qubit quantum processor in silicon. Nature 609, 919–924 (2022)

    2022

  43. [53]

    Takeda, K. et al. Rapid single-shot parity spin readout in a silicon double quantum dot with fidelity exceeding 99%. npj Quantum Inf 10, 1–6 (2024)

    2024

  44. [54]

    Shulman, M. D. et al. Suppressing qubit dephasing using real -time Hamiltonian estimation. Nat. Commun. 5, 5156 (2014)

    2014

  45. [55]

    Noiri, A. et al. Fast universal quantum gate above the fault -tolerance threshold in silicon. Nature 601, 338– 342 (2022)

    2022

  46. [56]

    Park, J. et al. Passive and active suppression of transduced noise in silicon spin qubits. Nat. Commun. 16, 78 (2025)

    2025

  47. [57]

    Doucet, N

    A. Doucet, N. De Freitas, and N. Gordon, Eds. Sequential Monte Carlo Methods in Practice. (Springer, New York, NY , 2001). doi:10.1007/978-1-4757-3437-9

    doi:10.1007/978-1-4757-3437-9 2001

  48. [58]

    Crisan, P

    D. Crisan, P. Del Moral & T. Lyons. Discrete Filtering Using Branching and Interacting Particle Systems. Markov Proc. Rel. Fields 5, 293–318 (1999)

    1999

  49. [59]

    & Doucet, A

    Crisan, D. & Doucet, A. A survey of convergence results on particle filtering methods for practitioners. IEEE Transactions on Signal Processing 50, 736–746 (2002)

    2002

  50. [60]

    Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022)

    2022

  51. [61]

    & DiVincenzo, D

    Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

    1998

  52. [62]

    Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature 569, 532–536 (2019)

    2019