Pith. sign in

REVIEW 3 major objections 6 minor 84 references

Variational quantum compiling for three-qubit gates design in quantum dots

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read A fixed anisotropic Heisenberg Hamiltonian, tuned by a variational compiling algorithm, realizes Toffoli and Fredkin gates with infidelity below 10^-4 and stays stable under charge and nuclear noise.

desk verdict Plausible noiseless compilation results, but the headline robustness claim rests on a sign-restricted noise model that needs a fix before this is a reliable reference. read the letter →

arxiv 2412.06276 v1 pith:5IXPRJRP submitted 2024-12-09 quant-ph

Yuanyang Zhou , Huaxin He , Fengtao Pang , Hao Lyu , Yongping Zhang , Xi Chen This is my paper · ORCID
classification quant-ph MSC 81P6881V65 PACS 03.67.Lx85.35.Gv
keywords variationalquantumcompilingQAQCToffoligateFredkindotspinqubitsanisotropicHeisenbergmodelchargenoisenuclear
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 show that a fixed, time-independent Hamiltonian can implement the three-qubit Toffoli and Fredkin gates in a semiconductor quantum-dot spin chain, and that a variational quantum compiling algorithm can find the required parameters. If true, it would remove a major source of control noise and simplify experimental gate design, since a static set of magnetic fields and exchange couplings would replace sequences of shaped pulses. The authors report noiseless infidelity below $10^{-4}$ for both gates, fidelity near 99% under charge and nuclear spin noise, and graceful degradation under amplitude damping. The broader payoff would be a practical route to multi-qubit gates in quantum dots and other platforms such as superconducting circuits and trapped ions.

What carries the argument

The machinery is the quantum-assisted quantum compiling (QAQC) loop combined with a Hamiltonian Variational Ansatz (HVA). The ansatz circuit, built from single-qubit rotations $R_\alpha(\theta_j)$ and two-qubit entangling gates $R_{\alpha,\alpha}(\theta_j)$, approximates $e^{-iH(\theta)t}$ through a Suzuki-Trotter decomposition with depth $m$. The Hilbert-Schmidt test measures the cost $C(\theta)=1-\frac{1}{2^{2n}}|\mathrm{Tr}[U_{\mathrm{target}}^\dagger U_{\mathrm{QC}}(\theta)]|^2$, which equals the gate infidelity. Gradient-based L-BFGS optimization is used in noiseless settings, and gradient-free Nelder-Mead optimization is used under incoherent noise, with both updating the 15 physical parameters $h_i^\alpha$ and $J_i^\alpha$ that define the time-independent Hamiltonian.

What would settle it

Run the same optimized parameters under zero-mean, qubit-dependent Gaussian fluctuations in $J_i^\alpha$ and $h_i^z$ at noise amplitudes matching the paper's and compare average gate fidelity; if fidelity falls well below the reported ~99% under both-signed fluctuations, the robustness claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the QAQC algorithm can find a set of fixed parameters $\theta=\{h_i^\alpha, J_i^\alpha\}$ for the time-independent anisotropic Heisenberg Hamiltonian $H=\sum_i\sum_{\alpha=x,y,z}h_i^\alpha\sigma_\alpha^{(i)}+\sum_{i=1,2}\sum_{\alpha}J_i^\alpha\sigma_\alpha^{(i)}\sigma_\alpha^{(i+1)}$ such that the evolution $e^{-iH(\theta)t}$ equals the Toffoli gate at Trotter depth $m=6$ and the Fredkin gate at $m=5$ up to an infidelity below $10^{-4}$. The optimized parameter sets differ meaningfully: the Toffoli gate relies mostly on local magnetic fields and sets $J_1^y=0$, while the Fredkin gate relies mostly on exchange couplings and sets $h_3^x=h_3^z=0$. With noise applied only after compilation, the same fixed parameters keep fidelity near 99% under charge and nuclear noise and degrade to roughly 92% (Toffoli) and 90% (Fredkin) under an amplitude-damping channel at $p=0.01$.

Load-bearing premise

The robustness results depend on the paper's assumption that charge and nuclear noise shift every exchange coupling and local field by the same non-negative amount on all three qubits, whereas real noise fluctuates with both signs and varies from qubit to qubit.

Editorial extensions

If this is right

  • Three-qubit gates can be produced from a static set of fields and couplings, so control electronics need not generate fast shaped pulses for each gate operation.
  • With $m=6$ Trotter steps the Toffoli gate reaches infidelity below $10^{-4}$, and even $m=3$ gives about 80% fidelity, so a modest circuit depth suffices for high precision.
  • Because the optimized parameters differ between the Toffoli and Fredkin gates, a device that wants both gates must switch between two fixed operating points rather than use one universal static Hamiltonian.
  • Under the paper's noise model, charge and nuclear noise that shift couplings and fields by non-negative amounts leave fidelity near 99%, establishing a quantitative tolerance budget for those error sources.
  • Under amplitude damping with $p=0.02$, both gates retain about 80% fidelity, indicating the compiled gates tolerate a moderate level of energy relaxation.

Reading between the lines

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

  • The noise-robustness claim is likely sensitive to the non-negative, identical-noise assumption; a zero-mean, qubit-dependent fluctuating environment could degrade the reported fidelity, and re-optimizing under that realistic model is the natural stress test.
  • The different parameter patterns suggest a single static Hamiltonian cannot serve both gates, so a practical device would need to tune between two configurations, which partially reintroduces the control overhead the method avoids.
  • The same QAQC loop should extend to other three-qubit gates and ultimately to a shared Hamiltonian for a small universal gate set, but the paper does not demonstrate such a set.
  • The no-barren-plateau argument is tied to 15 parameters and shallow circuit depth; whether the landscape stays trainable for larger qubit counts is not established.
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

3 major / 6 minor

Summary. The manuscript reports a numerical study in which the QAQC algorithm, using a Hamiltonian variational ansatz, is applied to the anisotropic Heisenberg Hamiltonian (Eq. (1)) to find control parameters such that the time evolution approximates the Toffoli and Fredkin gates. In the noiseless case the authors report operator infidelity below 10^-4 with six Trotter layers for the Toffoli gate and five for the Fredkin gate. They then examine robustness to static shifts of exchange couplings and local z-fields, and to amplitude-damping noise, and argue that the shallow symmetric ansatz avoids barren plateaus. The central numerical optimization is standard and reproducible in structure, but the physical noise modeling and the reporting of gate time leave gaps.

Significance. If the noiseless optimization and the noise robustness results are taken at face value, the paper provides a useful example of designing three-qubit gates with a time-independent physical Hamiltonian and variational compilation. Strengths include the use of a standard Hilbert-Schmidt cost function, multiple random initializations with reported standard deviations, explicit target unitaries as external benchmarks, and a clear distinction between fitting and prediction. The main value would be as a proof-of-principle for QAQC-based pulse design in quantum-dot spin qubits. However, the advertised robustness to physical charge and nuclear noise is not established by the positive-only uniform-shift model, so the significance of the robustness claim is currently limited.

major comments (3)
  1. [IV.A, Fig. 4] In Section IV.A the paper states 'we impose the condition that the noise contributions remain non-negative' and assumes the same noise profile for all three qubits. Physical charge noise and nuclear Overhauser fluctuations are quasi-static, approximately zero-mean, sign-changing, and inhomogeneous across dots; the adopted model therefore samples only one branch of the parameter perturbation and cannot substantiate the abstract's claim of robustness to charge and nuclear noise. The authors should repeat the fidelity analysis with zero-mean fluctuations (e.g., Gaussian or uniform delta_J_i^alpha and delta_h_i^z drawn independently per term and per qubit) and report typical and worst-case infidelities. This is the most load-bearing gap for the central robustness claim.
  2. [II.A, Eq. (3)] The total evolution time t (and hence t0=t/m) is never assigned a numerical value, and the optimized parameters in Fig. 3 are not connected to physical units via t and the reference energy scale. Since the goal is a time-independent Hamiltonian gate for quantum dots, the actual gate time is needed to convert the dimensionless parameters into fields and couplings and to assess decoherence; please report t and t0, and the unit conversion, or state explicitly that the theta_j absorb t0 in Eq. (3).
  3. [IV.C] The claim in Section IV.C that the QAQC algorithm 'does not suffer from the barren plateaus problem' is not established by the arguments given. Membership in SU(N) holds for essentially all parameterized unitaries and cannot by itself prevent exponentially vanishing gradients; the cited shallow-depth and symmetry results are qualitative, and no scaling analysis of gradient variances or optimization landscape curvature is provided for this 15-parameter ansatz. The statement should either be supported by numerical evidence as a function of qubit number or softened to an empirical observation for the three-qubit systems studied.
minor comments (6)
  1. [Fig. 2 caption] The caption states that initial parameters are 'randomly drawn from the range [-1,1] with a Gaussian distribution', which is internally inconsistent; please specify a truncated Gaussian or a uniform distribution.
  2. [III.B] The optimizer name 'L-BFSG' is a typo and should read 'L-BFGS'.
  3. [Eq. (7)] The displayed action of the Toffoli gate in Eq. (7) is garbled and should be rewritten in standard bit-vector notation.
  4. [V. Conclusion] The phrase 'A key different of our method' should read 'A key difference of our method'.
  5. [Fig. 4] The axes in Fig. 4 do not specify the units or range of the noise amplitude delta, nor whether charge and nuclear noise amplitudes are measured in the same dimensionless units as the parameters in Eq. (1); please clarify.
  6. [II.A] The sentence 'Since t and t0 are fixed, the evolution operator (3) becomes time-independent' is confusing; the unitary is parameter-fixed rather than time-dependent in the control sense, and this wording should be clarified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gate fidelities are transparently optimized objectives against external target unitaries, and the self-citations are not load-bearing.

full rationale

The paper's central derivation chain is an open numerical optimization, not a hidden reduction. The Hamiltonian in Eq. (1) is an independent physical input, and the target unitaries (Toffoli and Fredkin) are external benchmarks. The cost function in Eq. (6), C(θ) = 1 - |Tr[U_target† U_QC(θ)]|²/2^{2n}, is explicitly defined as infidelity, and the paper states that minimizing C maximizes fidelity. The reported fidelity error below 10^-4 in Sec. III.A is therefore the value of the optimized objective after fitting 15 parameters; the paper does not rename this fit as a prediction or derive it from a premise that already contains it. No fitted parameter is presented as an independent measurement. The QAQC algorithm itself is cited to external work [43], and the Hamiltonian ansatz follows an external HVA reference [51]. The several self-citations to X. Chen and co-authors ([33], [38], [55], [74], [75], [80]) appear only as background, alternative ansatz suggestions, or related prior control schemes; none carries the load of the main argument. There is no imported uniqueness theorem and no ansatz smuggled in through a self-citation. The manuscript does contain a substantive limitation: in Sec. IV.A it restricts charge and nuclear noise by stating 'we impose the condition that the noise contributions remain non-negative' and assumes a uniform noise profile across qubits, which limits the robustness claim to positive, common-mode shifts. This is an assumption or correctness risk, not a circular step, because the noise model is not defined in terms of the fidelity result it is meant to support. Similarly, the barren-plateau argument in Sec. IV.C is heuristic and its supporting citation does not directly prove the claim, but this is a support gap rather than circularity. Overall, the paper is self-contained against external gate benchmarks and is transparent about the optimization-based nature of its construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's design result rests on the physical Hamiltonian model, the expressibility of the HVA ansatz, the specific choice of noise model, and the absence of a barren plateau problem; these are assumptions rather than derived facts. The 15 optimized control parameters are fitted to the target unitaries, so they are free parameters, and the total evolution time t is an unspecified free parameter.

free parameters (3)
  • 15 HVA control parameters (theta_j) = Optimal values shown only as a bar chart in Fig. 3, exact numbers not given
    These are optimized to minimize infidelity to the target gate; they are the central design result and are fitted to match Toffoli and Fredkin unitaries.
  • Total evolution time t = Not specified
    The unitary e^{-iH(theta)t} depends on t, but the paper never states its value, only introduces t0 = t/m. This is a load-bearing but unreported parameter.
  • Noise amplitude delta range = Not specified in text, x-axis of Fig. 4 shown without numeric labels in extraction
    The robustness claim is over a chosen range of delta for charge and nuclear noise; the range is a modeling choice that affects the strength of the conclusion.
assumptions (4)
  • domain assumption The anisotropic Heisenberg Hamiltonian (Eq. 1) captures the physics of three exchange-coupled spin qubits with spin-orbit interactions.
    Invoked in Sec. II; relies on refs [44-47] but no experimental validation in this paper.
  • domain assumption The HVA circuit with m Trotter steps can represent the target Toffoli and Fredkin unitaries to the stated fidelity.
    The optimizer works within this ansatz; expressibility is assumed sufficient and demonstrated numerically, but not guaranteed for larger depths or other gates.
  • ad hoc to paper Noise contributions delta J and delta h^z are non-negative and identical across all three qubits.
    Sec. IV.A states 'we impose the condition that the noise contributions remain non-negative'. This restricts noise to positive shifts only, which is not a standard zero-mean fluctuation model.
  • ad hoc to paper The symmetry and shallow depth of the QAQC ansatz prevent barren plateaus.
    Sec. IV.C makes this claim without formal proof or scaling analysis; it is an assumption used to support the scalability statement.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Variational quantum compiling for three-qubit gates design in quantum dots." pith.science (2026). https://pith.science/paper/5IXPRJRP

@misc{pith2026241206276,
  author       = {Pith},
  title        = {Pith review of: Variational quantum compiling for three-qubit gates design in quantum dots},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5IXPRJRP}},
  note         = {Machine review of arXiv:2412.06276}
}
read the original abstract

Semiconductor quantum dots offer a promising platform for controlling spin qubits and realizing quantum logic gates, essential for scalable quantum computing. In this work, we utilize a variational quantum compiling algorithm to design efficient three-qubit gates using a time-independent Hamiltonian composed of only physical interaction terms. The resulting gates, including the Toffoli and Fredkin gates, demonstrate high fidelity and robustness against both coherent and incoherent noise sources, including charge and nuclear spin noise. This method is applicable to a wide range of physical systems, such as superconducting qubits and trapped ions, paving the way for more resilient and universal quantum computing architectures.

Figures

Figures reproduced from arXiv: 2412.06276 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Sketch of quantum circuits for VQA. The structure of the VQA begins with the preparation of an initial state, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The infidelity, as defined in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Parameter magnitudes for the Toffoli gate with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. The average fidelity as a function of the noise param [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

84 extracted references · 49 canonical work pages

  1. [1]

    Gradient-based optimization Gradient-based optimization methods leverage the gra- dient of the loss function with respect to the model pa- rameters to iteratively adjust those parameters in the direction that minimizes the loss, thereby improving the model’s performance. One of the most commonly used gradient-based opti- mizers is gradient descent, which ...

  2. [2]

    Common exam- ples of gradient-free optimizers include the Nelder-Mead method, Constrained Optimization by Linear Approxi- mations (COBYLA), and evolutionary algorithms

    Gradient-free optimization Gradient-free optimization methods do not require the computation of gradients for the objective function, mak- ing them especially useful for scenarios where the func- tion is non-differentiable, discontinuous, noisy, or com- putationally expensive to evaluate. Common exam- ples of gradient-free optimizers include the Nelder-Me...

  3. [3]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 78 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 78 (2018)

    2018

  4. [4]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lund- gren, and D. Preda, A quantum adiabatic evolution al- gorithm applied to random instances of an np-complete problem, Science 292, 472 (2001)

    2001

  5. [5]

    T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Quantum computers, Na- ture 464, 45 (2010)

    2010

  6. [6]

    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, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, Noisy intermediate-scale quantum algorithms, Rev. Mod. Phys.94, 015004 (2022)

    2022

  7. [7]

    Cerezo, A

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

    2021

  8. [8]

    P. W. Shor, Algorithms for quantum computation: dis- crete logarithms and factoring, in Proceedings 35th an- nual symposium on foundations of computer science (Ieee, 1994) pp. 124–134

    1994

Show all 84 references
  1. [9]

    Lloyd, Universal quantum simulators, Science 273, 1073 (1996)

    S. Lloyd, Universal quantum simulators, Science 273, 1073 (1996)

    1996

  2. [10]

    A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum al- gorithm for linear systems of equations, Phys. Rev. Lett. 103, 150502 (2009)

    2009

  3. [11]

    L. K. Grover, A fast quantum mechanical algorithm for database search, Association for Computing Machinery , 212 (1996)

    1996

  4. [12]

    M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, Vol. 2 (Cambridge university press Cambridge, 2001)

    2001

  5. [13]

    Kloeffel and D

    C. Kloeffel and D. Loss, Prospects for spin-based quan- tum computing in quantum dots, Annu. Rev. Condens. Matter Phys. 4, 51 (2013)

    2013

  6. [14]

    Zhang, H.-O

    X. Zhang, H.-O. Li, G. Cao, M. Xiao, G.-C. Guo, and G.-P. Guo, Semiconductor quantum computation, Natl. Sci. Rev. 6, 32 (2019)

    2019

  7. [15]

    D. M. Zajac, A. J. Sigillito, M. Russ, F. Borjans, J. M. Taylor, G. Burkard, and J. R. Petta, Resonantly driven cnot gate for electron spins, Science 359, 439 (2018)

    2018

  8. [16]

    Huang, C

    W. Huang, C. Yang, K. Chan, T. Tanttu, B. Hensen, R. Leon, M. Fogarty, J. Hwang, F. Hudson, K. M. Itoh, et al., Fidelity benchmarks for two-qubit gates in silicon, Nature 569, 532 (2019)

    2019

  9. [17]

    Watson, S

    T. Watson, S. Philips, E. Kawakami, D. Ward, P. Scar- lino, M. Veldhorst, D. Savage, M. Lagally, M. Friesen, S. Coppersmith, et al., A programmable two-qubit quan- tum processor in silicon, Nature 555, 633 (2018). 10

    2018

  10. [18]

    Hanson, L

    R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quan- tum dots, Rev. Mod. Phys. 79, 1217 (2007)

    2007

  11. [19]

    Dodson, N

    J. Dodson, N. Holman, B. Thorgrimsson, S. F. Neyens, E. MacQuarrie, T. McJunkin, R. H. Foote, L. Edge, S. Coppersmith, and M. Eriksson, Fabrication process and failure analysis for robust quantum dots in silicon, Nanotechnology 31, 505001 (2020)

    2020

  12. [20]

    Hansen, A

    I. Hansen, A. E. Seedhouse, K. W. Chan, F. Hudson, K. M. Itoh, A. Laucht, A. Saraiva, C. H. Yang, and A. S. Dzurak, Implementation of an advanced dressing proto- col for global qubit control in silicon, Appl. Phys. Rev. 9, 031409 (2022)

    2022

  13. [21]

    Yoneda, K

    J. Yoneda, K. Takeda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Honda, T. Kodera, S. Oda, Y. Hoshi, et al., A quantum-dot spin qubit with co- herence limited by charge noise and fidelity higher than 99.9%, Nat. Nanotechnol. 13, 102 (2018)

    2018

  14. [22]

    C. Yang, K. Chan, R. Harper, W. Huang, T. Evans, J. Hwang, B. Hensen, A. Laucht, T. Tanttu, F. Hud- son, et al., Silicon qubit fidelities approaching incoherent noise limits via pulse engineering, Nat. Electron. 2, 151 (2019)

    2019

  15. [23]

    Noiri, K

    A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sam- mak, G. Scappucci, and S. Tarucha, Fast universal quan- tum gate above the fault-tolerance threshold in silicon, Nature 601, 338 (2022)

    2022

  16. [24]

    X. Xue, M. Russ, N. Samkharadze, B. Undseth, A. Sam- mak, G. Scappucci, and L. M. Vandersypen, Quantum logic with spin qubits crossing the surface code thresh- old, Nature 601, 343 (2022)

    2022

  17. [25]

    A. J. Weinstein, M. D. Reed, A. M. Jones, R. W. An- drews, D. Barnes, J. Z. Blumoff, L. E. Euliss, K. Eng, B. H. Fong, S. D. Ha, et al., Universal logic with encoded spin qubits in silicon, Nature 615, 817 (2023)

    2023

  18. [26]

    van Dijk, E

    J. van Dijk, E. Kawakami, R. Schouten, M. Veldhorst, L. Vandersypen, M. Babaie, E. Charbon, and F. Sebas- tiano, Impact of classical control electronics on qubit fi- delity, Phys. Rev. Appl. 12, 044054 (2019)

    2019

  19. [27]

    Huang, N

    P. Huang, N. M. Zimmerman, and G. W. Bryant, Spin decoherence in a two-qubit CPHASE gate: the critical role of tunneling noise, npj Quantum Inf. 4, 62 (2018)

    2018

  20. [28]

    Khaneja, T

    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbr¨ uggen, and S. J. Glaser, Optimal control of coupled spin dynam- ics: design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005)

    2005

  21. [29]

    Caneva, T

    T. Caneva, T. Calarco, and S. Montangero, Chopped random-basis quantum optimization, Phys. Rev. A 84, 022326 (2011)

    2011

  22. [30]

    Zahedinejad, J

    E. Zahedinejad, J. Ghosh, and B. C. Sanders, Designing high-fidelity single-shot three-qubit gates: A machine- learning approach, Phys. Rev. Appl. 6, 054005 (2016)

    2016

  23. [31]

    An and D

    Z. An and D. L. Zhou, Deep reinforcement learning for quantum gate control, Europhysics Letters 126, 60002 (2019)

    2019

  24. [32]

    D. W. Kanaar, U. G¨ ung¨ ord¨ u, and J. P. Kestner, Two- qubit controlled-Z gates robust against charge noise in silicon while compensating for crosstalk using neural net- work, Phys. Rev. B 105, 245308 (2022)

    2022

  25. [33]

    G¨ ung¨ ord¨ u and J

    U. G¨ ung¨ ord¨ u and J. P. Kestner, Robust quantum gates using smooth pulses and physics-informed neural net- works, Phys. Rev. Res. 4, 023155 (2022)

    2022

  26. [34]

    D. W. Kanaar and J. Kestner, Neural-network-designed three-qubit gates robust against charge noise and crosstalk in silicon, Quantum Sci. Technol. 9, 035011 (2024)

    2024

  27. [35]

    T.-N. Xu, Y. Ding, J. D. Mart ´ ın-Guerrero, and X. Chen, Robust two-qubit gate with reinforcement learning and dropout, Phys. Rev. A 110, 032614 (2024)

    2024

  28. [36]

    Rimbach-Russ, S

    M. Rimbach-Russ, S. G. Philips, X. Xue, and L. M. Van- dersypen, Simple framework for systematic high-fidelity gate operations, Quantum Sci. Technol.8, 045025 (2023)

    2023

  29. [37]

    Banchi, N

    L. Banchi, N. Pancotti, and S. Bose, Quantum gate learning in qubit networks: Toffoli gate without time- dependent control, npj Quantum Inf. 2, 1 (2016)

    2016

  30. [38]

    Innocenti, L

    L. Innocenti, L. Banchi, A. Ferraro, S. Bose, and M. Paternostro, Supervised learning of time-independent hamiltonians for gate design, New J. Phys. 22, 065001 (2020)

    2020

  31. [39]

    Lewis, R

    D. Lewis, R. Wiersema, J. Carrasquilla, and S. Bose, Geodesic algorithm for unitary gate design with time- independent hamiltonians, arXiv:2401.05973

    arXiv

  32. [40]

    R. Xu, J. Tang, P. Chandarana, K. Paul, X. Xu, M. Yung, and X. Chen, Benchmarking hybrid digitized- counterdiabatic quantum optimization, Phys. Rev. Res. 6, 013147 (2024)

    2024

  33. [41]

    Farhi, J

    E. Farhi, J. Goldstone, and S. Gutmann, A quantum ap- proximate optimization algorithm, arXiv:1411.4028

    arXiv

  34. [42]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92, 015003 (2020)

    2020

  35. [43]

    Z.-C. Yang, A. Rahmani, A. Shabani, H. Neven, and C. Chamon, Optimizing variational quantum algorithms using pontryagin’s minimum principle, Phys. Rev. X 7, 021027 (2017)

    2017

  36. [44]

    A. B. Magann, C. Arenz, M. D. Grace, T.-S. Ho, R. L. Kosut, J. R. McClean, H. A. Rabitz, and M. Sarovar, From pulses to circuits and back again: A quantum op- timal control perspective on variational quantum algo- rithms, PRX Quantum 2, 010101 (2021)

    2021

  37. [45]

    Khatri, R

    S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sorn- borger, and P. J. Coles, Quantum-assisted quantum com- piling, Quantum 3, 140 (2019)

    2019

  38. [46]

    Geyer, B

    S. Geyer, B. Het´ enyi, S. Bosco, L. C. Camenzind, R. S. Eggli, A. Fuhrer, D. Loss, R. J. Warburton, D. M. Zumb¨ uhl, and A. V. Kuhlmann, Anisotropic exchange interaction of two hole-spin qubits, Nat. Phys. , 1 (2024)

    2024

  39. [47]

    Xue, Many-body interactions with single-electron quantum dots for topological quantum computation, Phys

    P. Xue, Many-body interactions with single-electron quantum dots for topological quantum computation, Phys. Rev. A 81, 052331 (2010)

    2010

  40. [48]

    Stepanenko and N

    D. Stepanenko and N. E. Bonesteel, Universal Quantum Computation through Control of Spin-Orbit Coupling, Phys. Rev. Lett. 93, 140501 (2004)

    2004

  41. [49]

    Baruffa, P

    F. Baruffa, P. Stano, and J. Fabian, Theory of Anisotropic Exchange in Laterally Coupled Quantum Dots, Phys. Rev. Lett. 104, 126401 (2010)

    2010

  42. [50]

    Arrasmith, M

    A. Arrasmith, M. Cerezo, P. Czarnik, L. Cincio, and P. J. Coles, Effect of barren plateaus on gradient-free optimization, Quantum 5, 558 (2021)

    2021

  43. [51]

    Broughton, G

    M. Broughton, G. Verdon, T. McCourt, A. J. Mar- tinez, J. H. Yoo, S. V. Isakov, P. Massey, R. Halavati, M. Y. Niu, A. Zlokapa, et al., Tensorflow quantum: A software framework for quantum machine learning, arxiv:2003.02989

    2003 arXiv

  44. [52]

    Kandala, A

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets, Nature 549, 242 11 (2017)

    2017

  45. [53]

    Wiersema, C

    R. Wiersema, C. Zhou, Y. de Sereville, J. F. Car- rasquilla, Y. B. Kim, and H. Yuen, Exploring Entangle- ment and Optimization within the Hamiltonian Varia- tional Ansatz, PRX Quantum 1, 020319 (2020)

    2020

  46. [54]

    H. F. Trotter, On the product of semi-groups of opera- tors, Proceedings of the American Mathematical Society 10, 545 (1959)

    1959

  47. [55]

    M. Suzuki, Generalized trotter’s formula and systematic approximants of exponential operators and inner deriva- tions with applications to many-body problems, Commu- nications in Mathematical Physics 51, 183 (1976)

    1976

  48. [56]

    M. A. Nielsen, A simple formula for the average gate fidelity of a quantum dynamical operation, Phys. Lett. A 303, 249 (2002)

    2002

  49. [57]

    N. N. Hegade, K. Paul, Y. Ding, M. Sanz, F. Albarr´ an- Arriagada, E. Solano, and X. Chen, Shortcuts to adia- baticity in digitized adiabatic quantum computing, Phys. Rev. Appl. 15, 024038 (2021)

    2021

  50. [58]

    G. E. Crooks, Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition, arXiv:1905.13311

    1905 arXiv

  51. [59]

    Mitarai, M

    K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quan- tum circuit learning, Phys. Rev. A 98, 032309 (2018)

    2018

  52. [60]

    X. Xu, J. Cui, Z. Cui, R. He, Q. Li, X. Li, Y. Lin, J. Liu, W. Liu, J. Lu, et al., Mindspore quantum: a user- friendly, high-performance, and ai-compatible quantum computing framework, arXiv preprint arXiv:2406.17248 (2024)

    2024 arXiv

  53. [61]

    Fredkin and T

    E. Fredkin and T. Toffoli, Conservative logic, Interna- tional Journal of theoretical physics 21, 219 (1982)

    1982

  54. [62]

    Zhang, Q

    Y. Zhang, Q. Chen, A. P. Alivisatos, and M. Salmeron, Dynamic charge carrier trapping in quantum dot field effect transistors, Nano Lett. 15, 4657 (2015)

    2015

  55. [63]

    A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, Charge noise and spin noise in a semiconductor quantum device, Nat. Phys. 9, 570 (2013)

    2013

  56. [64]

    J. P. Kestner, X. Wang, L. S. Bishop, E. Barnes, and S. Das Sarma, Noise-Resistant Control for a Spin Qubit Array, Phys. Rev. Lett. 110, 140502 (2013)

    2013

  57. [65]

    Chekhovich, M

    E. Chekhovich, M. Makhonin, A. Tartakovskii, A. Ya- coby, H. Bluhm, K. Nowack, and L. Vandersypen, Nu- clear spin effects in semiconductor quantum dots, Nat. Mater. 12, 494 (2013)

    2013

  58. [66]

    Barnes, L

    E. Barnes, L. Cywi´ nski, and S. Das Sarma, Nonperturba- tive Master Equation Solution of Central Spin Dephasing Dynamics, Phys. Rev. Lett. 109, 140403 (2012)

    2012

  59. [67]

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru- Guzik, The theory of variational hybrid quantum- classical algorithms, New Journal of Physics 18, 023023 (2016)

    2016

  60. [68]

    P. J. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jef- frey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, C. Quin...

    2016

  61. [69]

    J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S. Blok, M. E. Kimchi-Schwartz, J. R. McClean, J. Carter, W. A. de Jong, and I. Siddiqi, Computation of molecular spec- tra on a quantum processor with an error-resilient algo- rithm, Phys. Rev. X 8, 011021 (2018)

    2018

  62. [70]

    Schumacher, Sending entanglement through noisy quantum channels, Phys

    B. Schumacher, Sending entanglement through noisy quantum channels, Phys. Rev. A 54, 2614 (1996)

    1996

  63. [71]

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

    2018

  64. [72]

    S. Kazi, M. Larocca, M. Farinati, P. J. Coles, M. Cerezo, and R. Zeier, Analyzing the quantum approximate op- timization algorithm: ans \” atze, symmetries, and lie algebras, arXiv preprint arXiv:2410.05187 (2024)

    2024

  65. [73]

    Holmes, K

    Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Con- necting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022)

    2022

  66. [74]

    P. J. Ollitrault, G. Mazzola, and I. Tavernelli, Nonadia- batic molecular quantum dynamics with quantum com- puters, Phys. Rev. Lett. 125, 260511 (2020)

    2020

  67. [75]

    A. B. Magann, M. D. Grace, H. A. Rabitz, and M. Sarovar, Digital quantum simulation of molecular dy- namics and control, Phys. Rev. Res. 3, 023165 (2021)

    2021

  68. [76]

    Huang, Y

    T. Huang, Y. Ding, L. Dupays, Y. Ban, M.-H. Yung, A. del Campo, and X. Chen, Time-optimal control of driven oscillators by variational circuit learning, Phys. Rev. Res. 5, 023173 (2023)

    2023

  69. [77]

    D. Sun, P. Chandarana, Z.-H. Xin, and X. Chen, Op- timizing counterdiabaticity by variational quantum cir- cuits, Philosophical Transactions of the Royal Society A 380, 20210282 (2022)

    2022

  70. [78]

    M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frun- zio, S. M. Girvin, and R. J. Schoelkopf, Realization of three-qubit quantum error correction with superconduct- ing circuits, Nature 482, 382 (2012)

    2012

  71. [79]

    Fedorov, L

    A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a toffoli gate with super- conducting circuits, Nature 481, 170 (2012)

    2012

  72. [80]

    T. Monz, K. Kim, W. H¨ ansel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Realization of the quantum toffoli gate with trapped ions, Phys. Rev. Lett. 102, 040501 (2009)

    2009

  73. [81]

    Y. Li, L. Wan, H. Zhang, H. Zhu, Y. Shi, L. K. Chin, X. Zhou, L. C. Kwek, and A. Q. Liu, Quantum fredkin and toffoli gates on a versatile programmable silicon pho- tonic chip, npj Quantum Information 8, 112 (2022)

    2022

  74. [82]

    Y. Wang, Y. Ding, F. A. C´ ardenas-L´ opez, and X. Chen, Pulse-based variational quantum optimization and met- alearning in superconducting circuits, Phys. Rev. Appl. 22, 024009 (2024)

    2024

  75. [83]

    D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Program. 45, 503 (1989)

    1989

  76. [84]

    J. D. Head and M. C. Zerner, A broyden-Fletcher- Goldfarb-Shanno optimization procedure for molecular geometries, Chem. Phys. Lett. 122, 264 (1985)

    1985

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.