Pith. sign in

REVIEW 2 major objections 4 minor 51 references

Preserving Heisenberg-Limited Metrological Information during Storage via Correlated-Noise Correction

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read A correlated-noise correction protocol protects Heisenberg-limited metrological information during storage by entangling the probe with auxiliary qubits and extracting all syndromes once, after the memory stage.

desk verdict The stress test's amplitude-damping objection is wrong: the protocol actually preserves QFI under amplitude damping, though the paper's general framework condition Eq. (10) is not satisfied and the section lacks a real proof. read the letter →

arxiv 2608.08130 v1 pith:567R4OUT submitted 2026-08-08 quant-ph

Hang Xu , Xue-Ke Song , Jingzheng Huang , Tailong Xiao , Guihua Zeng This is my paper · ORCID
classification quant-ph
keywords quantummetrologyHeisenberglimitFisherinformationerrorcorrectionmemorycorrelated-noiseamplitudedampingmulti-qubitprobes
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

This paper tries to establish that the storage stage of a quantum sensing task—the waiting time after the unknown parameter has been encoded but before the probe is measured or reused—can be protected against noise without continuous error correction. It proposes a correlated-noise correction (CNC) protocol in which each memory error channel is coupled to an auxiliary qubit by a fixed two-body entangling gate; the auxiliary qubits coherently record whether errors occurred, and all syndromes are read out once at the end of storage. The paper argues that this preserves the quantum Fisher information of a probe that has already reached Heisenberg-limited encoding under dephasing, bit-flip, and amplitude-damping noise, and that the construction extends from one qubit to multi-qubit probes. It also argues that protecting the encoded Fisher information during storage is weaker than restoring the full probe state: partial correction suffices if the probe is measured immediately, while full state recovery is required if the probe will be reused. This matters because sensing is increasingly an intermediate step in larger quantum workflows, where probes must wait inside quantum memory before the next operation.

What carries the argument

The machinery is the set of entangling gates $T_i$ conjugating each memory error $L_i$ into a Pauli on the auxiliary qubit times the probe error, via Eq. (10). Each gate is fixed and two-body, applied before storage and inverted after storage; because the conjugation condition depends only on the memory error operators and not on the sensing Hamiltonian, the correction strategy decouples from the encoding stage. The same construction is tensored for multiple noise channels and for multi-qubit probes, so the resource count is one auxiliary qubit per independent error channel. The protocol deliberately reads syndromes only once at the end, avoiding repeated measurements that would disturb the stored phase.

What would settle it

Prepare a $Z$-encoded single-qubit probe in $|+\rangle$, let one amplitude-damping event $\sigma_-$ occur during storage, run the one-auxiliary CNC circuit of Sec. IV.C, and measure the ancilla in the $X$ basis many times. If the ancilla outcome is uncorrelated with the damping event, the recovered QFI will fall below $4t_s^2$, falsifying the claimed preservation of Heisenberg-limited information.

Watch

Extended reading notes

Core claim

The central claim is that storage-stage noise can be corrected with a protocol that never measures the probe and never touches it during memory. Before storage, the probe is entangled with auxiliary qubits through gates $T_i$ satisfying $T_i L_j = L_j T_i$ for $j \neq i$ and $T_i^\dagger L_i T_i = P^{(a_i)} \otimes L_i$, so each independent memory error becomes a correlated probe–auxiliary error. After storage, inverse gates map the accumulated errors onto the auxiliary qubits, a single $X$-basis measurement reads all syndromes, and conditional Pauli corrections restore either the quantum Fisher information or the full probe state. For a $Z$-encoded single qubit, one auxiliary qubit with a control-$X$ gate detects dephasing; a second auxiliary qubit detects bit-flip; and the paper argues the same one-auxiliary construction protects against amplitude damping for immediate readout because only the $Z$-degrading component matters. For $N$-qubit GHZ probes, local dephasing is corrected with one auxiliary qubit per probe qubit, preserving the Heisenberg-scaled QFI $4N^2 t_s^2$, and repeated sensing-storage rounds maintain the ideal QFI when bit-flip errors are fully corrected between rounds.

Load-bearing premise

The amplitude-damping result assumes that a single downward decay of the probe flips the auxiliary qubit in the same way a dephasing error does; if the decay instead leaves the auxiliary qubit untouched on the branch where the phase is erased, the one-ancilla protocol loses the parameter information silently.

Editorial extensions

If this is right

  • A probe at the Heisenberg limit can be stored for the full memory interval without loss: for a single-qubit $Z$-encoded probe the QFI remains $4t_s^2$, and for an $N$-qubit GHZ probe it remains $4N^2t_s^2$, provided the auxiliary qubits are effectively noiseless.
  • One syndrome extraction per storage interval suffices; continuous QEC during memory is unnecessary for preserving the Fisher information.
  • When the probe is measured immediately after storage, correcting only the parameter-degrading error component (for $Z$-encoding, the dephasing component) is enough to recover ideal precision even if bit-flip or amplitude-damping distortions remain in the state.
  • When the stored probe must be reused for further sensing or processing, full state recovery is required; the protocol supplies this by correcting all monitored error channels, enabling multi-round Heisenberg scaling.
  • The protocol extends to multi-qubit probes with one ancilla per independent local error channel, so overhead grows linearly with probe size for local noise.

Reading between the lines

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

  • A direct check implied by Eq. (10): for the control-$X$ gate in Eq. (13), the conjugation of a single amplitude-damping event $\sigma_-$ does not obviously produce a Pauli operator on the ancilla, so whether the one-ancilla construction actually detects a decay event is a concrete experiment that would settle the amplitude-damping claim.
  • Since the conjugation condition is independent of the sensing Hamiltonian, the same gate family should protect phase encodings beyond $\sigma_z$, such as collective or multiparameter encodings; the paper demonstrates only $Z$-encoding.
  • The partial-versus-full correction distinction suggests a resource-adaptive schedule: use the cheaper partial correction while the probe is only waiting, and apply full state recovery only immediately before the probe is reused in a later stage; the paper does not optimize this transition.
  • The numerics show QFI degrading with auxiliary dephasing rate $\kappa_a$; an extension would identify the maximum ancilla noise rate below which CNC still outperforms uncorrected storage.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper proposes a correlated-noise correction (CNC) protocol for protecting quantum Fisher information during the storage stage after signal encoding. The protocol entangles the probe with auxiliary qubits before storage, allows the memory channel to act, then applies the inverse entangling gates and reads out all syndromes at the end. The authors claim that this preserves Heisenberg-limited QFI for single- and multi-qubit probes under dephasing, bit-flip, and amplitude-damping noise, and they distinguish between preserving QFI for immediate readout and fully restoring the probe state for later quantum processing. The dephasing and bit-flip constructions are standard and appear sound; the amplitude-damping analysis, however, is not justified by the general framework as written, although the final QFI claim can be recovered by an explicit calculation that the manuscript does not provide.

Significance. The storage-stage viewpoint is a legitimate and relatively unexplored gap in QEC-enhanced metrology: once a parameter is encoded, the probe may need to survive a memory interval before further processing. The paper's key observation that preserving QFI does not require full state recovery when the probe is read out immediately is useful and illustrated clearly in the bit-flip/dephasing example. If the amplitude-damping section is corrected with a proper derivation, the central claim would be solid; the proposed protocol is simple, uses only fixed two-body gates, and naturally extends to multi-qubit probes. The numerical demonstrations support the main idea, though the figures lack sufficient detail for full reproducibility.

major comments (2)
  1. [Sec. IV C, Eq. (13)] The gate T_z does not satisfy the required correlation condition Eq. (10) for L=σ_-. A direct calculation gives T_z^†(I⊗σ_-)T_z = |0><0|⊗σ_- + |1><1|⊗σ_+, which is not of the form P^(a)⊗σ_-. Consequently, the statement that amplitude damping can be handled by 'the same one-auxiliary CNC construction used for dephasing noise' is not supported by the general framework. This is load-bearing because amplitude damping is explicitly listed in the abstract and conclusions. However, the conclusion of Fig. 4 can be recovered: modelling the channel by Kraus operators E_0=|0><0|+k|1><1| and E_1=c|0><1| with c=√(1-k²), and applying σ_z when the ancilla outcome is |−>, gives ρ_out = p|ψ><ψ|+(1-p)σ_x|ψ><ψ|σ_x with p=(1+k²)/2, and this state has exactly the same QFI (1 in the φ parametrization, i.e., 4t_s² for the σ_z encoding) for all k. The paper must either include such a derivation or weaken the amplitude-damping claim to what the current text actually proves.
  2. [Sec. III, Eq. (10)] The framework is presented as necessary: 'the entangling gate T_i is required to satisfy Eq. (10).' The amplitude-damping example violates this requirement, making the framework internally inconsistent. The correct statement is that Eq. (10) is sufficient for converting Pauli-type errors into clean ancilla syndromes, but it is not necessary for preserving QFI, as the amplitude-damping twirl effect shows. The authors should reformulate the general condition as a sufficient design rule, or generalize it to cover non-self-adjoint and non-Pauli noise, and they should explicitly flag where the amplitude-damping protocol departs from the clean-syndrome picture.
minor comments (4)
  1. [Sec. IV C] The correction rule for the amplitude-damping case is not specified. The reader must infer from the dephasing case that σ_z is applied when the ancilla is found in |−⟩. Please state the rule explicitly, together with the amplitude-damping Kraus operators and the relation between k, c, and the damping rate γ.
  2. [Figs. 2–6] The numerical simulations are not reproducible from the text: no master equations, damping rates, auxiliary-noise rates, or initialization/measurement details are given. Please add the parameter values and the precise protocol used for each figure, especially the amplitude-damping simulation in Fig. 4.
  3. [Eq. (4)] The QFI formula uses F(ρ_ω,ρ_{ω+dω}) without specifying whether F is the Uhlmann fidelity or its square. The standard relation is F_Q = 8(1−√F)/dω² when F is the Uhlmann fidelity; please clarify to avoid a factor-of-two ambiguity.
  4. [Sec. IV A] 'using a Shur code' should presumably read 'using a Shor code.' Also, several typographical issues appear in the extracted text (e.g., 'withωencoded', 'F C andF Q'); please correct these in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CNC protocol is constructed from stated algebraic conditions and standard QFI definitions; self-citations are contextual only, and the amplitude-damping issue is a correctness flaw, not a circular derivation.

full rationale

The derivation chain is self-contained. The protocol's central construction is the condition Eq. (10), and the dephasing and bit-flip gates are verified by explicit algebraic identities, Eqs. (14) and (17), that are independently checkable; the single-qubit claims are then evaluated by the standard QFI formula Eq. (4), with numerical results compared against the ideal noiseless case rather than fitted parameters. The multi-qubit generalization is a tensor-product extension, Eq. (21), and the multi-round analysis follows from repeated application of the same correction. I found no instance where a defined quantity is defined in terms of the target conclusion, no fitted input is renamed as a prediction, and no load-bearing premise is justified only by a self-citation: the author self-citations, Refs. [4], [5], [17], and [34], appear in the introduction and related-work discussion as contextual background, not as the justification for the CNC construction or for the QFI preservation claims. The paper also acknowledges limitations honestly, including the auxiliary-qubit noise dependence in Fig. 2 and the statement that amplitude damping is not completely corrected by a single auxiliary qubit when full state recovery is needed. The amplitude-damping section does contain a serious mathematical problem: the gate Tz of Eq. (13) does not satisfy the correlation condition Eq. (10) for L_- = sigma_-, so a single damping jump erases the encoded phase and yields an ambiguous ancilla syndrome. However, that is a correctness or fidelity-to-equations failure, not circularity, because the protocol is not defined in terms of the QFI conclusion it is supposed to reach. I therefore report no significant circularity with score 0.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The protocol relies on standard quantum mechanics and conventional QEC assumptions. No fitted parameters are introduced; all noise rates are inputs. The only questionable element is the implicit assumption that amplitude-damping noise is correctable by the dephasing-style syndrome, which is false.

assumptions (3)
  • domain assumption Memory noise is modeled as a discrete set of independent error operators L_i acting on the probe, with (L_i)^2 = I for Pauli errors.
    Section III assumes the memory channel is described by n independent error operators and that self-adjoint errors can be corrected by applying the same operator; this holds for Pauli noise but not for amplitude damping.
  • domain assumption The sensing stage is noiseless, either because it is protected by QEC or because its duration is much shorter than the storage time.
    Section II states this assumption, which decouples sensing from storage but limits applicability.
  • domain assumption Auxiliary qubits can be prepared in |+>, measured in the X basis, and the entangling gates T_i are noiseless (except in Fig. 2 where auxiliary dephasing is considered).
    Section IV.A and the general framework assume noise-free ancillas and gates; auxiliary noise is only partially addressed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Preserving Heisenberg-Limited Metrological Information during Storage via Correlated-Noise Correction." pith.science (2026). https://pith.science/paper/567R4OUT

@misc{pith2026260808130,
  author       = {Pith},
  title        = {Pith review of: Preserving Heisenberg-Limited Metrological Information during Storage via Correlated-Noise Correction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/567R4OUT}},
  note         = {Machine review of arXiv:2608.08130}
}
read the original abstract

Quantum error correction has become an indispensable tool for restoring Heisenberg-limited precision in noisy quantum metrology. Existing protocols, however, almost exclusively focus on correcting noise during the signal-encoding stage and implicitly assume that the probe is measured immediately after sensing. In many quantum information processing tasks, the encoded probe must instead be stored before subsequent quantum operations, during which environmental noise can significantly degrade the accumulated metrological information. Here, we propose a correlated-noise correction (CNC) protocol for protecting quantum probes during the storage stage. By correlating probe errors with auxiliary qubits through fixed two-body entangling gates, memory errors are converted into measurable syndromes that are extracted only once after storage. We show that the protocol naturally extends from single-qubit to multi-qubit probes and protects the stored quantum Fisher information against dephasing, bit-flip, and amplitude-damping noise. Furthermore, we demonstrate that preserving the quantum Fisher information does not necessarily require restoring the entire quantum state when the probe is measured immediately after storage, whereas full state recovery becomes essential for subsequent rounds of quantum signal processing. Our results establish correlated-noise correction as a practical framework for protecting metrological information during quantum memory and provide a useful building block for sensing-enabled quantum information processing.

Figures

Figures reproduced from arXiv: 2608.08130 by the authors.

Figure 1
Figure 1. FIG. 1. General framework of the correlated-noise correc [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Performance of the CNC protocol for a single [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Performance of the CNC protocol for a memory [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Performance of the CNC protocol for amplitude [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Two-qubit CNC for a single sensing-storage cycle [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Multi-round sensing-storage protocol with local bit [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 29 canonical work pages

  1. [1]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Physical Review Letters96, 010401 (2006)

    2006

  2. [2]

    J. Joo, W. J. Munro, and T. P. Spiller, Quantum metrol- ogy with entangled coherent states, Physical Review Let- ters107, 083601 (2011)

    work page 2011

  3. [3]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Reviews of Modern Physics89, 035002 (2017)

    2017

  4. [4]

    Xu, X.-K

    H. Xu, X.-K. Song, D. Wang, and L. Ye, Quantum sens- ing of control errors in three-level systems by coherent control techniques, Science China Physics, Mechanics & Astronomy66, 240314 (2023)

    work page 2023

  5. [5]

    H. Xu, T. Xiao, J. Huang, M. He, J. Fan, and G. Zeng, Toward heisenberg limit without critical slowing down via quantum reinforcement learning, Physical Review Letters134, 120803 (2025)

    work page 2025

  6. [6]

    X. Zhao, Y. Yang, and G. Chiribella, Quantum metrol- ogy with indefinite causal order, Physical Review Letters 124, 190503 (2020)

    work page 2020

  7. [7]

    P. Yin, X. Zhao, Y. Yang, Y. Guo, W.-H. Zhang, G.-C. Li, Y.-J. Han, B.-H. Liu, J.-S. Xu, G. Chiribella,et al., Experimental super-heisenberg quantum metrology with indefinite gate order, Nature Physics19, 1122 (2023)

    2023

  8. [8]

    X. Yu, X. Zhao, L. Li, X.-M. Hu, X. Duan, H. Yuan, and C. Zhang, Toward heisenberg scaling in non-hermitian metrology at the quantum regime, Science Advances10, eadk7616 (2024)

    work page 2024

Show all 51 references
  1. [9]

    McDonald and A

    A. McDonald and A. A. Clerk, Exponentially-enhanced quantum sensing with non-hermitian lattice dynamics, Nature communications11, 5382 (2020)

    2020

  2. [10]

    W. Ding, X. Wang, and S. Chen, Fundamental sensitiv- ity limits for non-hermitian quantum sensors, Physical Review Letters131, 160801 (2023)

    2023

  3. [11]

    Montenegro, U

    V. Montenegro, U. Mishra, and A. Bayat, Global sens- ing and its impact for quantum many-body probes with criticality, Physical Review Letters126, 200501 (2021)

    2021

  4. [12]

    Mishra and A

    U. Mishra and A. Bayat, Driving enhanced quantum sensing in partially accessible many-body systems, Phys- ical Review Letters127, 080504 (2021)

    2021

  5. [13]

    Escher, R

    B. Escher, R. L. de Matos Filho, and L. Davidovich, Gen- eral framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics7, 406 (2011)

    2011

  6. [14]

    Zhang, S

    Z. Zhang, S. Mouradian, F. N. Wong, and J. H. Shapiro, Entanglement-enhanced sensing in a lossy and noisy en- 8 vironment, Physical Review Letters114, 110506 (2015)

    2015

  7. [15]

    H.-V. Do, C. Lovecchio, I. Mastroserio, N. Fabbri, F. S. Cataliotti, S. Gherardini, M. M. M¨ uller, N. Dalla Pozza, and F. Caruso, Experimental proof of quantum zeno- assisted noise sensing, New Journal of Physics21, 113056 (2019)

    2019

  8. [16]

    Frascella, S

    G. Frascella, S. Agne, F. Y. Khalili, and M. V. Chekhova, Overcoming detection loss and noise in squeezing-based optical sensing, npj Quantum Information7, 72 (2021)

    2021

  9. [17]

    H. Xu, T. Xiao, J. Huang, J. Fan, and G. Zeng, Learning to restore heisenberg limit in noisy quantum sensing via quantum digital twin, arXiv preprint arXiv:2508.11198 (2025)

    2025

  10. [18]

    Bai and J.-H

    S.-Y. Bai and J.-H. An, Floquet engineering to overcome no-go theorem of noisy quantum metrology, Physical Re- view Letters131, 050801 (2023)

    2023

  11. [19]

    Xu, X.-K

    H. Xu, X.-K. Song, D. Wang, and L. Ye, Robust coherent control in three-level quantum systems using composite pulses, Optics Express30, 3125 (2022)

    2022

  12. [20]

    X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, Physically feasible three-level transitionless quantum driving with multiple schr¨ odinger dynamics, Physical Review A93, 052324 (2016)

    2016

  13. [21]

    T. Xiao, J. Fan, and G. Zeng, Parameter estimation in quantum sensing based on deep reinforcement learning, npj Quantum Information8, 2 (2022)

    2022

  14. [22]

    J. Yang, S. Pang, Z. Chen, A. N. Jordan, and A. Del Campo, Variational principle for optimal quantum controls in quantum metrology, Physical Review Letters 128, 160505 (2022)

    2022

  15. [23]

    Yamamoto, S

    K. Yamamoto, S. Endo, H. Hakoshima, Y. Matsuzaki, and Y. Tokunaga, Error-mitigated quantum metrology via virtual purification, Physical Review Letters129, 250503 (2022)

    2022

  16. [24]

    Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Hug- gins, Y. Li, J. R. McClean, and T. E. O’Brien, Quantum error mitigation, Reviews of Modern Physics95, 045005 (2023)

    2023

  17. [25]

    H. Liao, D. S. Wang, I. Sitdikov, C. Salcedo, A. Seif, and Z. K. Minev, Machine learning for practical quantum error mitigation, Nature Machine Intelligence6, 1478 (2024)

    2024

  18. [26]

    Sekatski, M

    P. Sekatski, M. Skotiniotis, and W. D¨ ur, Dynamical de- coupling leads to improved scaling in noisy quantum metrology, New Journal of Physics18, 073034 (2016)

    2016

  19. [27]

    L. M. Pham, N. Bar-Gill, C. Belthangady, D. Le Sage, P. Cappellaro, M. D. Lukin, A. Yacoby, and R. L. Walsworth, Enhanced solid-state multispin metrol- ogy using dynamical decoupling, Physical Review B—Condensed Matter and Materials Physics86, 045214 (2012)

    2012

  20. [28]

    E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Quantum error correction for metrology, Physical Review Letters112, 150802 (2014)

    2014

  21. [29]

    D¨ ur, M

    W. D¨ ur, M. Skotiniotis, F. Froewis, and B. Kraus, Im- proved quantum metrology using quantum error correc- tion, Physical Review Letters112, 080801 (2014)

    2014

  22. [30]

    Unden, P

    T. Unden, P. Balasubramanian, D. Louzon, Y. Vinkler, M. B. Plenio, M. Markham, D. Twitchen, A. Stacey, I. Lovchinsky, A. O. Sushkov,et al., Quantum metrology enhanced by repetitive quantum error correction, Physi- cal Review Letters116, 230502 (2016)

    2016

  23. [31]

    Reiter, A

    F. Reiter, A. S. Sørensen, P. Zoller, and C. Muschik, Dissipative quantum error correction and application to quantum sensing with trapped ions, Nature Communica- tions8, 1822 (2017)

    2017

  24. [32]

    S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achiev- ing the heisenberg limit in quantum metrology using quantum error correction, Nature Communications9, 78 (2018)

    2018

  25. [33]

    Layden and P

    D. Layden and P. Cappellaro, Spatial noise filtering through error correction for quantum sensing, npj Quan- tum Information4, 30 (2018)

    2018

  26. [34]

    H. Xu, X. Deng, Z. Zheng, T. Xiao, and G. Zeng, Noise-resilient heisenberg-limited quantum sensing via indefinite-causal-order error correction, Physical Review Letters137, 020801 (2026)

    2026

  27. [35]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsiout- sios, S. Ganjam, A. Miano, B. Brock, A. Ding, L. Frun- zio,et al., Real-time quantum error correction beyond break-even, Nature616, 50 (2023)

    2023

  28. [36]

    M. H. Michael, M. Silveri, R. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New class of quantum error-correcting codes for a bosonic mode, Physical Review X6, 031006 (2016)

    2016

  29. [37]

    Bharti, A

    K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke,et al., Noisy intermediate- scale quantum algorithms, Reviews of Modern Physics 94, 015004 (2022)

    2022

  30. [38]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Na- ture549, 195 (2017)

    2017

  31. [39]

    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 Communications12, 2631 (2021)

    2021

  32. [40]

    Cerezo, G

    M. Cerezo, G. Verdon, H.-Y. Huang, L. Cincio, and P. J. Coles, Challenges and opportunities in quantum machine learning, Nature Computational Science2, 567 (2022)

    2022

  33. [41]

    T. Xiao, X. Zhai, X. Wu, J. Fan, and G. Zeng, Practical advantage of quantum machine learning in ghost imag- ing, Communications Physics6, 171 (2023)

    2023

  34. [42]

    T. Xiao, X. Zhai, J. Huang, J. Fan, and G. Zeng, Quan- tum deep generative prior with programmable quantum circuits, Communications Physics7, 276 (2024)

    2024

  35. [43]

    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 Physics3, 625 (2021)

    2021

  36. [44]

    Lubasch, J

    M. Lubasch, J. Joo, P. Moinier, M. Kiffner, and D. Jaksch, Variational quantum algorithms for nonlinear problems, Physical Review A101, 010301 (2020)

    2020

  37. [45]

    Z.-C. Yang, A. Rahmani, A. Shabani, H. Neven, and C. Chamon, Optimizing variational quantum algorithms using pontryagin’s minimum principle, Physical Review X7, 021027 (2017)

    2017

  38. [46]

    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 sens- ing in a continuous-variable entangled network, Nature Physics16, 281 (2020)

    2020

  39. [47]

    Bugalho, M

    L. Bugalho, M. Hassani, Y. Omar, and D. Markham, Pri- vate and robust states for distributed quantum sensing, Quantum9, 1596 (2025)

    2025

  40. [48]

    Pompili, S

    M. Pompili, S. L. Hermans, S. Baier, H. K. Beukers, P. C. Humphreys, R. N. Schouten, R. F. Vermeulen, M. J. Tiggelman, L. dos Santos Martins, B. Dirkse,et al., Real- 9 ization of a multinode quantum network of remote solid- state qubits, Science372, 259 (2021)

    2021

  41. [49]

    Liao, W.-Q

    S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, et al., Satellite-relayed intercontinental quantum net- work, Physical Review Letters120, 030501 (2018)

    2018

  42. [50]

    S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters72, 3439 (1994)

    1994

  43. [51]

    J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum fisher information matrix and multiparameter estima- tion, Journal of Physics A: Mathematical and Theoretical 53, 023001 (2020)

    2020

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.