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REVIEW 4 major objections 6 minor 31 references

Quantum multi-output Gaussian Processes based Machine Learning for Line Parameter Estimation in Electrical Grids

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper demonstrates a quantum multi-output Gaussian process that uses HHL to invert a 32x32 kernel matrix and estimates power-grid line parameters on a real IBM quantum computer.

desk verdict Real 13-qubit HHL kernel inversion on hardware, but the rescaling step in §IV C makes the optimizer minimize the wrong objective—needs a major fix. read the letter →

arxiv 2411.09123 v1 pith:VDC64DWW submitted 2024-11-14 quant-ph

Priyanka Arkalgud Ganeshamurthy , Kumar Ghosh , Corey O'Meara , Giorgio Cortiana , Jan Schiefelbein-Lach , Antonello Monti This is my paper · ORCID
classification quant-ph
keywords quantumGaussianprocessHHLalgorithmkernelmatrixinversionapproximatecompilinglineparameterestimationpowersystemsNISQhardwaremulti-output
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 develops a quantum version of multi-output Gaussian process regression in which the costly kernel-matrix inversion inside GP training is carried out by the HHL quantum algorithm, with Approximate Quantum Compiling used to cut circuit depth and a diagonal scaling used to reduce the kernel condition number. The authors apply this QGP to a real power-systems task: estimating the resistance R and inductance L of a short transmission line from noisy voltage and current measurements. They report running the resulting HHL circuit, up to 13 qubits for a 32x32 kernel matrix, on the IBM Auckland quantum computer, and compare the learned parameters with outputs from a noise-free simulator and from classical GP. The result is a proof-of-concept that quantum Gaussian processes can be pushed onto current NISQ hardware for a practical engineering learning problem, even though the estimated parameters are only in the same decimal range as the true values.

What carries the argument

The load-bearing machinery is HHL as a subroutine inside GP hyper-parameter optimization: the term $y^T (K + \sigma_n^2 I)^{-1} y$ in the negative log marginal likelihood is rewritten as a norm of the solution to a linear system and evaluated by measuring the probability that HHL's auxiliary qubit is in $|1\rangle$. Because the raw kernel has a condition number around $O(2^{30})$, the authors add strong regularization and then scale the kernel matrix by a diagonal matrix $D = \mathrm{diag}(\kappa_{11}^{-1/2}, \ldots, \kappa_{nn}^{-1/2})$ to bring the condition number down to $O(2^9)$; the inner product is then rescaled by a single factor $d_{\min}$, the minimum entry of $D^{-1}$. To make the circuit executable, Approximate Quantum Compiling (AQC) replaces the QPE block by a shallow approximation with a bounded number of CNOT gates, using at most $E = 8$ evaluation qubits. The method therefore rests on three interacting approximations: regularization, diagonal scaling, and approximate compiling.

What would settle it

Take any positive-definite kernel matrix with unequal diagonal entries, compute $y^T (K + \sigma_n^2 I)^{-1} y$ classically, then compute the same quantity with the paper's D-scaling and $d_{\min}$ rescaling; if the two disagree by more than HHL's approximation error for a well-conditioned matrix, the rescaling step does not recover the original inner product. A concrete test is a 2x2 matrix with diagonal entries 1 and 10 and the paper's conditioning recipe.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a Gaussian process with multiple coupled outputs can be made to run on present-day quantum hardware by replacing the single expensive inversion $(K + \sigma_n^2 I)^{-1}$ with HHL, provided the ill-conditioned kernel is first regularized and scaled, and the quantum phase estimation section of HHL is approximated by Approximate Quantum Compiling. With this pipeline the authors implemented a 32x32 kernel inversion using up to 13 qubits on IBM Auckland and obtained R and L estimates in the same decimal range as the true values (approximately 0.089 $\Omega$ versus 0.064 $\Omega$ for R, and approximately $5.63 \times 10^{-5}$ H versus $2.64 \times 10^{-5}$ H for L), with the noise-less simulator and the noisy hardware giving close results. The paper presents this as larger than earlier HHL demonstrations on real quantum hardware, and as evidence that QGP-based line parameter estimation is feasible as a proof-of-concept.

Load-bearing premise

The whole demonstration depends on the assumption that the diagonal rescaling of the kernel matrix can be undone by multiplying the HHL output by a single number $d_{\min}$, which is exact only when every diagonal entry of the kernel is equal; for real measurement kernels with varying diagonal entries the rescaling silently changes the quantity being computed.

Editorial extensions

If this is right

  • A 13-qubit HHL circuit for a 32x32 kernel inversion can be executed on a real IBM quantum device, going beyond the 5-qubit, 2x2 HHL demonstrations cited in the paper.
  • The QGP optimizer estimates the line parameters R and L in the same decimal range as the true values, with the noisy hardware result close to the noise-less simulator, indicating the pipeline tolerates hardware noise at this scale.
  • With the hyper-parameters returned by QGP, the multi-output GP models can impute voltage and current signals over a full cycle, so the trained model retains predictive value even when production hardware would not be used online.
  • The reported execution time is far from practical for real-world deployment, so the authors position QGP as a proof-of-concept and expect near-term quantum computers to aid classical computers for offline applications.

Reading between the lines

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

  • If the diagonal-scaling rescaling is corrected or removed, the same pipeline could be tested on kernel matrices with strongly varying diagonal entries; a direct numerical comparison of the HHL-estimated quadratic form against exact classical values on such matrices would separate the conditioning approximation from the AQC approximation.
  • Because HHL natively returns only scalar expectations $\langle x|M|x\rangle$, the QGP approach is naturally suited to objective functions like the log marginal likelihood, but not to applications that require full posterior covariance samples; extending it would require a different quantum linear-algebra primitive.
  • The claimed speedup is asymptotic and assumes sparse, well-conditioned matrices; for dense 32x32 kernel matrices the classical $O(N^3)$ inversion is trivial, so the practical value of QGP will appear only at much larger N with sparse kernel approximations, a regime not tested here.
  • A testable extension is to use the same conditioning-and-AQC recipe on a kernel from a different power-system task, such as state estimation or load forecasting, to see whether the parameter errors stay within the same range as reported.
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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 / 6 minor

Summary. This paper proposes a quantum Gaussian process (QGP) for multi-output regression, replacing the kernel-matrix inversion in the GP marginal likelihood (Eq. (4)) with an HHL subroutine whose circuit depth is reduced using Approximate Quantum Compiling (AQC). The method is applied to estimating resistance R and inductance L of a short transmission line from noisy voltage and current measurements, with a 32×32 kernel matrix built from 32 training samples. The authors report results from the IBM Auckland quantum device and a noiseless simulator, compare them with classical GP, and claim the implementation of up to a 13-qubit HHL circuit for the 32×32 kernel inversion.

Significance. If correct, this would be a notable end-to-end NISQ demonstration of HHL-based Gaussian process training on a realistic power-systems task, and the AQC depth-reduction pipeline would be a useful engineering contribution. The paper is candid about hardware limitations and reports quantitative comparisons with classical GP, which is a strength. The work does not provide machine-checked proofs or reproducible code, and its central derivation has a gap that changes the optimized objective; the headline experimental claim is also not documented at the level needed to verify it. These issues preclude acceptance in the current form.

major comments (4)
  1. [IV C, Step 2] The rescaling step after diagonal conditioning is algebraically invalid. With κ′ = DκD and D = diag(κ_11^{-1/2}, ..., κ_nn^{-1/2}), the quadratic form computed on the conditioned matrix is y^T(κ′)^{-1}y = (D^{-1}y)^T κ^{-1}(D^{-1}y) = Σ_{ij} κ_ii^{1/2} y_i (κ^{-1})_{ij} y_j κ_jj^{1/2}. This is not a scalar multiple of y^T κ^{-1} y unless all diagonal entries of κ are equal. The stated multiplication by dmin, the smallest diagonal entry of D^{-1}, cannot compensate for the per-component weights κ_ii^{1/2}κ_jj^{1/2}. For the 32×32 kernel used in Section IV B, built from RBF kernels and three measurement signals with different noise variances, the diagonal entries are not equal. Therefore the quantity minimized during QGP optimization is not the GP log marginal likelihood of Eq. (4), and the R and L estimates in Table I do not correspond to the claimed QGP-LPE objective. This is a load-bearing error for the central demonstration.
  2. [IV C, Step 1] The mapping from the HHL norm readout to the quadratic form of Eq. (4) is not demonstrated. The HHL ancilla measurement produces ||x||^2 for x = A^{-1}|b⟩, i.e., ⟨b|A^{-2}|b⟩, not ⟨b|A^{-1}|b⟩. In Step 1 the manuscript asserts that ||z||^2 with z=κ^{-1}|y⟩ equals ⟨y|K|y⟩, where K=(K+σ_n^2I)^{-1}. This identity requires a specific relationship between K and κ, namely K=(κκ†)^{-1}, but the 'Schutz decomposition' is never defined and no proof is provided. Without this algebraic link, the quantity actually measured on the quantum device is not established to be the first term of Eq. (4).
  3. [V (Table I) and Abstract] The headline claim that 'up to 13-qubit HHL circuit has been implemented for a 32x32 kernel matrix inversion on IBM Quantum hardware' is not supported by the experimental reporting in Section V. The section provides only the final R and L estimates in Table I and graphical predictions in Fig. 6. It does not report the number of qubits used, the number of QPE evaluation qubits, the gate counts or circuit depths after AQC, or the hardware execution parameters. A reader cannot verify that a 13-qubit circuit corresponding to the 32×32 inversion was executed, as opposed to a smaller circuit or a simulator result. This claim should be removed or accompanied by the relevant circuit and execution metadata.
  4. [IV C, Step 3] The QPE truncation to E=8 evaluation qubits is an uncontrolled approximation. The paper states that when the condition number exceeds a limit, QPE is evaluated with only 8 qubits, but it gives no error analysis for the resulting eigenvalue estimates or for the norm ||x||^2. For the conditioned matrix with condition number near O(2^9), an 8-qubit eigenvalue register may be insufficient to resolve the small eigenvalues that dominate the inverse. The authors acknowledge in Section V that heavy approximations affect accuracy, but without a bound or a numerical study the effect on the QGP objective and on the reported line-parameter estimates is unknown. This is particularly important because the approximation interacts with the conditioning step in Major Comment 1.
minor comments (6)
  1. [Throughout] The manuscript contains many typos and grammatical errors (e.g., 'algrithm', 'another another', 'challanging', 'it’s', 'Posi tive', 'F ig'); a thorough language edit is needed.
  2. [IV C, Step 1] The symbol K is reused for the kernel matrix, its inverse, and the conditioned matrix, and κ/κ† are never precisely defined; please introduce distinct notation.
  3. [IV C, Step 1] The 'Schutz decomposition' is not defined and no reference is given; if it is a standard matrix factorization, the definition and the factorization algorithm should be provided.
  4. [V, Table I] Table I reports a single run for the quantum results; for NISQ hardware, confidence intervals or repeated-shot statistics are needed to assess the significance of the R and L estimates.
  5. [References] Reference [17] is incomplete (author list and title missing), and reference [19] lacks the article title; these should be completed.
  6. [V, Fig. 6] Figure 6 shows prediction curves without quantitative error metrics, so the statement that the hyper-parameters are 'optimized well enough' is not supported by the figure alone.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: QGP-LPE is benchmarked against classical GP and known R,L values; the self-citations to [2] and [23] are not load-bearing.

full rationale

The claimed derivation chain is self-contained against external benchmarks. The GP negative log marginal likelihood (Eq. 4) is a standard target, HHL is a standard algorithm, and AQC is imported from the external reference [22] (Madden and Simonetto), not from the authors' own prior work. The paper's contribution is the implementation of this pipeline for line-parameter estimation, and the resulting R and L estimates are compared against the actual values and against classical GP (Table I); no fitted parameter is relabeled as an independent prediction. The self-citations present are not load-bearing: [2] supplies the physics-informed multi-output GP construction, but that construction is stated to follow from the physical line equation (22) and the standard linear-operation closure of GPs, so the present result does not reduce to the citation; [23] is cited only as a previous application of AQC, while the AQC method itself is [22]. The rescaling in Section IV.C Step 2, multiplying the HHL-computed inner product by dmin, is algebraically questionable for a kernel with unequal diagonal entries; however, that is a validity and approximation concern rather than circularity, because the computed quantity is not definitionally equal to the target marginal-likelihood term. No uniqueness theorem is imported from the authors, no ansatz is smuggled via citation, and no known result is merely renamed.

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

The central claim rests on the HHL/AQC pipeline, the validity of the conditioning-rescaling step, and the power-system measurement model. The scaling-rescaling step is the main unproved assumption; the QPE truncation is an explicit approximation without error bounds. No new physical entities are introduced.

free parameters (4)
  • HHL normalization constant C
    Section III B Step 3: C must satisfy |C| < lambda_min and is used to extract the norm from the auxiliary qubit probability. Its value is not reported and affects all norm estimates.
  • QPE evaluation qubit cap E = 8
    Section IV C Step 3: chosen ad hoc because AQC fails to converge for high-dimensional unitaries. The cap limits eigenvalue resolution to 8 bits.
  • GP hyperparameters (sigma^2, ARD weights w_d, noise variances)
    Section V states that 9 hyperparameters including R and L are optimized against the quantum-computed negative log marginal likelihood. Fitted values are not listed.
  • Optimization iteration count = 100
    Section V: hardware experiments use at most 100 NLML evaluations, an implementation cap that affects convergence and accuracy.
assumptions (4)
  • ad hoc to paper The kernel matrix can be factored as kappa^dagger kappa with kappa Hermitian via a Schutz decomposition (Section IV C Step 1).
    The decomposition is not standard and is not defined or cited. The subsequent HHL use depends on this factorization.
  • ad hoc to paper Multiplying the scaled inner product by dmin, the minimum diagonal entry of D^{-1}, recovers the original quadratic form y^T kappa^{-1} y (Section IV C Step 2).
    This is not generally true: y^T(D kappa D)^{-1} y = (D^{-1} y)^T kappa^{-1} (D^{-1} y), which differs from dmin * y^T kappa^{-1} y unless D is a scalar matrix.
  • ad hoc to paper AQC with at most E=8 QPE qubits produces a sufficiently faithful approximation of the HHL circuit for the norm estimate (Section IV C Step 3).
    No error bounds or validation of the compiled circuit are given.
  • domain assumption The short-line Pi-model vi = R ii + L dii/dt + vj and i.i.d. Gaussian measurement noise hold for the test network (Section IV A).
    Standard for short transmission lines, but the parameter estimates inherit any error in this model.

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Cite this review

Pith. "Pith review of Quantum multi-output Gaussian Processes based Machine Learning for Line Parameter Estimation in Electrical Grids." pith.science (2026). https://pith.science/paper/VDC64DWW

@misc{pith2026241109123,
  author       = {Pith},
  title        = {Pith review of: Quantum multi-output Gaussian Processes based Machine Learning for Line Parameter Estimation in Electrical Grids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VDC64DWW}},
  note         = {Machine review of arXiv:2411.09123}
}
read the original abstract

Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs demanding immense resources make their practical usage highly challenging. In this article, we develop a quantum version of multi-output Gaussian Process (QGP) by implementing a well-known quantum algorithm called HHL, to perform the Kernel matrix inversion within the Gaussian Process. To reduce the large circuit depth of HHL a circuit optimization technique called Approximate Quantum Compiling (AQC) has been implemented. We further showcase the application of QGP for a real-world problem to estimate line parameters of an electrical grid. Using AQC, up to 13-qubit HHL circuit has been implemented for a 32x32 kernel matrix inversion on IBM Quantum hardware for demonstrating QGP based line parameter estimation experimentally. Finally, we compare its performance against noise-less quantum simulators and classical computation results.

Figures

Figures reproduced from arXiv: 2411.09123 by the authors.

Figure 1
Figure 1. FIG. 1. A schematic diagram for GP training and prediction. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. A schematic diagram for HHL algorithm. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Single line diagram of a two node network. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Proof-of-concept for quantum Gaussian process based [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. A pictorial representation of the QGP regression [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The qubit topology graph of IBM Auckland, which is [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Reference graph

Works this paper leans on

31 extracted references · 26 canonical work pages

  1. [15]

    Z. Zhao, J. K. Fitzsimons, and J. F. Fitzsimons, Physical Review A 99, 052331 (2019)

    work page 2019

  2. [16]

    The rest of the article is organized into five main sec- tions

    have shown HHL on 2x2 matrix with 5 qubits on real quantum hardware. The rest of the article is organized into five main sec- tions. Section II introduces background concepts of GP. Section III presents the QGP algrithm. Section IV in- troduces the mathematical formulation and test-set up for line parameter estimation as well as the adaptation of QGP for ...

    work page

  3. [23]

    Rebentrost, M

    P. Rebentrost, M. Mohseni, and S. Lloyd, Physical re- view letters 113, 130503 (2014). 9

    work page 2014

  4. [1]

    That is, perform the transformation |0⟩nb 7→ |b⟩nb

    Load the data |b⟩ ∈CN . That is, perform the transformation |0⟩nb 7→ |b⟩nb . (12)

    work page

  5. [2]

    = 1 2 y ′ (K + σn 2I)−1y + 1 2 log |K + σn 2I| + N 2 log 2π (4) where K(T, T) is simplified and written as K. After the training, for a given new test inputs T∗, we can predict its corresponding output f (T∗) by expressing f (T) and f (T∗) as joint distribution given by: f (T) f (T∗) ∼ N m(T) m(T∗) , K + σn2I K ∗ K ′ ∗ K∗∗ (5) where, K = K(T, T), K∗ = K(T...

    work page 2014

  6. [3]

    Add an auxiliary qubit and apply a rotation condi- tioned on |λj⟩, N −1X j=0 bj|λj⟩nl |uj⟩nb s 1 − C 2 λ2 j |0⟩ + C λj |1⟩ ! , (15) where C is a normalisation constant, and, as expressed in the current form above, should be less than the smallest eigenvalue λmin in magnitude, i.e., |C| < λmin

    work page

  7. [4]

    (13) The quantum state of the register expressed in the eigenbasis of A is now N −1X j=0 bj|λj⟩nl |uj⟩nb , (14) where |λj⟩nl is the nl-bit binary representation of λj

    Apply Quantum Phase Estimation (QPE) with U = eiAt := N −1X j=0 eiλj t|uj⟩⟨uj|. (13) The quantum state of the register expressed in the eigenbasis of A is now N −1X j=0 bj|λj⟩nl |uj⟩nb , (14) where |λj⟩nl is the nl-bit binary representation of λj

    work page

  8. [5]

    Measure the auxiliary qubit in the computational basis. If the outcome is 1, the register is in the post- measurement state s 1PN −1 j=0 |bj|2 / |λj|2 ! N −1X j=0 bj λj |0⟩nl |uj⟩nb , (17) which up to a normalisation factor corresponds to the solution

    work page

Show all 31 references
  1. [6]

    Ignoring possible errors from QPE, this results in N −1X j=0 bj|0⟩nl |uj⟩nb s 1 − C 2 λ2 j |0⟩ + C λj |1⟩ !

    Apply QPE †. Ignoring possible errors from QPE, this results in N −1X j=0 bj|0⟩nl |uj⟩nb s 1 − C 2 λ2 j |0⟩ + C λj |1⟩ ! . (16)

  2. [7]

    Dahale and B

    S. Dahale and B. Natarajan, 2021 IEEE Power and En- ergy Society General Meeting (PESGM) (2021)

    2021

  3. [8]

    Apply an observable M to calculate F (x) := ⟨x|M |x⟩. (18) C. Quantum phase estimation (QPE) within HHL Quantum phase estimation is the core quantum sub- routine in the HHL algorithm. Roughly speaking for given a unitary U with eigenvector |ψ⟩m and eigenvalue e2πiθ, QPE finds ...

  4. [9]

    Rasmussen and C

    C. Rasmussen and C. Williams, Gaussian Processes for Machine Learning (MIT Press, 2006)

    2006

  5. [10]

    A. G. Priyanka, A. Monti, and F. Ponci, in 2023 IEEE Power & Energy Society General Meeting (PESGM) (2023) pp. 1–5

    2023

  6. [11]

    Jalali, V

    M. Jalali, V. Kekatos, S. Bhela, H. Zhu, and V. A. Centeno, IEEE Transactions on Power Systems 37, 4409 (2022)

    2022

  7. [12]

    H. D. N. Parikshit Pareek, Chuan Wang, Physica D: Non- linear Phenomena 424, 132941 (2021)

    2021

  8. [13]

    D. Cao, J. Zhao, W. Hu, Q. Liao, Q. Huang, and Z. Chen, IEEE Transactions on Smart Grid 14, 1317 (2023)

    2023

  9. [14]

    Physics-informed gaussian process regres- sion for probabilistic states estimation and forecasting in power grids,

    T. Ma, D. A. Barajas-Solano, R. Tipireddy, and A. M. Tartakovsky, “Physics-informed gaussian process regres- sion for probabilistic states estimation and forecasting in power grids,” (2020), arXiv:2010.04591 [stat.ML]

    2020 arXiv

  10. [17]

    M. A. Nielsen and C. I. L., Quantum Computation and Quantum Information(Cambridge University Press, Cambridge, 2001)

    2001

  11. [18]

    L. K. Grover, Phys. Rev. Lett. 79, 325 (1997)

    1997

  12. [19]

    P. W. Shor, Proceedings 35th annual symposium on foun- dations of computer science , 124 (1994)

    1994

  13. [20]

    Quantum walk speedup of backtracking algorithms,

    A. Montanaro, “Quantum walk speedup of backtracking algorithms,” (2015)

    2015

  14. [21]

    Quantum al- gorithms for supervised and unsupervised machine learn- ing,

    S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum al- gorithms for supervised and unsupervised machine learn- ing,” (2013)

    2013

  15. [22]

    J. e. a. Biamonte, Nature 549, 195 (2017)

    2017

  16. [24]

    Quantum computing for power flow al- gorithms: Testing on real quantum computers,

    B. Sævarsson, S. Chatzivasileiadis, H. J´ ohannsson, and J. Østergaard, “Quantum computing for power flow al- gorithms: Testing on real quantum computers,” (2022), arXiv:2204.14028 [quant-ph]

    2022 arXiv

  17. [25]

    G. E. K. M. Raissi, Journal of Computational Physics (2017)

    2017

  18. [26]

    Abur and A

    A. Abur and A. G. Exposito, Power System State Esti- mation Theory and Implementation(Marcel Dekker, Inc, 2004)

    2004

  19. [27]

    Thurner, A

    L. Thurner, A. Scheidler, F. Schafer, J. H. Menke, J. Dol- lichon, F. Meier, S. Meinecke, and M. Braun, IEEE Transactions on Power Systems (2018), 10.1109/TP- WRS.2018.2829021

    2018

  20. [28]

    R. D. Braatz and M. Morari, SIAM Journal on Control and Optimization 32, 1763 (1994)

    1994

  21. [29]

    V. V. Shende, I. L. Markov, and S. S. Bullock, Physical Review A 69, 062321 (2004)

    2004

  22. [30]

    Madden and A

    L. Madden and A. Simonetto, ACM Transactions on Quantum Computing 3, 1 (2022)

    2022

  23. [31]

    Ghosh, K

    K. Ghosh, K. Yogaraj, G. Agliardi, P. Sabino, M. Fern´ andez-Campoamor, J. Bernab´ e-Moreno, G. Cortiana, O. Shehab, and C. O’Meara, IEEE Transactions on Quantum Engineering (2024), 10.1109/TQE.2024.3425969. Appendix A: Approximate Quantum Compiling During computation of the l...

    2024

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