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REVIEW 3 major objections 5 minor 65 references

Quantum Compressive Sensing Meets Quantum Noise: A Practical Exploration

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Quantum compressive sensing can be run on noisy cloud quantum hardware, with QITE projection and per-gate noise near 1e-4 or lower.

desk verdict A genuinely new empirical study of QITE-based QCS under noise, but the missing (A,x) to H construction keeps the main results from being checkable. read the letter →

arxiv 2501.12335 v1 pith:MXVVBNKT submitted 2025-01-21 quant-ph

Naveed Naimipour , Collin Frink , Harry Shaw , Haleh Safavi , Mojtaba Soltanalian This is my paper · ORCID
classification quant-ph
keywords quantumcompressivesensingQITEnoiseBornmachineLIDARAmazonBraketsignalreconstructiontensornetworks
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 claims that the Quantum Compressive Sensing (QCS) protocol can be put into practice on a noisy cloud quantum computer rather than only in classical simulation. The authors implement the full Quantum Imaginary Time Evolution projection on a five-pixel LIDAR waveform dataset, and report that under bit-flip, depolarizing, dephasing, and amplitude-damping noise, the mean scaled root-mean-square reconstruction error decreases as more pixels are measured classically. They also find that the pre-trained quantum average is preserved only when per-gate noise is around 1e-4 or lower, and that shot noise in QITE's tomography step can be mitigated by tuning shot counts and imaginary-time step sizes. If these results hold, they indicate that QCS is deployable on near-term quantum hardware without full error correction.

What carries the argument

The mechanism is the Born machine quantum average combined with QITE projection. The quantum average $|\Psi\rangle$ is a superposition of training samples prepared through a circuit with a control register; its squared amplitudes give the probability of each signal. QITE applies the imaginary-time evolution $e^{-\beta \hat{H}}$ to this state, exponentially suppressing basis states whose expectation values disagree with the measured outcome, and implements this non-unitary operation unitarily through quantum state tomography followed by Trotterized imaginary-time steps. A second ingredient is the pixel-qubit angle encoding, which maps each real pixel value to a single-qubit rotation so that the entire signal state remains an efficiently prepared product state.

What would settle it

Run the QCS plus QITE pipeline on a signal larger than five pixels with an arbitrary sensing matrix $A$ and a stated general rule for building the projection Hamiltonian from $A$ and the measurement outcome $x$. If the mean sRMSE stops decreasing as $N_c$ increases, or if no such general Hamiltonian construction can be given, the paper's central practicability claim fails.

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Extended reading notes

Core claim

The central discovery is that the QCS architecture, which had previously been studied only through classical simulation, can be implemented end-to-end on a real cloud quantum platform using the full QITE projection algorithm. Concretely, the paper shows that for a five-pixel LIDAR waveform dataset, a Born machine trained on 256 samples can be projected onto measurement-constrained states via QITE, and that under bit-flip, depolarizing, dephasing, and amplitude-damping noise, the mean per-pixel sRMSE of the reconstructed signal decreases as the number of classically measured pixels increases. The paper also reports that the trained quantum-average state is only preserved when the per-gate noise probability is on the order of 1e-4 or smaller, and that shot noise in QITE tomography can be controlled by increasing the number of shots per observable and by discarding failed imaginary-time iterations. The authors present this as evidence that QCS is a practical quantum data-driven approach for compressive sensing in the noisy intermediate-scale era.

Load-bearing premise

The result rests on the assumption that every measurement constraint can be encoded as a simple few-qubit energy operator whose ground state is the desired projected signal; the paper shows this for one hand-picked operator and does not give the general construction.

Editorial extensions

If this is right

  • Near-term quantum imaging pipelines can use QITE projection without full error correction when per-gate noise is at or below about 1e-4.
  • Classically measuring more pixels provides a practical knob to reduce reconstruction error under noise, as shown by the decreasing sRMSE with increasing $N_c$.
  • A 256-sample quantum average is sufficient to approximate the global average for five-pixel LIDAR waveforms, keeping the training circuit small.
  • Shot noise in QITE tomography can be managed by tuning shots-per-observable and the imaginary-time step size $d\beta$, making the projection robust enough for current hardware.

Reading between the lines

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

  • A general construction of the projection Hamiltonian from the sensing matrix $A$ and measurement outcome $x$ is the missing step; if one exists, QITE-based QCS would extend to arbitrary sensing matrices rather than only the hand-picked operator shown in the paper.
  • Because the paper only tests five-pixel signals, the observed monotone decrease in error with $N_c$ is a trend, not a scaling law; larger sparse datasets could make the benefit per measured pixel larger or smaller.
  • The encoding results hint that tuning pixel midpoints or adding one qubit per ambiguous pixel could remove a large share of reconstruction errors without any additional measurements.
  • QITE's tomography cost per step will dominate on larger images, so combining QITE with reduced-tomography methods that use fewer observables per step is a natural next test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper claims to implement the Quantum Compressive Sensing (QCS) architecture of Ref. [52] with Quantum Imaginary Time Evolution (QITE) as the projection method, using 5-pixel LIDAR-derived data mapped via Eq. (1). It reports fidelity benchmarks for training-subset quantum averages (Fig. 4a), fidelity degradation under bit-flip, depolarizing, and dephasing noise with a suggested noise threshold of about 1e-4 (Fig. 4b), sRMSE-versus-Nc curves for QCS reconstruction under noiseless and noisy QITE (Fig. 5), and a separate QITE shot-noise study on a fixed 3-qubit Hamiltonian (Fig. 6). The central assertion is that QCS can be practically deployed on Amazon Braket with full QITE under realistic noise, and that increasing the number of classically measured pixels decreases reconstruction error. However, the manuscript does not specify how the QITE Hamiltonian is constructed from the sensing matrix A and measurement outcome x, which leaves the central reconstruction claim uncheckable as written.

Significance. If the central claim could be verified, this would be the first demonstration that the projection stage of QCS can be implemented with full QITE on a cloud quantum platform, and the fidelity/noise-threshold data in Fig. 4 would be useful engineering input for small-scale QCS experiments. The paper is honest about the small dataset and limited sparsity, and the shot-noise mitigation experiments of Fig. 6 are a concrete empirical contribution on their own. That said, the paper ships no code or data, and the missing (A, x) -> H construction means the sRMSE curves cannot currently be attributed to the QCS projection objective. The hardware claim is also stronger than what the simulations actually demonstrate.

major comments (3)
  1. [Section 3.1.3 (Eqs. (5)-(6)), Fig. 5(a), (f)-(j)] The central projection step is not specified. Section 3.1.3 describes QITE only through the general tomography and Trotter formulas of Eqs. (5)-(6); the manuscript nowhere gives the map from the sensing matrix A and measurement outcome x to the Hamiltonian H used in the sRMSE experiments of Figs. 5(f)-5(j). The only explicit realization, H = -(ZIIII + IIZII) in Fig. 5(a), is a fixed operator: it has no dependence on which pixels were classically measured, no dependence on the measured values x, and no dependence on the pixel-qubit midpoint v of Eq. (1). Such an operator at best implements one particular projection (favoring the j1> state on two fixed qubits), not the general measurement-consistent projection |Psi_x> for arbitrary pixel sets and outcomes. Consequently the reported decrease of sRMSE with Nc cannot be verified as an effect of QCS projection; it could arise from QITE relaxing to a trivial fixed subspace. The revised manuscript must provide the explicit construction (A, x) -> H, including how Nc, the measured pixel indices, and the measured values enter the Hamiltonian coefficients, together with the tomography and Trotter implementation details.
  2. [Section 4.3, Fig. 6] The shot-noise study is not connected to the QCS pipeline. Figure 6 reports QITE convergence only for a fixed 3-qubit Hamiltonian H = -ZII - IIZ, varying shots per observable and d_beta; it does not report sRMSE, reconstruction error, or any metric tied to the QCS setup of Section 3.1.3. The statement that a check for highly perturbative shot-noise instances with a medium d_beta 'significantly mitigates' shot noise is therefore demonstrated only for a toy Hamiltonian, not for QCS. In addition, Section 3.2.4 says that shot noise 'will naturally exist' when implementing on quantum cloud resources, but the experiments in this paper are local statevector and density-matrix simulations; if finite-shot statistics were simulated, the exact simulation recipe should be described.
  3. [Introduction, Section 4.2, Section 3.2.3] The 'practical implementation on Amazon Braket' claim exceeds what the experiments demonstrate. The Introduction states that QITE is implemented 'on Amazon's quantum cloud computing services' and the abstract announces a 'practical implementation of QCS on Amazon Braket,' but Section 4.2 says that all Born machine circuits are generated using 'local, statevector simulations' via the Braket SDK, and Section 3.2.3 explicitly limits the noisy QITE results to 'density matrix simulations.' No QPU, device, or execution details are reported anywhere. The paper should either present hardware execution results or rephrase the contribution as a simulator-based implementation, because the current wording overstates the evidence for deployment on actual quantum computing resources.
minor comments (5)
  1. [Eq. (11)] Equation (11) uses K0 in both terms of the amplitude-damping channel; one of them should be K1 as defined in Eq. (13).
  2. [Fig. 5 caption] The caption for Fig. 5 is internally confusing: it says '(g)-(j) Same as (f) except for single-gate bit-flip noise...' and then '(h)-(j) being identical demonstrations for depolarizing, dephasing, and amplitude damping noise.' As written, the assignment of panels to noise types is contradictory and should be clarified.
  3. [Eq. (14)] The sRMSE formula appears to contain an unresolved LaTeX control sequence ('vuut'), and the printed formula lacks an explicit square-root symbol; the intended expression should be a standard sqrt( (1/nu) * sum_i ((P_i - R_i)/sigma_i)^2 ).
  4. [General formatting] Several superscripts are rendered with spaces rather than exponents (e.g., '2 15', '10 -4', '2 8'), which makes the text hard to read; these should be typeset as proper superscripts.
  5. [Section 5.2] In the data-encoding example, the midpoint parameter is called 'p', whereas Eq. (1) and the surrounding text use 'v'; the notation should be unified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the implementation results are measured on Amazon Braket against external metrics, and QITE is imported from independent literature.

full rationale

The paper's central claims are empirical: it reports fidelity of noisy quantum-average states to a global quantum average and mean sRMSE versus the number of classically measured pixels under four noise models. These are measurements on Amazon Braket, not quantities derived by fitting the framework's own equations and then relabeled as predictions. The QCS architecture and the pixel-qubit mapping are adopted from prior work, including the authors' own [52], but they serve as stated assumptions and prior-art context; the present contribution is a deployment and noise study, and its results are externally benchmarked against ground-truth pixel values through Equation (14). QITE is imported from the independent work of Motta et al. [53], and the paper does not invoke any uniqueness theorem or self-citation to force its choice. The one substantive weakness is that the paper never specifies how the QITE Hamiltonian H is constructed from the sensing matrix A and measurement outcome x, and the only displayed Hamiltonian appears independent of x; this is an omitted derivation and validation issue, not a circular reduction of a predicted quantity to its input. No equation in the paper equates an output to an input by construction, and no fitted parameter is renamed as a prediction. Under the hard rules, the absence of such a reduction means no circularity is established, so the score is 0.

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

The central claim rests on the QCS machinery from the authors' prior paper [52], the QITE algorithm from [53], and a set of hand-chosen experimental parameters (v, subset size, d_beta, discard count). No new physical entities are introduced. The most consequential unproven premise is the existence of a QITE Hamiltonian that implements the QCS projection for arbitrary sensing matrices.

free parameters (4)
  • Pixel-qubit mapping midpoint v = 0.5 (default); example with v=[0,0.75] in Sec. 5.2
    Eqs. (1)-(2) in Sec. 3.1.1 define the pixel-to-qubit encoding with free parameter v. The main results assume v=0.5, and Sec. 5.2 shows changing v changes reconstruction error, so the reported numbers depend on this choice.
  • Training subset size = 256 samples (2^8)
    Figure 4(a) selects 256 as the smallest subset with fidelity >=0.98 to the global quantum average; all QCS results in Figures 4-5 use a 256-sample Born machine.
  • QITE imaginary time step d_beta = 0.3, 0.05, 0.005 in Figure 6; unspecified for Figure 5
    The shot-noise study varies d_beta by hand, and Figure 6(i) indicates a 'medium' d_beta is best; the convergence results depend on this discretization.
  • Failed-iteration discard count = up to 30
    Sec. 4.3 and Figures 6(g-i): QITE iterations that raise the energy are discarded up to 30 times before the energy increase is accepted. This heuristic is a free parameter chosen by the authors and materially improves the shot-noise curves.
assumptions (5)
  • domain assumption The Born machine constructed as a uniform quantum average over the training set (Eqs. 3-4) is a faithful representation of the signal distribution, and measuring the control register in state 0 succeeds with probability >= 1/|D|.
    Invoked in Sections 3.1.1-3.1.2 to justify training; the fidelity to psi_global in Figure 4(a) is the only empirical check, and it uses the same construction rather than an external benchmark.
  • domain assumption Full QITE (Eqs. 5-6) correctly approximates imaginary-time evolution on a quantum computer, including the Trotter error O(delta_tau), and that quantum state tomography of the local Hamiltonian h[m] is feasible for the QCS circuits.
    Imported from Motta et al. [53] in Section 3.1.3; the paper does not re-derive or verify the tomography step for the QCS Born machine, which is assumed to work on Braket.
  • ad hoc to paper The QITE Hamiltonian H for projection can be chosen so that its imaginary-time evolution implements the QCS Gaussian projection onto the measurement-consistent subspace.
    Section 3.1.3 states QITE introduces a Gaussian operator suppressing mismatched basis states, but no construction of H from A and x is given. The only explicit H is the two-term demo in Figure 5(a). This is the paper's weakest premise.
  • domain assumption Single-qubit-gate bit-flip, depolarizing, dephasing, and amplitude-damping noise at probabilities 1e-4 to 1e-6 are representative enough of quantum noise to assess QCS behavior.
    Section 3.2 models noise as per-gate Pauli channels and Section 3.3 explicitly states real-world noise is beyond scope. The noise probabilities are order-of-magnitude choices, not calibrated to Braket hardware.
  • domain assumption A 5-pixel energy-quartile representation of LIDAR waveforms preserves the structure needed to test QCS reconstruction.
    Section 4.1 reduces each waveform to five numbers; the paper acknowledges (Sec. 4.3) that the small size and low sparsity hinder QCS, so the dataset choice is an assumption about what constitutes a valid demonstration.

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Pith. "Pith review of Quantum Compressive Sensing Meets Quantum Noise: A Practical Exploration." pith.science (2026). https://pith.science/paper/MXVVBNKT

@misc{pith2026250112335,
  author       = {Pith},
  title        = {Pith review of: Quantum Compressive Sensing Meets Quantum Noise: A Practical Exploration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MXVVBNKT}},
  note         = {Machine review of arXiv:2501.12335}
}
read the original abstract

Compressive sensing is a signal processing technique that enables the reconstruction of sparse signals from a limited number of measurements, leveraging the signal's inherent sparsity to facilitate efficient recovery. Recent works on the Quantum Compressive Sensing (QCS) architecture, a quantum data-driven approach to compressive sensing where the state of the tensor network is represented by a quantum state over a set of entangled qubits, have shown promise in advancing quantum data-driven methods for compressive sensing. However, the QCS framework has remained largely untested on quantum computing resources or in the presence of quantum noise. In this work, we present a practical implementation of QCS on Amazon Braket, utilizing the Quantum Imaginary Time Evolution (QITE) projection technique to assess the framework's capabilities under quantum noise. We outline the necessary modifications to the QCS framework for deployment on Amazon Braket, followed by results under four types of quantum noise. Finally, we discuss potential long-term directions aimed at unlocking the full potential of quantum compressive sensing for applications such as signal recovery and image processing.

Figures

Figures reproduced from arXiv: 2501.12335 by the authors.

Figure 1
Figure 1. General workflow diagram of the proposed protocol where it can be seen the Pixel-Qubit [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. This greatly reduces the dimensionality of the data while preserving key forest structure [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 2
Figure 2. Visualization of how the LIDAR waveforms are split into five energy quartiles for a [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: Steps for Data Processing is termed ψglobal. In order to determine the smallest random subset that sufficiently represents ψglobal, we randomly create 5 random independent training subsets of sizes 23 , 24 , up to 213 . Only three independent subsets can be generated o…
Figure 4
Figure 4. Figure 4: (a) Average fidelity of 5 datasets randomly selected from the training set with [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Demonstration of the QITE projection algorithm on a LIDAR dataset. (a) Con [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: QITE runs of three different tomography approaches while varying the number of shots [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

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Works this paper leans on

65 extracted references · 47 canonical work pages

  1. [52]

    Quantum compressive sensing: Mathematical machinery, quantum algorithms, and quantum circuitry,

    K. M. Sherbert, N. Naimipour, H. Safavi, H. C. Shaw, and M. Soltanalian, “Quantum compressive sensing: Mathematical machinery, quantum algorithms, and quantum circuitry,” Applied Sciences , vol. 12, no. 15, p. 7525, Jul. 2022. [Online]. Available: http://dx.doi.org/10.3390/app12157525

    work page doi:10.3390/app12157525 2022

  2. [1]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cam- bridge University Press, 6 2012

    work page 2012

  3. [2]

    Colloquium: Protecting quantum information against environmental noise,

    D. Suter and G. A. ´Alvarez, “Colloquium: Protecting quantum information against environmental noise,” Rev. Mod. Phys., vol. 88, p. 041001, Oct 2016. [Online]. Available: https://link.aps.org/doi/10.1103/RevModPhys.88.041001

    doi:10.1103/revmodphys.88.041001 2016

  4. [3]

    1/f noise: Implications for solid-state quantum information,

    E. Paladino, Y . M. Galperin, G. Falci, and B. L. Altshuler, “1/f noise: Implications for solid-state quantum information,” Rev. Mod. Phys. , vol. 86, pp. 361–418, Apr 2014. [Online]. Available: https://link.aps.org/doi/10.1103/RevModPhys.86.361

    doi:10.1103/revmodphys.86.361 2014

  5. [4]

    Quantum circuit engineering for correcting coherent noise,

    M. Ahsan, S. A. Z. Naqvi, and H. Anwer, “Quantum circuit engineering for correcting coherent noise,” Phys. Rev. A , vol. 105, p. 022428, Feb 2022. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.105.022428

    work page doi:10.1103/physreva.105.022428 2022

  6. [5]

    Noise gates for decoherent quantum circuits,

    A. Bassi and D. A. Deckert, “Noise gates for decoherent quantum circuits,” Physical Review A, vol. 77, 03 2008

    work page 2008

  7. [6]

    Classical simulation of quantum dephasing and depolarizing noise,

    D. Crow and R. Joynt, “Classical simulation of quantum dephasing and depolarizing noise,” Phys. Rev. A , vol. 89, p. 042123, Apr 2014. [Online]. Available: https: //link.aps.org/doi/10.1103/PhysRevA.89.042123

    work page doi:10.1103/physreva.89.042123 2014

  8. [7]

    Mitigating depolarizing noise on quantum computers with noise-estimation circuits,

    M. Urbanek, B. Nachman, V . R. Pascuzzi, A. He, C. W. Bauer, and W. A. de Jong, “Mitigating depolarizing noise on quantum computers with noise-estimation circuits,” Phys. Rev. Lett. , vol. 127, p. 270502, Dec 2021. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.127.270502

    work page doi:10.1103/physrevlett.127.270502 2021

Show all 65 references
  1. [8]

    Standard forms of noisy quantum operations via depolarization,

    W. D ¨ur, M. Hein, J. I. Cirac, and H.-J. Briegel, “Standard forms of noisy quantum operations via depolarization,” Phys. Rev. A , vol. 72, p. 052326, Nov 2005. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.72.052326

    2005 doi

  2. [9]

    From quantum communication fundamentals to decoherence mitigation strategies: Addressing global quantum network challenges and projected applications,

    M. A. Khan, S. Ghafoor, S. M. H. Zaidi, H. Khan, and A. Ahmad, “From quantum communication fundamentals to decoherence mitigation strategies: Addressing global quantum network challenges and projected applications,” Heliyon, vol. 10, no. 14, p. e34331, 2024. [Online]. Availabl...

    2024

  3. [10]

    Special session: Impact of noise on quantum algorithms in noisy intermediate-scale quantum systems,

    D. V olya and P. Mishra, “Special session: Impact of noise on quantum algorithms in noisy intermediate-scale quantum systems,” in2020 IEEE 38th International Conference on Com- puter Design (ICCD), 2020, pp. 1–4

    2020

  4. [11]

    Characterization and control of open quantum systems beyond quantum noise spectroscopy,

    A. Youssry, G. Paz Silva, and C. Ferrie, “Characterization and control of open quantum systems beyond quantum noise spectroscopy,”npj Quantum Information, vol. 6, 12 2020

    2020

  5. [12]

    Quantum shot noise,

    C. Beenakker and C. Sch ¨onenberger, “Quantum shot noise,” Physics Today, vol. 56, no. 5, pp. 37–42, 05 2003. [Online]. Available: https://doi.org/10.1063/1.1583532 18

    2003 doi

  6. [13]

    Quantum shot noise,

    M. Reznikov, R. de Picciotto, M. Heiblum, D. Glattli, A. Kumar, and L. Saminadayar, “Quantum shot noise,”Superlattices and Microstructures, vol. 23, no. 3, pp. 901–915, 1998. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0749603697905590

    1998

  7. [14]

    Quantum synchronization in presence of shot noise,

    F. H ¨ohe, L. Danner, C. Padurariu, B. I. C. Donvil, J. Ankerhold, and B. Kubala, “Quantum synchronization in presence of shot noise,” 2024. [Online]. Available: https://arxiv.org/abs/2306.15292

    2024 arXiv

  8. [15]

    Noise-aware quantum amplitude estima- tion,

    S. Herbert, I. Williams, R. Guichard, and D. Ng, “Noise-aware quantum amplitude estima- tion,” IEEE Transactions on Quantum Engineering, vol. 5, pp. 1–23, 2024

    2024

  9. [16]

    Protecting quantum entanglement from amplitude damping,

    M. Al-Amri and M. Zubairy, “Protecting quantum entanglement from amplitude damping,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 46, 07 2013

    2013

  10. [17]

    Quantum circuits for collective amplitude damping in two-qubit systems,

    Y . Hama, “Quantum circuits for collective amplitude damping in two-qubit systems,” 2020. [Online]. Available: https://arxiv.org/abs/2012.02410

    2020 arXiv

  11. [18]

    Manipulating the flow of thermal noise in quantum devices,

    S. Barzanjeh, M. Aquilina, and A. Xuereb, “Manipulating the flow of thermal noise in quantum devices,” Phys. Rev. Lett. , vol. 120, p. 060601, Feb 2018. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.120.060601

    2018 doi

  12. [19]

    Optimal feedback control of linear quantum systems in the presence of thermal noise,

    M. G. Genoni, S. Mancini, and A. Serafini, “Optimal feedback control of linear quantum systems in the presence of thermal noise,” Phys. Rev. A , vol. 87, p. 042333, Apr 2013. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.87.042333

    2013 doi

  13. [20]

    Dissipation and thermal noise in hybrid quantum systems in the ultrastrong- coupling regime,

    A. Settineri, V . Macr ´ı, A. Ridolfo, O. Di Stefano, A. F. Kockum, F. Nori, and S. Savasta, “Dissipation and thermal noise in hybrid quantum systems in the ultrastrong- coupling regime,” Phys. Rev. A , vol. 98, p. 053834, Nov 2018. [Online]. Available: https://link.aps.org/do...

    2018 doi

  14. [21]

    Performance of quantum data transmission systems in the presence of thermal noise,

    G. Cariolaro and G. Pierobon, “Performance of quantum data transmission systems in the presence of thermal noise,” IEEE Transactions on Communications, vol. 58, no. 2, pp. 623– 630, 2010

    2010

  15. [22]

    The power of quantum neural networks,

    A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and S. Woerner, “The power of quantum neural networks,” Nature Computational Science, vol. 1, no. 6, p. 403–409, Jun

  16. [23]

    Quantum machine learning,

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,” Nature, vol. 549, no. 7671, p. 195–202, Sep. 2017. [Online]. Available: http://dx.doi.org/10.1038/nature23474

    2017 doi

  17. [24]

    Training variational quantum algorithms is np-hard,

    L. Bittel and M. Kliesch, “Training variational quantum algorithms is np-hard,” Phys. Rev. Lett. , vol. 127, p. 120502, Sep 2021. [Online]. Available: https: //link.aps.org/doi/10.1103/PhysRevLett.127.120502

    2021 doi

  18. [25]

    Power of data in quantum machine learning,

    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, vol. 12, no. 1, May 2021. [Online]. Available: http://dx.doi.org/10.1038/s41467-021-22539-9 19

    2021 doi

  19. [26]

    Noise-assisted quantum autoencoder,

    C. Cao and X. Wang, “Noise-assisted quantum autoencoder,” Phys. Rev. Appl., vol. 15, p. 054012, May 2021. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevApplied. 15.054012

    2021 doi

  20. [27]

    Rigorous noise reduction with quantum autoencoders,

    W.-K. Mok, H. Zhang, T. Haug, X. Luo, G.-Q. Lo, Z. Li, H. Cai, M. S. Kim, A. Q. Liu, and L.-C. Kwek, “Rigorous noise reduction with quantum autoencoders,”AVS Quantum Science, vol. 6, no. 2, p. 023803, 05 2024. [Online]. Available: https://doi.org/10.1116/5.0192456

    2024 doi

  21. [28]

    Learning high-accuracy error decoding for quantum processors,

    J. Bausch, A. Senior, F. Heras, T. Edlich, A. Davies, M. Newman, C. Jones, K. Satzinger, Y . Niu, S. Blackwell, G. Holland, D. Kafri, J. Atalaya, C. Gidney, D. Hassabis, S. Boixo, H. Neven, and P. Kohli, “Learning high-accuracy error decoding for quantum processors,” Nature, v...

    2024

  22. [29]

    Machine learning for practical quantum error mitigation,

    H. Liao, D. S. Wang, I. Sitdikov, C. Salcedo, A. Seif, and Z. K. Minev, “Machine learning for practical quantum error mitigation,” Nature Machine Intelligence , vol. 6, no. 12, p. 1478–1486, Nov. 2024. [Online]. Available: http://dx.doi.org/10.1038/s42256-024-00927-2

    2024 doi

  23. [30]

    Quantum error correction for the toric code using deep reinforcement learning,

    P. Andreasson, J. Johansson, S. Liljestrand, and M. Granath, “Quantum error correction for the toric code using deep reinforcement learning,” Quantum, vol. 3, p. 183, Sep. 2019. [Online]. Available: https://doi.org/10.22331/q-2019-09-02-183

    2019 doi

  24. [31]

    Enhancing adversarial robustness of quantum neural networks by adding noise layers,

    C. Huang and S. Zhang, “Enhancing adversarial robustness of quantum neural networks by adding noise layers,” New Journal of Physics, vol. 25, no. 8, p. 083019, aug 2023. [Online]. Available: https://dx.doi.org/10.1088/1367-2630/ace8b4

    2023 doi

  25. [32]

    Flexible error mitigation of quantum processes with data augmentation empowered neural model,

    M. Liao, Y . Zhu, G. Chiribella, and Y . Yang, “Flexible error mitigation of quantum processes with data augmentation empowered neural model,” 2023. [Online]. Available: https://arxiv.org/abs/2311.01727

    2023 arXiv

  26. [34]

    The restricted isometry property and its implications for compressed sensing,

    E. J. Cand `es, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique , vol. 346, no. 9, pp. 589–592, 2008. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1631073X08000964

    2008

  27. [35]

    Donoho, “Donoho, d.l.: For most large underdetermined systems of linear equations the minimal l(1)-norm solution is also the sparsest solution

    D. Donoho, “Donoho, d.l.: For most large underdetermined systems of linear equations the minimal l(1)-norm solution is also the sparsest solution. communications on pure and applied mathematics 59(6), 797-829,” Communications on Pure and Applied Mathematics, vol. 59, pp. 797 –...

    2006

  28. [36]

    Compressed sensing,

    ——, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006

    2006

  29. [37]

    An introduction to compressive sampling,

    E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, 2008. 20

    2008

  30. [38]

    Enhancing sparsity by reweighted l1 minimization,

    E. Cand `es, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted l1 minimization,” Journal of Fourier Analysis and Applications, vol. 14, pp. 877–905, 11 2007

    2007

  31. [39]

    Robust uncertainty principles: exact signal recon- struction from highly incomplete frequency information,

    E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal recon- struction from highly incomplete frequency information,”IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006

    2006

  32. [40]

    Near-Optimal Signal Recovery From Random Projections: Uni- versal Encoding Strategies?

    E. J. Candes and T. Tao, “Near-Optimal Signal Recovery From Random Projections: Uni- versal Encoding Strategies?” IEEE Transactions on Information Theory, vol. 52, no. 12, pp. 5406–5425, 2006

    2006

  33. [41]

    Sparsity and incoherence in compressive sampling,

    E. Cand `es and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Problems , vol. 23, no. 3, pp. 969–985, apr 2007. [Online]. Available: https://doi.org/10.1088/0266-5611/23/3/008

    2007 doi

  34. [42]

    Underwater laser serial imaging using compressive sensing and digital mirror device,

    B. Ouyang, F. R. Dalgleish, F. M. Caimi, T. E. Giddings, J. J. Shirron, A. K. Vuorenkoski, G. Nootz, W. Britton, and B. Ramos, “Underwater laser serial imaging using compressive sensing and digital mirror device,” in Laser Radar Technology and Applications XVI , M. D. Turner a...

    2011 doi

  35. [43]

    Compressive sensing matrices and hash fami- lies,

    C. J. Colbourn, D. Horsley, and C. McLean, “Compressive sensing matrices and hash fami- lies,” IEEE Transactions on Communications, vol. 59, no. 7, pp. 1840–1845, 2011

    2011

  36. [44]

    Introducing the counter mode of operation to compressed sensing based encryption,

    R. Fay, “Introducing the counter mode of operation to compressed sensing based encryption,” Information Processing Letters, vol. 116, no. 4, pp. 279–283, 2016. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0020019015001945

    2016

  37. [45]

    Single-pixel imaging via compressive sampling: Building simpler, smaller, and less-expensive digital cameras,

    M. F. Duarte, M. A. Davenport, D. Takbar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling: Building simpler, smaller, and less-expensive digital cameras,”IEEE Signal Processing Magazine, vol. 25, pp. 83–91, 2008

    2008

  38. [46]

    Compressive sensing lidar for 3d imaging,

    G. A. Howland, P. Zerom, R. W. Boyd, and J. C. Howell, “Compressive sensing lidar for 3d imaging,” in CLEO: 2011 - Laser Science to Photonic Applications, 2011, pp. 1–2

    2011

  39. [47]

    Information Perspective to Probabilistic Modeling: Boltz- mann Machines versus Born Machines,

    S. Cheng, J. Chen, and L. Wang, “Information Perspective to Probabilistic Modeling: Boltz- mann Machines versus Born Machines,” Entropy, vol. 20, no. 8, 2018

    2018

  40. [48]

    Differentiable learning of quantum circuit Born machines,

    J.-G. Liu and L. Wang, “Differentiable learning of quantum circuit Born machines,” Phys. Rev. A, vol. 98, p. 062324, Dec 2018. [Online]. Available: https://link.aps.org/doi/10.1103/ PhysRevA.98.062324

    2018

  41. [49]

    Supervised learning with quantum-inspired tensor networks,

    E. M. Stoudenmire and D. J. Schwab, “Supervised learning with quantum-inspired tensor networks,” arXiv, 2016. [Online]. Available: https://arxiv.org/abs/1605.05775

    2016 arXiv

  42. [50]

    Unsupervised Generative Modeling Using Matrix Product States,

    Z. Y . Han, J. Wang, H. Fan, L. Wang, and P. Zhang, “Unsupervised Generative Modeling Using Matrix Product States,” Physical Review X, vol. 8, 7 2018. 21

    2018

  43. [51]

    Tensor network compressed sensing with unsupervised machine learning,

    S.-J. Ran, Z.-Z. Sun, S.-M. Fei, G. Su, and M. Lewenstein, “Tensor network compressed sensing with unsupervised machine learning,” Phys. Rev. Research, vol. 2, p. 033293, Aug

  44. [53]

    Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution,

    M. Motta, C. Sun, A. T. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. Brand ˜ao, and G. K. L. Chan, “Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution,” Nature Physics, vol. 16, no. 2, pp. 205–210, 2020. [Online]. Availa...

    2020 doi

  45. [54]

    Amazon Braket,

    Amazon Web Services, “Amazon Braket,” 2020. [Online]. Available: https://aws.amazon. com/braket/

    2020

  46. [55]

    Rodeo algorithm for quantum com- puting,

    K. Choi, D. Lee, J. Bonitati, Z. Qian, and J. Watkins, “Rodeo algorithm for quantum com- puting,” arXiv, no. 1, pp. 1–7, 2021

    2021

  47. [56]

    Modeling and simulating the noisy behavior of near-term quantum computers,

    K. Georgopoulos, C. Emary, and P. Zuliani, “Modeling and simulating the noisy behavior of near-term quantum computers,” Physical Review A, vol. 104, p. 062432, 12 2021

    2021

  48. [57]

    Microwave Imaging of Nonweak Targets via Compressive Sensing and Virtual Experiments,

    M. T. Bevacqua, L. Crocco, L. Di Donato, and T. Isernia, “Microwave Imaging of Nonweak Targets via Compressive Sensing and Virtual Experiments,” IEEE Antennas and Wireless Propagation Letters, vol. 14, pp. 1035–1038, 2015

    2015

  49. [58]

    A Configurable Energy-Efficient Compressed Sensing Architecture with its Application on Body Sensor Networks,

    A. Wang, F. Lin, Z. Jin, and W. Xu, “A Configurable Energy-Efficient Compressed Sensing Architecture with its Application on Body Sensor Networks,” IEEE Transactions on Indus- trial Informatics, vol. 12, no. 1, pp. 15–27, 2016

    2016

  50. [59]

    Compressive sensing matrix design for fast encoding and decoding via sparse fft,

    S.-H. Hsieh, C.-S. Lu, and S.-C. Pei, “Compressive sensing matrix design for fast encoding and decoding via sparse fft,” IEEE Signal Processing Letters , vol. 25, no. 4, pp. 591–595, 2018

    2018

  51. [60]

    Sparse mri: The application of compressed sensing for rapid mr imaging,

    M. Lustig, D. Donoho, and J. Pauly, “Sparse mri: The application of compressed sensing for rapid mr imaging,” Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, vol. 58, pp. 1182–95, 12 2007

    2007

  52. [61]

    Quantum state tomography via compressed sensing,

    D. Gross, Y .-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Physical Review Letters, vol. 105, p. 150401, 10 2010

    2010

  53. [62]

    Quantum circuit for the fast fourier transform,

    R. Asaka, K. Sakai, and R. Yahagi, “Quantum circuit for the fast fourier transform,” Quan- tum Information Processing, vol. 19, no. 8, Aug. 2020, publisher Copyright: © 2020, The Author(s). 22

    2020

  54. [63]

    Schuld and F

    M. Schuld and F. Petruccione, Machine Learning with Quantum Computers . Springer International Publishing, 2021

    2021

  55. [64]

    Review of quantum image processing,

    Z. Wang, M. Xu, and Y . Zhang, “Review of quantum image processing,” Archives of Com- putational Methods in Engineering, vol. 29, 05 2021. 23

    2021

  56. [2020]

    Available: https://link.aps.org/doi/10.1103/PhysRevResearch.2.033293

    [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevResearch.2.033293

    doi

  57. [2021]

    Available: http://dx.doi.org/10.1038/s43588-021-00084-1

    [Online]. Available: http://dx.doi.org/10.1038/s43588-021-00084-1

    doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.