Pith. sign in

REVIEW 3 major objections 5 minor 45 references

Enhancing the Dynamic Range of Quantum Sensing via Quantum Circuit Learning

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read By training global quantum gates applied after field exposure, a dense qubit sensor can recover a monotonic readout and measure a wider range of field strengths.

desk verdict A plausible variational approach to extend the dynamic range of dense qubit sensors, undercut by a demonstration that secretly uses the coupling information the method claims to do without. read the letter →

arxiv 2505.04958 v1 pith:EYFRVQY6 submitted 2025-05-08 quant-ph cond-mat.mes-hallstat.ML

Hideaki Kawaguchi , Yuichiro Mori , Takahiko Satoh , Yuichiro Matsuzaki This is my paper · ORCID
classification quant-phcond-mat.mes-hallstat.ML
keywords quantumsensingdynamicrangecircuitlearningmetrologyparameterizedcircuitsmany-bodyinteractionsqubitensemblesvariationalalgorithms
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

In dense qubit arrays used for field sensing, interactions between qubits make the measured expectation value oscillate many times as the external field grows, so a single reading no longer identifies a unique field strength. This paper proposes training a parameterized quantum circuit, applied after the qubits interact with the field, so that the measured observable matches a chosen monotonic target function of the current. In numerical simulations with 2, 3, and 4 qubits, optimized circuits make the expectation value monotonic over the target current range, restoring the one-to-one correspondence between reading and field. The authors conclude that the approach works even when the inter-qubit coupling parameters are not known, and that it offers a route to high-density, strongly interacting sensors without the need for adaptive feedback.

What carries the argument

The load-bearing object is the parameterized circuit $U(\theta)=\prod_{d=1}^{D} U^{(d)}(\theta^{(d)})$, where each layer applies evolutions under three gradient-field Hamiltonians followed by global $R_x$, $R_y$, and $R_z$ rotations with parameters shared across all qubits. This circuit is expressive enough to reshape the many-body oscillatory expectation value into a designed monotone curve. The training objective is the mean-squared error against the target $f(I)$, which defines where the sensor must be one-to-one; the observable $\hat M_z$ turns the reshaped state into a single calibration curve.

What would settle it

Re-run the same training protocol with the target function built from a deliberately wrong or incomplete estimate of $\sum_j h_j$, or with couplings held out from training, and test whether the optimized circuit still yields a monotonic response across the target interval; if monotonicity fails, the claim that unknown couplings do not need to be known is unsupported.

Watch

Extended reading notes

Core claim

The central claim is that the dynamic range of a quantum sensor is not fixed by the qubit Hamiltonian: it can be reshaped by learning. After the qubits evolve under a field-dependent Hamiltonian $H_{\mathrm{data}}$ that includes unknown inter-qubit couplings $J_{ij}$, the authors apply a layered unitary $U(\theta)$ built from global $x$-, $y$-, and $z$-rotation gates interleaved with evolutions under gradient-field Hamiltonians, then measure $\hat M_z$. The parameters $\theta$ are optimized by SLSQP to minimize the mean-squared error between the observed expectation value and a chosen monotonic target $f(I)=A L \sin(\sum_j h_j I t/(B L))$ over $N=200$ sample currents in $[-1,1]$. After training, the response becomes monotonic across the target range, the cost drops to order $10^{-7}$ to $10^{-9}$, and the estimated current uncertainty $\delta I$ is comparable to the ideal non-interacting formula near $I=0$ and smaller near the endpoints $I=\pm 0.8$. The authors state that this learned monotonicity enhances the dynamic range compared with untrained random parameters and that the method applies when inter-qubit coupling strengths are unknown.

Load-bearing premise

The demonstration assumes the target function $f(I)=A L \sin(\sum_j h_j I t/(B L))$ can be written down, which requires knowing the sum of the relative coupling strengths $\sum_j h_j$, even though the paper claims those couplings are unknown.

Editorial extensions

If this is right

  • After training, a single expectation value maps unambiguously to one field amplitude across the target range, so multi-qubit sensors can be packed densely without losing dynamic range.
  • Sensors can be calibrated by applying known currents and optimizing gate parameters rather than by fully characterizing the interaction Hamiltonian.
  • The trained circuits achieve sensitivity comparable to the ideal no-interaction bound near zero field and better sensitivity near the edges of the working range.
  • The method requires no adaptive measurement feedback, keeping the control overhead to global gates plus classical optimization.
  • The demonstrated improvement holds for the simulated sizes $L=2,3,4$, with larger circuits requiring greater depth for successful training.

Reading between the lines

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

  • If a trained circuit's monotonicity is tied to a particular coupling realization, the practical protocol may need per-device training; generalization across coupling distributions is not tested in the paper.
  • Because the target function depends on $\sum_j h_j$, a cheaper calibration estimating just that sum rather than full tomography might suffice, and the target could also be replaced by an empirically measured monotone curve.
  • The improvement in $\delta I$ near the endpoints suggests the trained circuit actively reshapes sensitivity rather than merely restoring linear response, so optimizing the target function itself could be a natural next step.
  • The paper's numerics reach only four qubits, so scaling behavior, trainability, and possible barren-plateau effects at larger $L$ remain open questions.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes a quantum circuit learning (QCL) approach to extend the dynamic range of an ensemble quantum magnetometer. After the qubits interact with an external magnetic field produced by a current I, a parameterized global quantum circuit U(theta) is applied, and the expectation value of M_z is used as the sensing signal. The circuit parameters are trained by minimizing the squared error between this expectation value and a predefined monotonic target function f(I) over N=200 current values sampled from [-1,1]. The authors simulate L=2,3,4 qubits with random inhomogeneous couplings h_j and random interactions J_ij, and report that after training the output becomes monotonic in I, with the cost converging to approximately 1e-7 to 1e-9. They also compare the resulting sensitivity delta-I with a theoretical no-interaction expression and claim improved sensitivity near the endpoints of the range.

Significance. The idea of using a variational post-processing circuit to restore a one-to-one mapping between current and signal in a dense, strongly interacting ensemble is well motivated and clearly presented. The numerical experiments show that the chosen circuit ansatz is expressive enough to reproduce the target on the training points for L=2,3,4, and the comparison with the untrained response highlights the role of training. No analytical proofs or code are provided, but the simulations are simple and in principle reproducible. However, the demonstration falls short of the central claim: the target function uses the summed coupling strength sum_j h_j, which the paper declares unknown, and the sensitivity comparison is made against a theoretical expression derived for a different measurement protocol. As written, the results establish that the circuit can fit a known target, not that the method works when the couplings are unknown.

major comments (3)
  1. [Sec. IV.A, Eq. (15)] The target function f(I) = A*L*sin((sum_j h_j) I t / (B*L)) contains the sum of the coupling strengths h_j, but Sec. IV.A explicitly assumes that the exact values of the coupling strengths are unknown and that full tomography is impractical. Since evaluating Eq. (15) at the training inputs requires the numerical value of sum_j h_j, the supervised labels are not constructible in the scenario the paper claims to address. The observed monotonic response in Fig. 3 is therefore a fit to a target that depends on the very parameters declared unknown, and it does not demonstrate the unknown-parameter capability stated in the Conclusion. A minimal fix is to replace Eq. (15) by a coupling-independent target (e.g., f(I) = A*L*sin(alpha*I) for some hyperparameter alpha) and retrain; the authors should show that the trained circuit still yields a monotonic response and an extended dynamic range in that setting.
  2. [Sec. IV.C, Fig. 4] The theoretical values shown in Fig. 4 are derived from Eq. (12), which describes the protocol of Sec. II with initial state |+>^L, Hamiltonian proportional to sigma_z, and observable M_y. The numerical simulations in Sec. IV instead start from |0...0>, use H_data in Eq. (16) with the field coupled to sigma_y, and measure M_z. These are different physical protocols, and the sensitivity formula Eq. (12) does not apply to the simulated measurement. Consequently, the claim that the trained model achieves higher sensitivity near the endpoints is a comparison against an inappropriate baseline. The authors should either derive the no-interaction delta-I for the actual protocol (sigma_y coupling, M_z measurement) or use the untrained model as the reference.
  3. [Sec. IV.B, Sec. IV.C] The entire evaluation is confined to the training range and distribution: N=200 inputs are sampled uniformly from [-1,1], and the delta-I curve in Fig. 4 is also evaluated on points in [-0.8,0.8]. The paper does not report a train/test split, statistics over random initializations, or error bars. As a result, the generality and robustness of the trained response are not established. The authors should test on an independent set of currents (e.g., a hold-out range) and report the mean and variance of the trained cost and response over multiple random seeds.
minor comments (5)
  1. [Sec. IV.B, after Eq. (21)] The passage following Eq. (21) is garbled: the tensor-product notation appears as the token NL and the sentence about the operators commuting with H_I is incomplete; it should read The tensor products of the single-qubit rotations with H_I commute.
  2. [Sec. II, Eq. (5)] The derivation of Eq. (5) would benefit from an explicit statement of the error-propagation convention; the current typesetting of the quotient is ambiguous, and the definition of delta-sigma_y should be made explicit before it is used.
  3. [Abstract and Sec. IV.B] The abstract says a sequence of parameterized quantum gates is applied, while Sec. IV.B specifies that the gates are global (the same parameters are shared across all qubits); the terminology should be harmonized to avoid confusion.
  4. [Sec. IV.A] The cost function for the proposed protocol is defined in the text but is not numbered; numbering it (e.g., as part of Eq. (14)) would make subsequent references to it clearer.
  5. [Figs. 2 and 3] Fig. 2 shows the response with all parameters set to zero, whereas Fig. 3 compares against randomly chosen untrained parameters; the captions should clarify this difference so that the two baselines are not conflated.

Circularity Check

2 steps flagged · score 7.0 of 10

The central unknown-coupling claim rests on a target function that requires the very coupling knowledge the paper says is unavailable; the demonstrated monotonic response is the training objective itself.

  1. self definitional [Sec. IV.A (Setup) and Sec. IV.B, Eq. (15)]
    "Thus, we assume that the exact values of the coupling strengths are unknown. ... The target function f(I) is defined as follows: f(I) =A·L· sin(Σ_j h_j I t/(B·L)), where A and B are hyperparameters ... We set A = B = 1 in this study."

    The paper's central claim is that the QCL method works when inter-qubit couplings are unknown (Sec. IV.A and Conclusion). But the supervised target used to train the circuit, Eq. (15), is evaluated at the numerical values of h_j that were 'set in advance' in Sec. IV.B. Computing f(I_i) for the training inputs requires the exact value of Σ_j h_j, so the demonstration presupposes precisely the knowledge the protocol claims not to need. The resulting trained monotonic response is therefore evidence for a scenario in which the summed field coupling is known, not for the unknown-coupling scenario advertised. A coupling-independent target, such as f(I) = L·sin(α I) with a fixed α, would avoid this, but no such variant is proposed or tested.

  2. fitted input called prediction [Sec. IV.A (cost function) and Sec. IV.C (Fig. 3)]
    "we define a cost function L(θ) = Σ_i |⟨ψθ,I_i|M_z|ψθ,I_i⟩ − f(I_i)|^2. Finally, we optimize this cost function with respect to θ using a classical optimization algorithm. ... By optimizing the gate parameters, the expectation value was adjusted to exhibit a monotonic response within the target range of field amplitudes, thereby expanding the dynamic range."

    The cost function directly penalizes deviation from the monotonic target f(I), and the reported result is that the trained expectation value matches this target within the training range [−1, 1]. The observed monotonic response in Fig. 3 is therefore the minimization outcome, not an independent or predictive consequence of the method. Calling this an 'expanded dynamic range' restates the training objective: the model was trained to be monotonic and then shown to be monotonic. The later δI comparison in Fig. 4 is a more independent check, but it does not repair the unknown-coupling claim, because the target that produced the trained model still depends on Σ_j h_j.

full rationale

The paper does not rely on self-citation chains or imported uniqueness theorems; its citations to the authors' prior work are peripheral. The most serious circularity is internal to the numerical demonstration. Section IV.A states that the exact coupling strengths are unknown and that full tomography is impractical, but the training target in Eq. (15) uses Σ_j h_j explicitly, and Sec. IV.B describes setting h_j in advance for the simulation. Thus the 'unknown-parameter' version of the claim is not actually demonstrated; it is assumed away by the construction of the labels. Additionally, the central demonstration of improved dynamic range is a supervised fit: the cost function (Eq. (14) and the analogous cost in Sec. IV.A) is minimized against a monotonic target, so the trained model's monotonic response in Fig. 3 is the optimization result by construction, not a prediction. Some independent content exists—e.g., the δI comparison to the non-interacting theoretical curve in Eq. (12) and Fig. 4, and the expressive-power question of whether the circuit can fit the target at all—but these do not resolve the unknown-coupling issue. Overall, the core claim is partially circular and conditional: it holds for a known-Σ_j h_j training target, while the advertised unknown-coupling scenario remains untested. Score 7 reflects that the main 'prediction' reduces to the training objective and that the central claim is undermined by the h_j-dependent target.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central validation rests on six unproved premises. Most load-bearing is the final axiom: the target function uses the summed coupling strength that the protocol claims not to need. The others are standard untested assumptions about representability, optimizer convergence, and stability of the sensing Hamiltonian.

free parameters (4)
  • A = 1
    Scale factor in the target function f(I) = A*L*sin(sum h_j I t / (B L)); set by hand and stated to control delta-I and dynamic range.
  • B = 1
    Scale factor in the target function that controls the argument of the sine and thus the target dynamic range; set by hand.
  • Circuit depth D = 20 for L=2,3; 40 for L=4
    Depth chosen to provide sufficient expressive power; no criterion or ablation is given for this choice.
  • Gradient field strength B0 = 1
    Strength of the gradient magnetic fields in Eq. (19); set to B0=1, and the profile B0_j is not fully specified.
assumptions (6)
  • domain assumption The random coupling values h_j and J_ij drawn from uniform distributions are representative of dense qubit sensors.
    The numerical validation uses one random realization family; the paper does not show robustness across different distributions or parameter regimes.
  • ad hoc to paper The parameterized circuit family U(theta) can express the target function f(I) with negligible error for L=2,3,4.
    Convergence of the cost to 1e-7 to 1e-9 is observed in the chosen instances, but no expressibility or convergence guarantee is provided.
  • ad hoc to paper SLSQP optimization converges to a near-global minimum for these small instances.
    The paper reports successful training but does not discuss local minima, initialization dependence, or optimizer hyperparameters.
  • domain assumption The Heisenberg interaction and global rotations used in U(theta) are available as control operations in the sensing device.
    The protocol requires coherent application of interaction-based unitary operations after the sensing evolution, which may be hard in the dense ensembles the paper targets.
  • domain assumption Training data and sensing runs share the same Hamiltonian realization, and that realization is stable over time.
    The method is not tested against drift or slow changes in h_j or J_ij between calibration and measurement.
  • ad hoc to paper The target function f(I) can be constructed from known quantities even though h_j are assumed unknown.
    Eq. (15) uses sum_j h_j directly, while Section IV.A states that the exact coupling strengths are unknown; this is the load-bearing gap in the demonstration.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Enhancing the Dynamic Range of Quantum Sensing via Quantum Circuit Learning." pith.science (2026). https://pith.science/paper/EYFRVQY6

@misc{pith2026250504958,
  author       = {Pith},
  title        = {Pith review of: Enhancing the Dynamic Range of Quantum Sensing via Quantum Circuit Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EYFRVQY6}},
  note         = {Machine review of arXiv:2505.04958}
}
read the original abstract

Quantum metrology is a promising application of quantum technologies, enabling the precise measurement of weak external fields at a local scale. In typical quantum sensing protocols, a qubit interacts with an external field, and the amplitude of the field is estimated by analyzing the expectation value of a measured observable. Sensitivity can, in principle, be enhanced by increasing the number of qubits within a fixed volume, thereby maintaining spatial resolution. However, at high qubit densities, inter-qubit interactions induce complex many-body dynamics, resulting in multiple oscillations in the expectation value of the observable even for small field amplitudes. This ambiguity reduces the dynamic range of the sensing protocol. We propose a method to overcome the limitation in quantum metrology by adopting a quantum circuit learning framework using a parameterized quantum circuit to approximate a target function by optimizing the circuit parameters. In our method, after the qubits interact with the external field, we apply a sequence of parameterized quantum gates and measure a suitable observable. By optimizing the gate parameters, the expectation value is trained to exhibit a monotonic response within a target range of field amplitudes, thereby eliminating multiple oscillations and enhancing the dynamic range. This method offers a strategy for improving quantum sensing performance in dense qubit systems.

Figures

Figures reproduced from arXiv: 2505.04958 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the proposed method. A system of ran [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Evaluation of the dynamic range for different num [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Dynamic range improvement of quantum sensors through QCL. Panels (a), (b), and (c) correspond to [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. Estimated values of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 20 canonical work pages

  1. [1]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature photonics 5, 222 (2011)

    2011

  2. [2]

    M. A. Taylor and W. P. Bowen, Quantum metrology and its application in biology, Physics Reports 615, 1 (2016)

    2016

  3. [3]

    D. S. Simon, G. Jaeger, A. V. Sergienko, D. S. Si- mon, G. Jaeger, and A. V. Sergienko,Quantum metrology (Springer, 2017)

    work page 2017

  4. [4]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Reviews of modern physics 89, 035002 (2017)

    2017

  5. [5]

    J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, High-sensitivity diamond magnetometer with nanoscale resolution, Nature Physics 4, 810 (2008)

    2008

  6. [6]

    J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. G. Dutt, E. Togan, A. Zibrov, et al. , Nanoscale magnetic sensing with an individual electronic spin in diamond, Nature 455, 644 (2008)

    work page 2008

  7. [7]

    Balasubramanian, I

    G. Balasubramanian, I. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, et al. , Nanoscale imaging magnetometry with diamond spins under ambient conditions, Nature 455, 648 (2008)

    2008

  8. [8]

    J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for nv-diamond magnetometry, Reviews of 7 Modern Physics 92, 015004 (2020)

    work page 2020

Show all 45 references
  1. [9]

    V. M. Acosta, E. Bauch, M. P. Ledbetter, C. Santori, K.- M. Fu, P. E. Barclay, R. G. Beausoleil, H. Linget, J. F. Roch, F. Treussart, et al. , Diamonds with a high den- sity of nitrogen-vacancy centers for magnetometry ap- plications, Physical Review B—Condensed Matter and Mat...

    2009

  2. [10]

    Bauch, S

    E. Bauch, S. Singh, J. Lee, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, L. M. Pham, N. Bar-Gill, S. F. Yelin, et al. , Decoherence of ensembles of nitrogen- vacancy centers in diamond, Physical Review B 102, 134210 (2020)

    2020

  3. [11]

    Hayashi, Y

    K. Hayashi, Y. Matsuzaki, T. Ashida, S. Onoda, H. Abe, T. Ohshima, M. Hatano, T. Taniguchi, H. Morishita, M. Fujiwara, et al., Experimental and theoretical analysis of noise strength and environmental correlation time for ensembles of nitrogen-vacancy centers in diamond, Jour-...

    2020

  4. [12]

    M. W. Mitchell and S. Palacios Alvarez, Colloquium: Quantum limits to the energy resolution of magnetic field sensors, Reviews of Modern Physics 92, 021001 (2020)

    2020

  5. [13]

    Yoshinaga, H

    A. Yoshinaga, H. Hakoshima, T. Imoto, Y. Matsuzaki, and R. Hamazaki, Emergence of hilbert space fragmenta- tion in ising models with a weak transverse field, Physical Review Letters 129, 090602 (2022)

    2022

  6. [14]

    S. E. Spielman, A. Handian, N. P. Inman, T. J. Carroll, and M. W. Noel, Quantum many-body scars in few-body dipole-dipole interactions, Physical Review Research 6, 043086 (2024)

    2024

  7. [15]

    Sugiyama, Precision-guaranteed quantum metrology, Physical Review A 91, 042126 (2015)

    T. Sugiyama, Precision-guaranteed quantum metrology, Physical Review A 91, 042126 (2015)

    2015

  8. [16]

    H. Zhou, J. Choi, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro, et al., Quantum metrology with strongly interacting spin systems, Physical review X 10, 031003 (2020)

    2020

  9. [17]

    Biteri-Uribarren, A

    A. Biteri-Uribarren, A. Martin, and J. Casanova, Mi- croscale sensing with strongly interacting nv ensembles at high fields, arXiv preprint arXiv:2410.21182 (2024)

    2024

  10. [18]

    H. Zhou, L. S. Martin, M. Tyler, O. Makarova, N. Leitao, H. Park, and M. D. Lukin, Robust higher-order hamilto- nian engineering for quantum sensing with strongly in- teracting systems, Physical Review Letters 131, 220803 (2023)

    2023

  11. [19]

    Schuld, I

    M. Schuld, I. Sinayskiy, and F. Petruccione, An intro- duction to quantum machine learning, Contemporary Physics 56, 172 (2015)

    2015

  12. [20]

    Schuld and N

    M. Schuld and N. Killoran, Quantum machine learning in feature hilbert spaces, Physical review letters 122, 040504 (2019)

    2019

  13. [21]

    Carleo, I

    G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborov´ a, Machine learning and the physical sciences, Reviews of Modern Physics 91, 045002 (2019)

    2019

  14. [22]

    P´ erez-Salinas, A

    A. P´ erez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, Data re-uploading for a universal quantum classifier, Quantum 4, 226 (2020)

    2020

  15. [23]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Na- ture 549, 195 (2017)

    2017

  16. [24]

    Mitarai, M

    K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Physical Review A 98, 032309 (2018)

    2018

  17. [25]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al., Variational quantum algorithms, Nature Reviews Physics 3, 625 (2021)

    2021

  18. [26]

    Havl´ ıˇ cek, A

    V. Havl´ ıˇ cek, A. D. C´ orcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Super- vised learning with quantum-enhanced feature spaces, Nature 567, 209 (2019)

    2019

  19. [27]

    Schuld, Supervised quantum machine learning mod- els are kernel methods, arXiv preprint arXiv:2101.11020 (2021)

    M. Schuld, Supervised quantum machine learning mod- els are kernel methods, arXiv preprint arXiv:2101.11020 (2021)

    2021 arXiv

  20. [28]

    Jerbi, L

    S. Jerbi, L. J. Fiderer, H. Poulsen Nautrup, J. M. K¨ ubler, H. J. Briegel, and V. Dunjko, Quantum machine learning beyond kernel methods, Nature Communications 14, 517 (2023)

    2023

  21. [29]

    Y. Liu, S. Arunachalam, and K. Temme, A rigorous and robust quantum speed-up in supervised machine learn- ing, Nature Physics 17, 1013 (2021)

    2021

  22. [30]

    J¨ ager and R

    J. J¨ ager and R. V. Krems, Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines, Nature Communications 14, 576 (2023)

    2023

  23. [31]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Bab- bush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature communications 9, 4812 (2018)

    2018

  24. [32]

    Cerezo, A

    M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, Cost function dependent barren plateaus in shal- low parametrized quantum circuits, Nature communica- tions 12, 1791 (2021)

    2021

  25. [33]

    Larocca, S

    M. Larocca, S. Thanasilp, S. Wang, K. Sharma, J. Bia- monte, P. J. Coles, L. Cincio, J. R. McClean, Z. Holmes, and M. Cerezo, Barren plateaus in variational quantum computing, Nature Reviews Physics , 1 (2025)

    2025

  26. [34]

    Huang, M

    H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, Power of data in quantum machine learning, Nature communications 12, 2631 (2021)

    2021

  27. [35]

    Thanasilp, S

    S. Thanasilp, S. Wang, M. Cerezo, and Z. Holmes, Expo- nential concentration in quantum kernel methods, Nature communications 15, 5200 (2024)

    2024

  28. [36]

    Suzuki, H

    Y. Suzuki, H. Kawaguchi, and N. Yamamoto, Quantum fisher kernel for mitigating the vanishing similarity issue, Quantum Science and Technology 9, 035050 (2024)

    2024

  29. [37]

    Huang, M

    H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill, et al. , Quantum advantage in learning from experiments, Science 376, 1182 (2022)

    2022

  30. [38]

    Kaubruegger, P

    R. Kaubruegger, P. Silvi, C. Kokail, R. van Bijnen, A. M. Rey, J. Ye, A. M. Kaufman, and P. Zoller, Varia- tional spin-squeezing algorithms on programmable quan- tum sensors, Physical review letters 123, 260505 (2019)

    2019

  31. [39]

    Koczor, S

    B. Koczor, S. Endo, T. Jones, Y. Matsuzaki, and S. C. Benjamin, Variational-state quantum metrology, New Journal of Physics 22, 083038 (2020)

    2020

  32. [40]

    R. Said, D. Berry, and J. Twamley, Nanoscale magne- tometry using a single-spin system in diamond, Physical Review B—Condensed Matter and Materials Physics 83, 125410 (2011)

    2011

  33. [41]

    Waldherr, J

    G. Waldherr, J. Beck, P. Neumann, R. Said, M. Nitsche, M. Markham, D. Twitchen, J. Twamley, F. Jelezko, and J. Wrachtrup, High-dynamic-range magnetometry with a single nuclear spin in diamond, Nature nanotechnology 7, 105 (2012)

    2012

  34. [42]

    S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency 8 standards with quantum entanglement, Physical Review Letters 79, 3865 (1997)

    1997

  35. [43]

    Hakoshima and Y

    H. Hakoshima and Y. Matsuzaki, Single spin detec- tion with entangled states, Japanese Journal of Applied Physics 59, SGGI09 (2020)

    2020

  36. [44]

    Hakoshima and Y

    H. Hakoshima and Y. Matsuzaki, Efficient detection of inhomogeneous magnetic fields from a single spin with dicke states, Physical Review A 102, 042610 (2020)

    2020

  37. [45]

    Hakoshima, Y

    H. Hakoshima, Y. Matsuzaki, and T. Ishikawa, Pro- posed rapid detection of nuclear spins with entanglement- enhanced sensors, Japanese Journal of Applied Physics 60, 070909 (2021)

    2021

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.