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REVIEW 4 major objections 5 minor 2 cited by

Quantum Computational-Sensing Advantage

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Quantum computational sensing is the claim that a quantum sensor should compute a task-relevant function of the sensed signal before measurement, yielding a quantum computational-sensing advantage that does not require large or…

desk verdict A clear, useful perspective that names a real pattern in recent sensing protocols, but the evidence for QCSA rests on unpublished companions and the 'quantum advantage' language outruns the formal baseline. read the letter →

arxiv 2507.16918 v1 pith:6LOOAEXR submitted 2025-07-22 quant-ph

Saeed A. Khan , Sridhar Prabhu , Logan G. Wright , Peter L. McMahon This is my paper
classification quant-ph
keywords quantumcomputationalsensingadvantagemetrologysignalprocessingmachinelearningdistributedtask-specificestimation
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

Quantum computational sensing (QCS) is the proposal to combine a quantum sensor with a quantum processor so that the sensor's output is a function of the sensed signal, not a raw estimate of the signal itself. The paper argues that for tasks such as classification, threshold detection, and decoding, this task-specific arrangement yields a quantum computational-sensing advantage (QCSA): better task accuracy for the same sensing time, number of qubits, and signal strength, compared with a conventional quantum sensor followed by arbitrarily powerful classical postprocessing. Because the advantage comes from concentrating the small amount of classical information released by a quantum measurement into task-relevant bits, it can appear in systems with just a single qubit or a few modes, including systems small enough to simulate classically. The paper's aim is to define QCSA, show that many recent proposals and experiments already fit the definition, and offer a taxonomy of QCS architectures to guide future design.

What carries the argument

The load-bearing object is the quantum computational sensor, a quantum system whose total evolution is chosen for the task rather than for estimating the signal. Its two canonical structures are single-sensing-operation protocols $U_{\text{QCS}} = U_{\text{meas}} U_{\text{sense}}(u) U_{\text{probe}}$, in which optimization acts on the measurement basis or on both probe state and measurement basis, and coherent-processing protocols $U_{\text{QCS}} = U_{\text{meas}} \prod_{\ell=1}^{L} U_{\text{sense}}(u^{(\ell)}) U_{\text{coh}}^{(\ell)}$, in which sensing and quantum computation alternate before a single readout. The mechanism these architectures exploit is the measurement information bottleneck: only one classical bit per qubit survives measurement, and classical postprocessing of noisy estimates can degrade the signal-to-noise ratio, sometimes exponentially, when the target function is nonlinear. By computing $F^\star(u)$ coherently before measurement, the protocol aims to put the task-relevant information into those few bits. The paper also separates design strategies into analytic, when $F^\star$ is known, and learned, when the processing unitaries are trained from data.

What would settle it

Take any protocol the paper lists as achieving QCSA, such as single-shot threshold detection with bosonic quantum signal processing or Grover-based AC-field detection, and run the same task with the same physical hardware, sensing time, and number of shots, but replace the coherent pre-measurement computation with the best classical computational-sensing pipeline applied to the raw measurement record; if the classical pipeline matches or beats the quantum computational sensor's classification error, the central claim is falsified. A simpler preliminary check is to compute whether the reported error curves ever dip below the optimal classical decision rule on the same measurement statistics.

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Extended reading notes

Core claim

The central claim is that a quantum sensor's job need not be to estimate the unknown signal $u$; it can instead be to compute a target function $F^\star(u)$ that defines the task. A quantum computational sensor replaces the conventional protocol $U_{\text{QS}} = U_{\text{meas}} U_{\text{sense}}(u) U_{\text{probe}}$ with a task-engineered evolution $U_{\text{QCS}}$ whose measurement reveals some function $F_{\text{QCS}}(u)$ of the sensed parameters, ideally close to $F^\star$. Since a single qubit measurement returns only one bit and is subject to sampling noise, the paper's key claim is that coherently computing $F^\star$ before measurement can concentrate the limited classical output into task-relevant information and reshape the noise so that task accuracy improves; this is the origin of QCSA. The paper supports the claim by organizing a wide set of recent results --- joint-detection receivers, quantum sensor networks, bosonic quantum signal processing, Grover-enhanced signal search, trajectory sensing, and quantum neural networks --- as instances of the same pattern, with reported advantages ranging from constant factors to polynomial scaling and, in some settings, the possibility of exponential advantage.

Load-bearing premise

The load-bearing premise is that the comparison baseline is a conventional quantum sensor followed by arbitrarily powerful classical postprocessing, and that classical computational sensing is not part of the baseline; if a purely classical computational sensor can match the task accuracy from the same raw measurement record, the claimed quantum advantage becomes a classical algorithmic advantage.

Editorial extensions

If this is right

  • QCSA can be demonstrated with small quantum systems that are classically simulable, so the advantage does not require fault-tolerant or large-scale quantum computing hardware.
  • The same sensing hardware that is already a state-of-the-art quantum sensor, such as single nitrogen-vacancy centers or superconducting cavity-qubit systems, is a candidate platform for a quantum computational sensor.
  • Standard quantum algorithms, including Grover search, quantum signal processing, and quantum neural networks, can be converted into sensing protocols, and at least one such protocol is asymptotically optimal for AC-field detection.
  • The advantage can appear in unentangled single-qubit systems, in entangled networks, and in protocols that exploit temporal coherence, so the design space for quantum-enhanced sensing is broader than conventional metrology suggests.
  • For some tasks, such as single-shot trajectory sensing, a quantum computational sensor can achieve zero classification error where a conventional quantum sensor makes errors near 20 percent.

Reading between the lines

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

  • Editorial inference: if QCSA holds up, the practical route to quantum advantage may be to build small task-specific sensor-processors rather than large general-purpose quantum computers, because the relevant metric is task accuracy per sensing time rather than computational speedup.
  • Editorial inference: the definition's baseline excludes classical computational sensing, so the cleanest test is to benchmark every QCS protocol against the best classical computational-sensing pipeline using the same raw measurement record; where classical processing matches the accuracy, the advantage would be algorithmic rather than quantum.
  • Editorial inference: the paper's taxonomy suggests a design heuristic that goes beyond it: for a new sensing task, first check whether the target function can be approximated by a low-depth coherent circuit; if so, the same sensor can potentially be upgraded to a quantum computational sensor without waiting for fault tolerance.
  • Editorial inference: the connection to exponential advantages in learning from quantum experiments hints that stochastic signals, rather than fixed unknown parameters, may be where the largest QCSA values appear; this is a testable direction the paper raises but does not resolve.
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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

4 major / 5 minor

Summary. This Perspective introduces the term "quantum computational sensing" (QCS) for protocols in which a quantum sensor is combined with quantum computation so that measurement outcomes yield a function F_QCS(u) of an unknown signal u rather than an estimate of u itself. It defines quantum computational-sensing advantage (QCSA) as the ability of such a protocol to estimate a target function F*(u) more accurately than a conventional quantum sensor followed by arbitrary classical postprocessing, given the same sensing resources. The paper surveys recent proposals and experiments (quantum sensor networks, bosonic QSP threshold detection, joint-detection receivers, quantum trajectory sensing, SLAEN, Grover-enhanced AC-field search, single-qubit QSP/QNN classification), organizes them into a taxonomy based on single versus multiple sensing operations per shot, probe/measurement optimization, and analytic versus learned target functions, and discusses hardware requirements, decoherence challenges, and open questions. It concludes that QCSA can be achieved with small, classically simulable quantum systems and may lead to practical sensing advantages.

Significance. If the QCSA notion is accepted as defined, the paper provides a useful organizing framework for a growing body of work that combines quantum sensing with quantum computation. Its main strengths are the clear conceptual definitions in Boxes 1 and 2, the breadth of the survey, the protocol taxonomy in Figs. 3 and 5, and the summary tables (Tables I and II), which should help researchers position new results. The authors are also explicit in Sec. V.C.2 that QCSA as defined is a proof-of-concept advantage over a conventional quantum sensor and that practical advantage would additionally require comparison with the best quantum and classical sensors; this is an important and honest limitation. The paper does not contain new derivations, and the quantitative claims in several central examples are drawn from cited works, including an unpublished companion manuscript, so the conceptual contribution rather than any new proof is what is being evaluated.

major comments (4)
  1. [Box 2; V.C.2; Abstract] The definition of QCSA in Box 2 compares a quantum computational sensor only with a conventional quantum sensor whose output is a classical estimate of u, followed by arbitrarily complex classical postprocessing. It does not include a classical computational sensor that directly processes the raw measurement record or an equivalent classical detector output. The paper itself acknowledges in V.C.2 that a practical advantage would need to be established against "the best other quantum and classical sensors," so the formal notion is internally coherent as a proof-of-concept definition. However, the abstract and opening claims describe QCSA as "a new kind of quantum advantage" and state that it "can be realized with far lower hardware requirements than purely computational quantum advantage," without the qualification that this is an advantage over a conventional quantum sensor under the same sensing resources. As written, these headline statements overstate what is established, because for classically simulable small systems a classical computational-sensing baseline may achieve the same task accuracy, in which case the demonstrated advantage would be a classical algorithmic or postprocessing effect rather than a distinctly quantum sensing advantage. I recommend either restricting the headline claims to "advantage over conventional quantum sensing" or adding a substantive discussion of the classical computational-sensing baseline and its relation to QCSA.
  2. [Box 2; Sec. III A 1; Sec. III B 1] The resource accounting in Box 2 counts only sensing resources (number of sensing qubits/modes, interaction Hamiltonian, sensing time) and not the additional quantum-computing hardware used by the QCS protocol. Several examples use additional quantum registers or processors: BPQM in Sec. III A 1 uses entangling unitaries on qubits in a trapped-ion device, and Grover-enhanced search in Sec. III B 1 uses computing qubits to represent frequency bins. If total hardware or total qubit count is included in the resource budget, the claimed advantage over a conventional quantum sensor may be reduced or disappear, because the conventional baseline is not allowed the same quantum-computing resources. The abstract's "far lower hardware requirements" claim is therefore in tension with the fact that some QCS protocols require a quantum processor in addition to the sensor. The definition should either account for all quantum resources or explicitly state that QCSA is defined per unit of sensing time with computational hardware held separate, and the practical-hardware discussion in V.C.2 should be linked to this accounting.
  3. [Sec. III B 2; Fig. 4f; Box 2] The QCSA label in the QSP/QNN examples is not fully supported by the definition in Box 2, which requires a more accurate estimate than is possible with a conventional quantum sensor with arbitrarily complex classical postprocessing. The comparisons in Sec. III B 2 are against particular conventional strategies: Ramsey interferometry followed by a classical neural network for the MEG task, and Ramsey estimation plus threshold postprocessing for the single-qubit classification task. No argument is given that these baselines are optimal among conventional QS protocols, nor that arbitrary classical postprocessing of the raw measurement records cannot reach the same classification error. The Grover-enhanced search example in Sec. III B 1 is different, because Ref. [63] is cited as providing a lower bound on conventional QS; however, the learned-protocol examples do not have such a bound. As a result, Fig. 4f's "QCSA" labels overstate what is demonstrated; the text should either prove or cite optimality/lower-bound results for the baselines, or explicitly relabel these as advantages over a specified conventional protocol rather than QCSA as defined in Box 2.
  4. [Sec. III B 2; Fig. 4; Refs. [62,63]] The central quantitative examples for the learned QCS protocols (single-qubit QSP classification, QNN classification of MEG fields, nonlinear amplifiers) are taken from Refs. [62] and [63], the first of which is an unpublished companion manuscript by the same group and the second is a preprint. The manuscript does not reproduce or summarize the derivations, datasets, or optimization procedures needed to check whether these examples satisfy the Box 2 definition. For a Perspective this reliance on the literature is acceptable, but because the paper's central claim of a "new kind of quantum advantage" rests on these specific examples, the authors should either state clearly that the associated quantitative claims are from unpublished/preprint sources and are subject to peer review, or provide sufficient detail in an appendix (e.g., the baseline definitions and error curves) for the reader to assess the comparisons.
minor comments (5)
  1. [V.B] The text refers to "Fig. 4d" when discussing the trajectory-sensing result of Ref. [68]; the correct panel is Fig. 4c.
  2. [Sec. III A 3] The word "estiamte" appears in the description of the d=1 cat-state protocol; it should be "estimate."
  3. [Sec. III B 2] The phrase "from a experimental measurements" should be corrected, for example to "from experimental measurements" or "from an experimental dataset."
  4. [Fig. 5 caption] The caption contains "Entnaglement," which should be "Entanglement."
  5. [Box 2] The conventional-QS example uses the phrase "a M-qubit conventional quantum sensor"; it should be "an M-qubit conventional quantum sensor."

Circularity Check

1 steps flagged · score 4.0 of 10

Single-qubit QCSA claim rests on a companion self-citation, but the framework is largely a survey with independent external examples; no equation-level circularity found.

  1. self citation load bearing [Sec. I, p. 2 (footnote 3) and Sec. III.B.2, p. 15]
    "It can be realized in systems that are unentangled—including ones comprising just a single qubit that is used to perform both sensing and computing 3—and in entangled systems ... 3 It might at first seem surprising that any useful computation can be done with a single qubit; we discuss an example in Sec. III B under Protocols using learning. ... Ref. [62] reported a QCSA where the probability of error was as much as 25 percentage points lower for QCS than for conventional QS, given an equal number of sensing operations N for both."

    The paper's prominent claim that QCSA can be achieved with just a single qubit is anchored, through the footnote, to Sec. III.B.2, and the only evidence reported there for that claim is Ref. [62], an arXiv preprint by the same four authors (Khan, Prabhu, Wright, McMahon). The present manuscript provides no independent derivation, external benchmark, or machine-checked verification of that single-qubit result; it simply relays the companion paper's numerical finding. Because this self-citation is load-bearing for a central advertised feature of QCSA, it counts as circularity under the self-citation rule. The rest of the framework, however, is supported by external works (e.g., Refs. [61], [63], [68]), so the central claim is not wholly reduced to the self-citation.

full rationale

This is a Perspective rather than a derivation paper: the only formal equations, Eqs. (1) and (2), are generic circuit decompositions, and the QCSA definition in Box 2 is a coherent comparative definition rather than a tautology. I found no equation-level circularity in which a predicted quantity is equal to a fitted input by construction. The main circularity concern is self-citation: the single-qubit QCSA example, highlighted in the introduction's 'far lower hardware requirements' claim, is supported solely by Ref. [62], a companion preprint by the same authors. Ref. [142], also by the same group, appears only in the speculative outlook about exponential QCSA and is not load-bearing. The paper itself explicitly limits its working notion of QCSA to a proof-of-concept advantage over a conventional quantum sensor, and it acknowledges that practical advantage would require beating 'the best other quantum and classical sensors'; that limitation is a scope restriction, not a circular step. The absence of a classical computational-sensing baseline is a genuine correctness and interpretation risk, but it is a missing comparison rather than a circular reduction. On balance, the organizational and taxonomical content is independent, and most surveyed examples come from external groups, so the paper deserves a moderate rather than high circularity score.

Assumptions & free parameters 2 free parameters · 4 assumptions · 2 invented entities

The ledger captures the assumptions this Perspective imports: quantum measurement limits, the circuit-model idealization of sensing, the noise-propagation claim for nonlinear postprocessing, and the trust in the authors' companion manuscripts. No new free parameters are fitted in this paper; the listed parameters are from the cited protocols that supply the concrete QCSA evidence.

free parameters (2)
  • BQSP layer count d (Ref [61]) = not specified (values up to ~20 shown in Fig. 4b)
    The paper quotes a d^{-0.82} scaling for single-shot threshold-detection error from Ref [61]; d is a tunable protocol parameter whose performance trade-off is imported rather than derived.
  • Learned unitary parameters in QSP/QNN protocols (Ref [62]) = not provided
    The 16-25 percentage point error reductions reported in Sec. III B 2 are taken from the authors' companion arXiv:2507.15845, where unitary parameters are optimized on training data; the fitted parameters and datasets are absent from this paper.
assumptions (4)
  • domain assumption A projective measurement of a qubit yields at most 1 bit of classical information per shot
    Used at the start of Sec. II and Box 1 to argue QCS concentrates task-relevant information into the measured bit; this is stated, not proved.
  • domain assumption Sensing interactions can be turned on and off, permitting a circuit-model decomposition U_QCS = U_meas (prod of U_sense U_coh) U_probe
    Stated as a 'standard simplification' in Sec. III A and used to define the protocol taxonomy (Eqs. 1 and 2); always-on sensing is explicitly deferred.
  • domain assumption Classical postprocessing of noisy estimates of u can exponentially degrade SNR for nonlinear target functions
    Invoked in Sec. II to motivate QCS, citing Refs [51,52]; no proof is given in this paper.
  • ad hoc to paper The performance figures reported in the cited companion papers are correct and complete
    The most detailed QCSA claims rest on Ref [62] (same authors, arXiv:2507.15845) and Ref [142] (same group, arXiv:2504.21745); these are not re-derived here.
invented entities (2)
  • Quantum computational sensing (QCS) as a named paradigm independent evidence
    purpose: Unify existing protocols that compute functions of sensed parameters inside the quantum processor before measurement.
    The referent protocols already exist with independent demonstrations (sensor networks, joint detection receivers, barcode discrimination), though several flagship examples are from the authors' own companion manuscripts.
  • Quantum computational-sensing advantage (QCSA) independent evidence
    purpose: Name the advantage of QCS over conventional quantum sensing for task-specific information extraction.
    Operationalized in Box 2 via error probabilities versus sensing resources; the falsifiable handle is a controlled comparison of QCS versus conventional QS, but the strongest reported comparisons are in self-cited preprints.

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Cite this review

Pith. "Pith review of Quantum Computational-Sensing Advantage." pith.science (2026). https://pith.science/paper/6LOOAEXR

@misc{pith2026250716918,
  author       = {Pith},
  title        = {Pith review of: Quantum Computational-Sensing Advantage},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6LOOAEXR}},
  note         = {Machine review of arXiv:2507.16918}
}
read the original abstract

Quantum computing has the potential to deliver large advantages on computational tasks, but advantages for practical tasks are not yet achievable with current hardware. Quantum sensing is an entirely separate quantum technology that can provide its own kind of a quantum advantage. In this Perspective, we explain how the merger of quantum sensing with quantum computing has recently given rise to the notion of quantum computational sensing, and a new kind of quantum advantage: a quantum computational-sensing advantage. This advantage can be realized with far lower hardware requirements than purely computational quantum advantage. We explain how several recent proposals and experiments can be understood as quantum computational sensing, and discuss categorizations of the general architectures that quantum-computational-sensing protocols can have. We conclude with an outlook on open questions and the prospects for quantum computational sensors and quantum computational-sensing advantage.

Figures

Figures reproduced from arXiv: 2507.16918 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

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Forward citations

Cited by 2 Pith papers

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  2. Remote entanglement need not be the bottleneck for modular trapped-ion quantum computing

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    A projected architecture for trapped-ion quantum modules combines single-photon heralding, integrated photonics, recoil correction, and one distillation round to deliver 99.9%-fidelity remote Bell pairs at 10^5 s^-1 cm^-2.

Reference graph

Works this paper leans on

151 extracted references · 71 canonical work pages · cited by 2 Pith papers

  1. [63]

    Zhuang and Z

    Q. Zhuang and Z. Zhang, Physical-Layer Supervised Learning Assisted by an Entangled Sensor Network. Physical Review X 9, 041023 (2019)

    2019

  2. [62]

    Loretz, T

    M. Loretz, T. Rosskopf, and C. L. Degen, Radio-Frequency Magnetometry Using a Single Electron Spin. Physical Review Letters 110, 017602 (2013)

    2013

  3. [1]

    Consider the situation where a weak, time-varying field—whose magnitude, frequency, and phase are all unknown—might or might not be present

    Protocol for an analytic target function Grover-enhanced search sensing—An example of a coherent processing protocol has recently been proven to be the optimal protocol for the task of detecting the presence or absence of an oscillating, time-varying signal [63]. Consider the situation where a weak, time-varying field—whose magnitude, frequency, and phase...

  4. [2]

    Protocols for learned target functions Quantum signal processing —Learning schemes can be used to optimize processing operations U (l) coh in coherent processing protocols when the target function F ⋆ is not a priori known. Consider the task of classifying, into one of two classes, the phase θ sensed by a single qubit, where the two classes are defined im...

  5. [3]

    Zhong, et al

    H.-S. Zhong, et al. Quantum computational advantage using photons. Science 370, 1460–1463 (2020)

    2020

  6. [4]

    Probe-state and measurement-basis (encoder and decoder) optimization for learned target functions Supervised learning assisted by an entangled sensor network —The optimization of both the probe-state and mea- surement basis-preparation steps for QCS protocols can also be performed by learning from data. Supervised Learning Assisted by an Entangled sensor ...

  7. [5]

    Proof-of-principle demonstrations of advantage A central challenge is how to handle hardware imperfections, especially decoherence. Any physical realization of quantum hardware suffers from decoherence and loss, so there are strong practical constraints on how much fidelity one can expect a system’s quantum state to maintain, especially when running longe...

  8. [6]

    Practical advantage A natural first step for experimental realization of each QCS protocol is to show a proof-of-concept that the protocol can provide an advantage when compared with a conventional quantum sensing protocol run on exactly the same physical hardware. QCSA is defined in Box 2 in this way, and this is similar to how advantages in conventional...

Show all 151 references
  1. [7]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019)

    2019

  2. [8]

    Morvan, et al

    A. Morvan, et al. Phase transitions in random circuit sampling. Nature 634, 328–333 (2024)

    2024

  3. [9]

    L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais, T. Vincent, J. F. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, A. E. Lita, T. Gerrits, S. W. Nam, V. D. Vaidya, M. Menotti, I. Dhand, Z. Vernon, N. Quesada, and J. Lavoie, Quantum computational advanta...

    2022

  4. [10]

    Mohseni, P

    M. Mohseni, P. Read, H. Neven, S. Boixo, V. Denchev, R. Babbush, A. Fowler, V. Smelyanskiy, and J. Martinis, Commercialize quantum technologies in five years. Nature 543, 171–174 (2017)

    2017

  5. [11]

    Cerezo, G

    M. Cerezo, G. Verdon, H.-Y. Huang, L. Cincio, and P. J. Coles, Challenges and opportunities in quantum machine learning. Nature Computational Science 2, 567–576 (2022)

    2022

  6. [12]

    Zimbor´ as, B

    Z. Zimbor´ as, B. Koczor, Z. Holmes, E.-M. Borrelli, A. Gily´ en, H.-Y. Huang, Z. Cai, A. Ac ´ ın, L. Aolita, L. Banchi et al. 23 Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don’t. arXiv:2501.05694 (2025)

    2025 arXiv

  7. [13]

    Degen, F

    C. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing. Reviews of Modern Physics 89 (2017)

    2017

  8. [14]

    W. Jia, V. Xu, K. Kuns, M. Nakano, L. Barsotti, M. Evans, N. Mavalvala et al. Squeezing the quantum noise of a gravitational-wave detector below the standard quantum limit. Science 385, 1318–1321 (2024)

    2024

  9. [15]

    K. M. Backes, D. A. Palken, S. A. Kenany, B. M. Brubaker, S. Cahn, A. Droster, G. C. Hilton, S. Ghosh, H. Jackson, S. K. Lamoreaux et al. A quantum enhanced search for dark matter axions. Nature 590, 238–242 (2021)

    2021

  10. [16]

    Agrawal, A

    A. Agrawal, A. V. Dixit, T. Roy, S. Chakram, K. He, R. K. Naik, D. I. Schuster, and A. Chou, Stimulated emission of signal photons from dark matter waves. Physical Review Letters 132, 140801 (2024)

    2024

  11. [17]

    Braggio, L

    C. Braggio, L. Balembois, R. Di Vora, Z. Wang, J. Travesedo, L. Pallegoix, G. Carugno, A. Ortolan, G. Ruoso, U. Gam- bardella et al. Quantum-enhanced sensing of axion dark matter with a transmon-based single microwave photon counter. Physical Review X 15, 021031 (2025)

    2025

  12. [18]

    Stray, A

    B. Stray, A. Lamb, A. Kaushik, J. Vovrosh, A. Rodgers, J. Winch, F. Hayati, D. Boddice, A. Stabrawa, A. Niggebaum et al. Quantum sensing for gravity cartography. Nature 602, 590–594 (2022)

    2022

  13. [19]

    Bongs, S

    K. Bongs, S. Bennett, and A. Lohmann, Quantum sensors will start a revolution—if we deploy them right. Nature 617, 672–675 (2023)

    2023

  14. [20]

    Gschwendtner, Y

    M. Gschwendtner, Y. Bormuth, H. Soller, A. Stein, and R. L. Walsworth, Quantum Sensing Can Already Make a Difference. But Where? Journal of Innovation Management 12, I–XI (2024)

    2024

  15. [21]

    Muradoglu, M

    M. Muradoglu, M. T. Johnsson, N. M. Wilson, Y. Cohen, D. Shin, T. Navickas, T. Pyragius, D. Thomas, D. Thompson, S. I. Moore et al. Quantum-assured magnetic navigation achieves positioning accuracy better than a strategic-grade INS in airborne and ground-based field trials. ar...

    2025 arXiv

  16. [22]

    Van der Spiegel, (1996) Computational sensors: The basis for truly intelligent machines

    J. Van der Spiegel, (1996) Computational sensors: The basis for truly intelligent machines. In Handbook of Sensors and Actuators. (Elsevier) Vol. 3, pp. 19–37

    1996

  17. [23]

    Ballard, C

    Z. Ballard, C. Brown, A. M. Madni, and A. Ozcan, Machine learning and computation-enabled intelligent sensor design. Nature Machine Intelligence 3, 556–565 (2021)

    2021

  18. [24]

    M. A. Nielsen and I. L. Chuang, (2010) Quantum computation and quantum information . (Cambridge University Press)

    2010

  19. [25]

    L. G. Wright and P. L. McMahon, The Capacity of Quantum Neural Networks. arXiv:1908.01364 (2019)

    2019 arXiv

  20. [26]

    F. Hu, G. Angelatos, S. A. Khan, M. Vives, E. T¨ ureci, L. Bello, G. E. Rowlands, G. J. Ribeill, and H. E. T¨ ureci, Tackling Sampling Noise in Physical Systems for Machine Learning Applications: Fundamental Limits and Eigentasks. Physical Review X 13, 041020 (2023)

    2023

  21. [27]

    Gyurik, R

    C. Gyurik, R. Molteni, and V. Dunjko, Limitations of measure-first protocols in quantum machine learning. arXiv.2311.12618 (2023)

    2023 arXiv

  22. [28]

    Recio-Armengol, J

    E. Recio-Armengol, J. Eisert, and J. J. Meyer, Single-shot quantum machine learning. Physical Review A 111, 042420 (2025)

    2025

  23. [29]

    Zhang and Q

    Z. Zhang and Q. Zhuang, Distributed quantum sensing. Quantum Science and Technology 6, 043001 (2021)

    2021

  24. [30]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning. Nature 549, 195–202 (2017)

    2017

  25. [31]

    J. M. Martyn, Z. M. Rossi, A. K. Tan, and I. L. Chuang, Grand unification of quantum algorithms. PRX Quantum 2, 040203 (2021)

    2021

  26. [32]

    Aharonov, J

    D. Aharonov, J. Cotler, and X.-L. Qi, Quantum algorithmic measurement. Nature Communications 13 (2022)

    2022

  27. [33]

    Huang, M

    H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill, and J. R. McClean, Quantum advantage in learning from experiments. Science 376, 1182–1186 (2022)

    2022

  28. [34]

    S. Chen, S. Zhou, A. Seif, and L. Jiang, Quantum advantages for Pauli channel estimation. Physical Review A 105 (2022)

    2022

  29. [35]

    C. Oh, S. Chen, Y. Wong, S. Zhou, H.-Y. Huang, J. A. Nielsen, Z.-H. Liu, J. S. Neergaard-Nielsen, U. L. Andersen, L. Jiang et al. Entanglement-enabled advantage for learning a bosonic random displacement channel. Physical Review Letters 133, 230604 (2024)

    2024

  30. [36]

    Z.-M. Zhai, M. Moradi, L.-W. Kong, and Y.-C. Lai, Detecting weak physical signal from noise: A machine-learning approach with applications to magnetic-anomaly-guided navigation. Physical Review Applied 19, 034030 (2023)

    2023

  31. [37]

    Ashraf, T

    A. Ashraf, T. Abbas, and A. Ejaz, Magnetic Anamoly-Based Detection of a Submarine. In 2023 International Multi- disciplinary Conference in Emerging Research Trends (IMCERT) Vol. 1, 1–5 (2023)

    2023

  32. [38]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology. Physical Review Letters 96, 010401 (2006)

    2006

  33. [39]

    Kaubruegger, P

    R. Kaubruegger, P. Silvi, C. Kokail, R. van Bijnen, A. M. Rey, J. Ye, A. M. Kaufman, and P. Zoller, Variational spin-squeezing algorithms on programmable quantum sensors. Physical Review Letters 123, 260505 (2019)

    2019

  34. [40]

    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

  35. [41]

    Kaubruegger, D

    R. Kaubruegger, D. V. Vasilyev, M. Schulte, K. Hammerer, and P. Zoller, Quantum variational optimization of Ramsey interferometry and atomic clocks. Physical Review X 11, 041045 (2021)

    2021

  36. [42]

    C. D. Marciniak, T. Feldker, I. Pogorelov, R. Kaubruegger, D. V. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, and T. Monz, Optimal metrology with programmable quantum sensors. Nature 603, 604–609 (2022)

    2022

  37. [43]

    Zheng, A

    T.-X. Zheng, A. Li, J. Rosen, S. Zhou, M. Koppenh¨ ofer, Z. Ma, F. T. Chong, A. A. Clerk, L. Jiang, and P. C. Maurer, Preparation of metrological states in dipolar-interacting spin systems. npj Quantum Information 8, 150 (2022)

    2022

  38. [44]

    Kaubruegger, A

    R. Kaubruegger, A. Shankar, D. V. Vasilyev, and P. Zoller, Optimal and Variational Multiparameter Quantum Metrology and Vector-Field Sensing. PRX Quantum 4, 020333 (2023)

    2023

  39. [45]

    MacLellan, P

    B. MacLellan, P. Roztocki, S. Czischek, and R. G. Melko, End-to-end variational quantum sensing. npj Quantum 24 Information 10, 118 (2024)

    2024

  40. [46]

    Direkci, R

    S. Direkci, R. Finkelstein, M. Endres, and T. Gefen, Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits. arXiv:2407.06006 (2024)

    2024

  41. [47]

    Z. Ma, P. Gokhale, T.-X. Zheng, S. Zhou, X. Yu, L. Jiang, P. Maurer, and F. T. Chong, Adaptive circuit learning for quantum metrology. In 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) , 419–430 (2021)

    2021

  42. [48]

    Wang, Z.-J

    W. Wang, Z.-J. Chen, X. Liu, W. Cai, Y. Ma, X. Mu, X. Pan, Z. Hua, L. Hu, Y. Xu et al. Quantum-enhanced radiometry via approximate quantum error correction. Nature Communications 13, 3214 (2022)

    2022

  43. [49]

    Zhuang, J

    Q. Zhuang, J. Preskill, and L. Jiang, Distributed quantum sensing enhanced by continuous-variable error correction. New Journal of Physics 22, 022001 (2020)

    2020

  44. [50]

    E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Quantum error correction for metrology. Physical Review Letters 112, 150802 (2014)

    2014

  45. [51]

    Arrad, Y

    G. Arrad, Y. Vinkler, D. Aharonov, and A. Retzker, Increasing sensing resolution with error correction. Physical Review Letters 112, 150801 (2014)

    2014

  46. [52]

    S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achieving the Heisenberg limit in quantum metrology using quantum error correction. Nature communications 9, 78 (2018)

    2018

  47. [53]

    Titum, K

    P. Titum, K. Schultz, A. Seif, G. Quiroz, and B. Clader, Optimal control for quantum detectors.npj Quantum Information 7, 53 (2021)

    2021

  48. [54]

    K. R. Motes, J. P. Olson, E. J. Rabeaux, J. P. Dowling, S. J. Olson, and P. P. Rohde, Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit. Physical Review Letters 114, 170802 (2015)

    2015

  49. [55]

    Vorobyov, S

    V. Vorobyov, S. Zaiser, N. Abt, J. Meinel, D. Dasari, P. Neumann, and J. Wrachtrup, Quantum Fourier transform for nanoscale quantum sensing. npj Quantum Information 7, 1–8 (2021)

    2021

  50. [56]

    M. P. da Silva, D. Bozyigit, A. Wallraff, and A. Blais, Schemes for the observation of photon correlation functions in circuit QED with linear detectors. Physical Review A 82, 043804 (2010)

    2010

  51. [57]

    C. A. Ryan, B. R. Johnson, J. M. Gambetta, J. M. Chow, M. P. da Silva, O. E. Dial, and T. A. Ohki, Tomography via correlation of noisy measurement records. Physical Review A 91, 022118 (2015)

    2015

  52. [58]

    Eldredge, M

    Z. Eldredge, M. Foss-Feig, J. A. Gross, S. L. Rolston, and A. V. Gorshkov, Optimal and secure measurement protocols for quantum sensor networks. Physical Review A 97, 042337 (2018)

    2018

  53. [59]

    K. Qian, Z. Eldredge, W. Ge, G. Pagano, C. Monroe, J. V. Porto, and A. V. Gorshkov, Heisenberg-scaling measurement protocol for analytic functions with quantum sensor networks. Physical Review A 100, 042304 (2019)

    2019

  54. [60]

    Bringewatt, A

    J. Bringewatt, A. Ehrenberg, T. Goel, and A. V. Gorshkov, Optimal function estimation with photonic quantum sensor networks. Physical Review Research 6, 013246 (2024)

    2024

  55. [61]

    M. Bal, C. Deng, J.-L. Orgiazzi, F. R. Ong, and A. Lupascu, Ultrasensitive magnetic field detection using a single artificial atom. Nature Communications 3, 1324 (2012)

    2012

  56. [64]

    Y. Xia, W. Li, Q. Zhuang, and Z. Zhang, Quantum-Enhanced Data Classification with a Variational Entangled Sensor Network. Physical Review X 11, 021047 (2021)

    2021

  57. [66]

    Sinanan-Singh, G

    J. Sinanan-Singh, G. L. Mintzer, I. L. Chuang, and Y. Liu, Single-shot Quantum Signal Processing Interferometry. Quantum 8, 1427 (2024)

    2024

  58. [67]

    S. A. Khan, S. Prabhu, L. G. Wright, and P. L. McMahon, Quantum computational sensing using quantum signal processing, quantum neural networks, and Hamiltonian engineering. arXiv:2507.15845 (2025)

    2025 arXiv

  59. [68]

    R. R. Allen, F. Machado, I. L. Chuang, H.-Y. Huang, and S. Choi, Quantum Computing Enhanced Sensing. (2025)

    2025

  60. [69]

    Rengaswamy, K

    N. Rengaswamy, K. P. Seshadreesan, S. Guha, and H. D. Pfister, Belief propagation with quantum messages for quantum- enhanced classical communications. npj Quantum Information 7, 1–12 (2021)

    2021

  61. [70]

    Delaney, K

    C. Delaney, K. P. Seshadreesan, I. MacCormack, A. Galda, S. Guha, and P. Narang, Demonstration of a quantum advantage by a joint detection receiver for optical communication using quantum belief propagation on a trapped-ion device. Physical Review A 106, 032613 (2022)

    2022

  62. [71]

    Crossman, S

    J. Crossman, S. Dimitroff, L. Cincio, and M. Sarovar, Quantum computer-enabled receivers for optical communication. Quantum Science and Technology 9, 045005 (2024)

    2024

  63. [72]

    Banchi, Q

    L. Banchi, Q. Zhuang, and S. Pirandola, Quantum-Enhanced Barcode Decoding and Pattern Recognition. Physical Review Applied 14, 064026 (2020)

    2020

  64. [73]

    Z. E. Chin, D. R. Leibrandt, and I. L. Chuang, Quantum entanglement enables single-shot trajectory sensing for weakly interacting particles. arXiv:2405.05888 (2024)

    2024 arXiv

  65. [74]

    S. Guha, Z. Dutton, and J. H. Shapiro, On quantum limit of optical communications: concatenated codes and joint- detection receivers. In 2011 IEEE International Symposium on Information Theory Proceedings , 274–278 (2011)

    2011

  66. [75]

    Guha, Structured Optical Receivers to Attain Superadditive Capacity and the Holevo Limit

    S. Guha, Structured Optical Receivers to Attain Superadditive Capacity and the Holevo Limit. Physical Review Letters 106, 240502 (2011)

    2011

  67. [76]

    J. Chen, J. L. Habif, Z. Dutton, R. Lazarus, and S. Guha, Optical codeword demodulation with error rates below the 25 standard quantum limit using a conditional nulling receiver. Nature Photonics 6, 374–379 (2012)

    2012

  68. [77]

    J. M. Renes, Belief propagation decoding of quantum channels by passing quantum messages. New Journal of Physics 19, 072001 (2017)

    2017

  69. [78]

    C. W. Helstrom, Quantum detection and estimation theory. Journal of Statistical Physics 1, 231–252 (1969)

    1969

  70. [79]

    C. M. Caves, Quantum limits on noise in linear amplifiers. Physical Review D 26, 1817–1839 (1982)

    1982

  71. [80]

    J. M. Epstein, K. B. Whaley, and J. Combes, Quantum limits on noise for a class of nonlinear amplifiers. Physical Review A 103, 052415 (2021)

    2021

  72. [81]

    C. Cui, W. Horrocks, S. Hao, S. Guha, N. Peyghambarian, Q. Zhuang, and Z. Zhang, Quantum receiver enhanced by adaptive learning. Light: Science & Applications 11, 344 (2022)

    2022

  73. [82]

    W. Ge, K. Jacobs, Z. Eldredge, A. V. Gorshkov, and M. Foss-Feig, Distributed quantum metrology with linear networks and separable inputs. Physical Review Letters 121, 043604 (2018)

    2018

  74. [83]

    T. J. Proctor, P. A. Knott, and J. A. Dunningham, Multiparameter estimation in networked quantum sensors. Physical Review Letters 120, 080501 (2018)

    2018

  75. [84]

    X. Guo, C. R. Breum, J. Borregaard, S. Izumi, M. V. Larsen, T. Gehring, M. Christandl, J. S. Neergaard-Nielsen, and U. L. Andersen, Distributed quantum sensing in a continuous-variable entangled network. Nature Physics 16, 281–284 (2020)

    2020

  76. [85]

    Rubio, P

    J. Rubio, P. A. Knott, T. J. Proctor, and J. A. Dunningham, Quantum sensing networks for the estimation of linear functions. Journal of Physics A: Mathematical and Theoretical 53, 344001 (2020)

    2020

  77. [86]

    T. Qian, J. Bringewatt, I. Boettcher, P. Bienias, and A. V. Gorshkov, Optimal measurement of field properties with quantum sensor networks. Physical Review A 103, L030601 (2021)

    2021

  78. [87]

    Bringewatt, I

    J. Bringewatt, I. Boettcher, P. Niroula, P. Bienias, and A. V. Gorshkov, Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance. Physical Review Research 3, 033011 (2021)

    2021

  79. [88]

    B. K. Malia, Y. Wu, J. Mart ´ ınez-Rinc´ on, and M. A. Kasevich, Distributed quantum sensing with mode-entangled spin- squeezed atomic states. Nature 612, 661–665 (2022)

    2022

  80. [89]

    Y. Xia, A. R. Agrawal, C. M. Pluchar, A. J. Brady, Z. Liu, Q. Zhuang, D. J. Wilson, and Z. Zhang, Entanglement-enhanced optomechanical sensing. Nature Photonics 17, 470–477 (2023)

    2023

  81. [90]

    E. A. Van Milligen, C. N. Gagatsos, E. Kaur, D. Towsley, and S. Guha, Utilizing probabilistic entanglement between sensors in quantum networks. Physical Review Applied 22, 064085 (2024)

    2024

  82. [91]

    Hillery, H

    M. Hillery, H. Gupta, and C. Zhan, Discrete outcome quantum sensor networks. Physical Review A 107, 012435 (2023)

    2023

  83. [92]

    Ali and M

    N. Ali and M. Hillery, Discrete-outcome sensor networks. II. Multiple detection events and grouping detectors. Physical Review A 110, 012619 (2024)

    2024

  84. [93]

    S. L. Braunstein, Squeezing as an irreducible resource. Physical Review A 71, 055801 (2005)

    2005

  85. [94]

    P. Liao, B. Zhang, and Q. Zhuang, Quantum-enhanced learning with a controllable bosonic variational sensor network. Quantum Science and Technology 9, 045040 (2024)

    2024

  86. [95]

    Ortolano, C

    G. Ortolano, C. Napoli, C. Harney, S. Pirandola, G. Leonetti, P. Boucher, E. Losero, M. Genovese, and I. Ruo-Berchera, Quantum-enhanced pattern recognition. Physical Review Applied 20, 024072 (2023)

    2023

  87. [96]

    L. K. Grover, A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing , 212–219 (1996)

    1996

  88. [97]

    H. G. Yeom, J. S. Kim, and C. K. Chung, A magnetoencephalography dataset during three-dimensional reaching move- ments for brain-computer interfaces. Scientific Data 10, 552 (2023)

    2023

  89. [98]

    Farhi and H

    E. Farhi and H. Neven, Classification with quantum neural networks on near term processors. arXiv:1802.06002 (2018)

    2018 arXiv

  90. [99]

    Mitarai, M

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

    2018

  91. [100]

    Tsujino, D

    K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, Quantum receiver beyond the standard quantum limit of coherent optical communication. Physical Review Letters 106, 250503 (2011)

    2011

  92. [101]

    R. Han, G. Leuchs, and J. A. Bergou, Helstrom measurement: A nondestructive implementation. Physical Review A 101, 032103 (2020)

    2020

  93. [102]

    Sasaki and O

    M. Sasaki and O. Hirota, Optimum decision scheme with a unitary control process for binary quantum-state signals. Physical Review A 54, 2728 (1996)

    1996

  94. [103]

    Warke, J

    A. Warke, J. N¨ otzel, K. Takase, W. Asavanant, H. Nagayoshi, K. Fukui, S. Takeda, A. Furusawa, and P. van Loock, Photonic Quantum Receiver Attaining the Helstrom Bound. arXiv:2410.21800 (2024)

    2024 arXiv

  95. [104]

    Burenkov, M

    I. Burenkov, M. Jabir, and S. Polyakov, Practical quantum-enhanced receivers for classical communication.A VS Quantum Science 3 (2021)

    2021

  96. [105]

    Jabir, I

    M. Jabir, I. Burenkov, N. F. R. Annafianto, A. Battou, and S. Polyakov, Experimental demonstration of the near-quantum optimal receiver. OSA Continuum 3, 3324–3331 (2020)

    2020

  97. [106]

    Becerra, J

    F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination. Nature Photonics 7, 147–152 (2013)

    2013

  98. [107]

    Becerra, J

    F. Becerra, J. Fan, and A. Migdall, Photon number resolution enables quantum receiver for realistic coherent optical communications. Nature Photonics 9, 48–53 (2015)

    2015

  99. [108]

    S. J. Dolinar, (1976) Ph.D. thesis (Massachusetts Institute of Technology)

    1976

  100. [109]

    Tsang, R

    M. Tsang, R. Nair, and X.-M. Lu, Quantum theory of superresolution for two incoherent optical point sources. Physical Review X 6, 031033 (2016)

    2016

  101. [110]

    A. K. Jha, S. Fleming, N. Deshler, A. Sajjad, M. Neifeld, A. Ashok, and S. Guha, Multi-aperture telescopes at the quantum limit of superresolution imaging: Detecting subRayleigh object near a star. Acta Astronautica 226, 531–541 (2025). 26

    2025

  102. [111]

    M. R. Grace, Z. Dutton, A. Ashok, and S. Guha, Approaching quantum-limited imaging resolution without prior knowl- edge of the object location. Journal of the Optical Society of America A 37, 1288–1299 (2020)

    2020

  103. [112]

    K. K. Lee, C. Gagatsos, S. Guha, and A. Ashok, Quantum-limited Optical Super-resolution Imaging of Multiple Point- sources. In Computational Optical Sensing and Imaging , CW3B–2 (2022)

    2022

  104. [113]

    Y. Jo, S. Lee, Y. S. Ihn, Z. Kim, and S.-Y. Lee, Quantum illumination receiver using double homodyne detection. Physical Review Research 3, 013006 (2021)

    2021

  105. [114]

    A. Cox, Q. Zhuang, J. H. Shapiro, and S. Guha, Quantum Illumination Advantage for Classification Among an Arbitrary Library of Targets. In 2024 IEEE International Symposium on Information Theory (ISIT) , 551–556 (2024)

    2024

  106. [115]

    Fukuda, Y

    H. Fukuda, Y. Matsuzaki, and T. Sichanugrist, Directional search for light dark matter with quantum sensors. arXiv:2506.19614 (2025)

    2025 arXiv

  107. [116]

    S. Guha, T. C. John, and P. Basu, Quantum-enhanced quickest change detection of transmission loss. arXiv:2503.12276 (2025)

    2025

  108. [117]

    Meinel, V

    J. Meinel, V. Vorobyov, P. Wang, B. Yavkin, M. Pfender, H. Sumiya, S. Onoda, J. Isoya, R.-B. Liu, and J. Wrachtrup, Quantum nonlinear spectroscopy of single nuclear spins. Nature Communications 13, 5318 (2022)

    2022

  109. [118]

    Zhan and H

    C. Zhan and H. Gupta, Quantum sensor network algorithms for transmitter localization. In 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) Vol. 1, 659–669 (2023)

    2023

  110. [119]

    Huang, R

    H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements. Nature Physics 16, 1050–1057 (2020)

    2020

  111. [120]

    Aaronson, Shadow tomography of quantum states

    S. Aaronson, Shadow tomography of quantum states. In Proceedings of the 50th annual ACM SIGACT symposium on theory of computing , 325–338 (2018)

    2018

  112. [121]

    I. Cong, S. Choi, and M. D. Lukin, Quantum convolutional neural networks. Nature Physics 15, 1273–1278 (2019)

    2019

  113. [122]

    K. Wada, K. Fukuchi, and N. Yamamoto, Quantum-enhanced mean value estimation via adaptive measurement.Quantum 8, 1463 (2024)

    2024

  114. [123]

    Huang, Y

    H.-Y. Huang, Y. Tong, D. Fang, and Y. Su, Learning many-body Hamiltonians with Heisenberg-limited scaling. Physical Review Letters 130, 200403 (2023)

    2023

  115. [124]

    Deutsch and R

    D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 439, 553–558 (1992)

    1992

  116. [125]

    Bernstein and U

    E. Bernstein and U. Vazirani, Quantum complexity theory. In Proceedings of the twenty-fifth annual ACM symposium on Theory of computing , 11–20 (1993)

    1993

  117. [126]

    D. R. Simon, On the power of quantum computation. SIAM journal on computing 26, 1474–1483 (1997)

    1997

  118. [127]

    A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum Algorithm for Linear Systems of Equations. Physical Review Letters 103, 150502 (2009)

    2009

  119. [128]

    Fujii and K

    K. Fujii and K. Nakajima, Quantum reservoir computing: a reservoir approach toward quantum machine learning on near-term quantum devices. Reservoir Computing: Theory, Physical Implementations, and Applications pp. 423–450 (2021)

    2021

  120. [129]

    Mujal, R

    P. Mujal, R. Mart ´ ınez-Pe˜ na, J. Nokkala, J. Garc ´ ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Opportunities in quantum reservoir computing and extreme learning machines. Advanced Quantum Technologies 4, 2100027 (2021)

    2021

  121. [130]

    Krisnanda, S

    T. Krisnanda, S. Ghosh, T. Paterek, W. Laskowski, and T. C. Liew, Phase measurement beyond the standard quantum limit using a quantum neuromorphic platform. Physical Review Applied 18, 034011 (2022)

    2022

  122. [131]

    Senanian, S

    A. Senanian, S. Prabhu, V. Kremenetski, S. Roy, Y. Cao, J. Kline, T. Onodera, L. G. Wright, X. Wu, V. Fatemi et al. Microwave signal processing using an analog quantum reservoir computer. Nature Communications 15, 7490 (2024)

    2024

  123. [132]

    Gily´ en, Y

    A. Gily´ en, Y. Su, G. H. Low, and N. Wiebe, Quantum singular value transformation and beyond: exponential im- provements for quantum matrix arithmetics. In Proceedings of the 51st annual ACM SIGACT symposium on theory of computing, 193–204 (2019)

    2019

  124. [133]

    Lloyd, M

    S. Lloyd, M. Mohseni, and P. Rebentrost, Quantum principal component analysis. Nature physics 10, 631–633 (2014)

    2014

  125. [134]

    Rebentrost, M

    P. Rebentrost, M. Mohseni, and S. Lloyd, Quantum support vector machine for big data classification. Physical Review Letters 113, 130503 (2014)

    2014

  126. [135]

    Ghosh, A

    S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. Liew, Quantum reservoir processing. npj Quantum Infor- mation 5, 35 (2019)

    2019

  127. [136]

    Fujii and K

    K. Fujii and K. Nakajima, Harnessing disordered-ensemble quantum dynamics for machine learning. Physical Review Applied 8, 024030 (2017)

    2017

  128. [137]

    Farhi, J

    E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm. arXiv:1411.4028 (2014)

    2014 arXiv

  129. [138]

    S. P. Jordan, N. Shutty, M. Wootters, A. Zalcman, A. Schmidhuber, R. King, S. V. Isakov, and R. Babbush, Optimization by decoded quantum interferometry. arXiv:2408.08292 (2024)

    2024

  130. [139]

    Holmes, N

    Z. Holmes, N. J. Coble, A. T. Sornborger, and Y. Suba¸ sı, Nonlinear transformations in quantum computation. Physical Review Research 5, 013105 (2023)

    2023

  131. [140]

    H. Yao, Y. Liu, T. Lin, and X. Wang, Nonlinear functions of quantum states. arXiv:2412.01696 (2024)

    2024 arXiv

  132. [141]

    Riberi and L

    F. Riberi and L. Viola, Optimal asymptotic precision bounds for nonlinear quantum metrology under collective dephasing. APL Quantum 2 (2025)

    2025

  133. [142]

    Luis, Nonlinear transformations and the Heisenberg limit

    A. Luis, Nonlinear transformations and the Heisenberg limit. Physics Letters A 329, 8–13 (2004)

    2004

  134. [143]

    Tellinghuisen, Statistical error propagation

    J. Tellinghuisen, Statistical error propagation. The Journal of Physical Chemistry A 105, 3917–3921 (2001)

    2001

  135. [144]

    T. M. Cover and J. A. Thomas, (2006) Elements of Information Theory . (Wiley-Interscience, USA)

    2006

  136. [145]

    Aaronson, A

    S. Aaronson, A. M. Childs, E. Farhi, A. W. Harrow, and B. C. Sanders, Future of Quantum Computing.arXiv:2506.19232 (2025). 27

    2025

  137. [146]

    Y.-X. Wang, J. Bringewatt, A. Seif, A. J. Brady, C. Oh, and A. V. Gorshkov, Exponential entanglement advantage in sensing correlated noise. arXiv:2410.05878 (2024)

    2024 arXiv

  138. [147]

    Prabhu, V

    S. Prabhu, V. Kremenetski, S. A. Khan, R. Yanagimoto, and P. L. McMahon, Exponential advantage in quantum sensing of correlated parameters. arXiv:2504.21745 (2025)

    2025

  139. [148]

    Yamamoto, S

    K. Yamamoto, S. Endo, H. Hakoshima, Y. Matsuzaki, and Y. Tokunaga, Error-mitigated quantum metrology via virtual purification. Physical Review Letters 129, 250503 (2022)

    2022

  140. [149]

    Huerta Alderete, M

    C. Huerta Alderete, M. H. Gordon, F. Sauvage, A. Sone, A. T. Sornborger, P. J. Coles, and M. Cerezo, Inference-based quantum sensing. Physical Review Letters 129, 190501 (2022)

    2022

  141. [150]

    Preskill, Quantum computing in the NISQ era and beyond

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

    2018

  142. [151]

    C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute. Physical Review X 9, 031045 (2019)

    2019

  143. [152]

    Pezze, A

    L. Pezze, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles. Reviews of Modern Physics 90, 035005 (2018)

    2018

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.