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arxiv: 2605.21756 · v1 · pith:FOROLX74new · submitted 2026-05-20 · 🪐 quant-ph

Towards a quantum decision tree in a laser pumped four-level system

Dawit Hailuf Hailu This is my paper

Pith reviewed 2026-05-22 08:28 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum decision treefour-level systemdiamond configurationLie-algebraic methodslaser pulsespopulation redistributionquantum computing
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The pith

Laser pulses with identical timing but different amplitudes can simulate a quantum decision tree in a four-level atomic system.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a method to implement quantum decision trees in a laser-driven four-level atomic system arranged in a diamond configuration. Using Lie-algebraic analysis, it shows how Stokes and pump pulses with the same time dependence but varying strengths can move the atomic population from the ground state to other levels in a controlled way. This population movement is designed to replicate the branching logic of a decision tree. The framework is scalable to larger N-level systems and may find use in quantum computing and decision-making tasks.

Core claim

In the diamond configuration, the system dynamics under the Stokes pulse β_j(t) for transitions between |0>, |3> and |1>, |2>, and the pump laser α_j(t) for |0>, |1> and |2>, |3>, permit controlled population redistribution from the initial state by using pulse profiles that have identical temporal structures but different amplitudes, which simulates the operation of a quantum decision tree.

What carries the argument

The Lie-algebraic formalism applied to the diamond-shaped four-level system driven by Stokes and pump laser pulses with matched temporal profiles but differing amplitudes.

If this is right

  • The approach scales to N-level systems for implementing more complex decision trees.
  • It provides a physical platform for quantum computing applications involving decision processes.
  • Controlled population redistribution enables mimicry of decision tree logic in atomic systems.
  • Enhances potential utility in various decision-making applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This could be extended to include decoherence effects to test robustness in real quantum systems.
  • Similar pulse control techniques might apply to other quantum information processing tasks in atomic ensembles.
  • Integrating actual measurements could turn the simulation into a functional quantum decision device.

Load-bearing premise

That the selected pulse profiles analyzed via Lie-algebraic methods implement quantum decision tree logic through population transfers without requiring models of decoherence or measurement.

What would settle it

Applying the proposed pulse profiles to the four-level system and measuring the resulting populations to verify if they correspond to the branches expected from a quantum decision tree.

Figures

Figures reproduced from arXiv: 2605.21756 by Dawit Hailuf Hailu.

Figure 2
Figure 2. Figure 2: FIG. 2: Truth table for the OR logic gate. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Four-level diamond-shaped, with coupling lasers. Blue pump laser, and red Stokes laser. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Plots of the (a) Time evolution of the pulse profiles and the populations of the four states in a four [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (a) Time evolution of pulse profiles and state populations in a four-level diamond-shaped quantum system [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The proposed quantum tree with colored paths [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

In this study, we examine an innovative framework towards implementing quantum decision trees utilizing a laser-driven four-level system. We discuss a diamond-shaped atomic configuration, in which we apply Lie-algebraic formalisms to analyze the dynamics of the system. The system is perturbed by a Stokes pulse, represented as $\beta_j(t)$ (for $j=1,2$), which interacts with the atomic states $|0\rangle, |3\rangle$ and $|1\rangle, |2\rangle$. In addition, a pump laser, denoted as $\alpha_j(t)$, couples the states $|0\rangle, |1\rangle$ and $|2\rangle, |3\rangle$. By employing pulse profiles that possess identical temporal behavior but differ in amplitude, one can effectively redistribute the population from the initial ground state to the other energy levels. This technique facilitates the mimicry of a quantum decision tree. We highlight that the proposed methodology is scalable to N-level systems, enhancing its adaptability and potential utility in quantum computing and various decision-making applications. We introduce a novel framework for implementing quantum decision trees using a four-level laser-driven atomic system. Employing a diamond-shaped energy configuration, we analyze system dynamics through Lie-algebraic methods. Using pulse profiles with identical temporal structures but varying amplitudes, we achieve controlled population redistribution among energy levels, effectively simulating a quantum decision tree. This methodology is scalable to systems of \(N\) levels, offering potential applications in quantum computing and decision-making processes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a framework for implementing quantum decision trees in a laser-driven four-level atomic system in a diamond configuration. Lie-algebraic methods are used to analyze the dynamics under Stokes pulses β_j(t) (j=1,2) coupling states |0⟩,|3⟩ and |1⟩,|2⟩ and pump pulses α_j(t) coupling |0⟩,|1⟩ and |2⟩,|3⟩. Pulses with identical temporal structures but differing amplitudes are claimed to achieve controlled population redistribution from the initial ground state, thereby simulating a quantum decision tree. The approach is asserted to be scalable to N-level systems with applications in quantum computing and decision-making.

Significance. If the described pulse-driven population transfers can be rigorously mapped to the branching logic, superposition of paths, and measurement outcomes of a quantum decision tree, the work would offer a concrete physical platform for quantum decision processes using atomic systems. The application of Lie-algebraic controllability analysis is a positive element for establishing state reachability. However, the significance is currently limited because the manuscript presents the simulation claim as an assertion without explicit verification of the decision-tree functional.

major comments (2)
  1. [Abstract and main results section] Abstract and results description: The assertion that identical-temporal-structure pulses with varying amplitudes 'effectively simulating a quantum decision tree' is load-bearing for the central claim but unsupported by any explicit mapping. The Lie-algebraic analysis shows reachability of target populations, yet no construction is given of a superposition |path0⟩ + |path1⟩ whose subsequent projective measurement reproduces the tree's output distribution, nor is there verification that the dynamics implement conditional branching without external classical logic.
  2. [Discussion of scalability] Scalability claim: The statement that the methodology 'is scalable to systems of N levels' is presented without a general construction, inductive argument, or explicit extension beyond the four-level diamond case that preserves the decision-tree simulation property.
minor comments (1)
  1. [Pulse definitions] The exact functional forms of the temporal profiles for β_j(t) and α_j(t), and the specific amplitude values used, are not provided in the abstract or summary description, making it difficult to reproduce the claimed population transfers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us identify areas where the manuscript can be strengthened. We address each major comment below and outline the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and main results section] Abstract and results description: The assertion that identical-temporal-structure pulses with varying amplitudes 'effectively simulating a quantum decision tree' is load-bearing for the central claim but unsupported by any explicit mapping. The Lie-algebraic analysis shows reachability of target populations, yet no construction is given of a superposition |path0⟩ + |path1⟩ whose subsequent projective measurement reproduces the tree's output distribution, nor is there verification that the dynamics implement conditional branching without external classical logic.

    Authors: We agree that an explicit mapping between the controlled population transfers and the functional elements of a quantum decision tree would strengthen the central claim. In the revised manuscript, we will add a dedicated subsection in the results section that constructs the superposition of paths using coherent superpositions of the amplitude-varied pulses. We will also demonstrate how the final state populations, upon projective measurement, reproduce the probabilistic outcomes of the decision tree, confirming that the branching is implemented entirely through the quantum dynamics without requiring external classical logic. This addition will directly address the gap identified. revision: yes

  2. Referee: [Discussion of scalability] Scalability claim: The statement that the methodology 'is scalable to systems of N levels' is presented without a general construction, inductive argument, or explicit extension beyond the four-level diamond case that preserves the decision-tree simulation property.

    Authors: We acknowledge that the scalability claim requires a more rigorous justification. In the revised version, we will include an inductive argument in the discussion section. Starting from the four-level diamond configuration, we will show how to extend the system to N levels by adding additional atomic states and corresponding laser couplings while maintaining the Lie-algebraic controllability and the decision-tree simulation via identical temporal pulse profiles with adjusted amplitudes. This will provide the general construction requested. revision: yes

Circularity Check

0 steps flagged

No circularity: proposal frames population control as an application of Lie-algebraic controllability without definitional reduction or fitted predictions

full rationale

The manuscript proposes that identical-shape Stokes and pump pulses of differing amplitudes, analyzed via Lie-algebraic methods in the diamond configuration, achieve population redistribution that can mimic a quantum decision tree. This is presented as a direct physical consequence of the chosen pulse profiles and the resulting reachable states, without any parameter fitted to decision-tree outputs, without self-citation chains supporting a uniqueness claim, and without redefining the decision-tree logic in terms of the population transfers themselves. The Lie-algebraic controllability analysis stands as an independent tool for reachability; the decision-tree interpretation is offered as an interpretive application rather than a derived equivalence that collapses back to the input dynamics by construction. No load-bearing step reduces to its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The proposal rests on the applicability of Lie-algebraic methods to the driven four-level system and on the unverified claim that the chosen pulse amplitudes produce decision-tree logic. No independent evidence for these elements is given in the abstract.

free parameters (1)
  • pulse amplitudes
    The abstract states that pulses differ in amplitude to achieve the desired population redistribution; these amplitudes function as adjustable parameters.
axioms (1)
  • domain assumption Lie-algebraic formalisms accurately capture the dynamics of the laser-driven diamond four-level system.
    Invoked to analyze system evolution under the Stokes and pump pulses.

pith-pipeline@v0.9.0 · 5786 in / 1263 out tokens · 39988 ms · 2026-05-22T08:28:37.976349+00:00 · methodology

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Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    Buhrman and R

    H. Buhrman and R. de Wolf, Theoretical Computer Science288, 21 (2002)

    work page 2002

  2. [2]

    Fresch, D

    B. Fresch, D. Hiluf, E. Collini, R. D. Levine, and F. Remacle, Proc. Natl. Acad. Sci. U. S. A.110, 17183 (2013), ISSN 0027-8424

    work page 2013

  3. [3]

    Fresch, M

    B. Fresch, M. Cipolloni, T.-M. Yan, E. Collini, R. D. Levine, and F. Remacle, The Journal of Physical Chemistry Letters6, 1714 (2015)

    work page 2015

  4. [4]

    Fresch, J

    B. Fresch, J. Bocquel, D. Hiluf, S. Rogge, R. D. Levine, and F. Remacle, ChemPhysChem18, 1790 (2017)

    work page 2017

  5. [5]

    Kohavi and N

    Z. Kohavi and N. K. Jha,Switching and finite automata theory(Cambridge University Press, 2010)

    work page 2010

  6. [6]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature549, 195 (2017)

    work page 2017

  7. [7]

    An introduction to quantum machine learn- ing

    M. Schuld, I. Sinayskiy, and F. Petruccione, Contemporary Physics56, 172 (2015), URLhttps://doi.org/ 10.1080/00107514.2014.964942

    work page doi:10.1080/00107514.2014.964942 2015

  8. [8]

    T. Monz, D. Nigg, E. A. Martinez, M. F. Brandl, P. Schindler, R. Rines, S. X. Wang, I. L. Chuang, and R. Blatt, Science351, 1068 (2016), URLhttps://www.science.org/doi/10.1126/science.aad9480

    work page doi:10.1126/science.aad9480 2016

  9. [9]

    Shore, Bergmann, Kuhn, Schiemann, Oreg, and Eberly, Phys Rev A45, 5297 (1992)

    work page 1992

  10. [10]

    B. W. Shore and N. V. Vitanov, Contemp. Phys.47, 341 (2006)

    work page 2006

  11. [11]

    B. W. SHORE, K. BERGMANN, J. OREG, and S. ROSENWAKS, Phys. Rev. A44, 7442 (1991)

    work page 1991

  12. [12]

    B. W. Shore, Acta Phys. Slovaca58, 243 (2008)

    work page 2008

  13. [13]

    Garcia-Fernandez, B

    R. Garcia-Fernandez, B. W. Shore, K. Bergmann, A. Ekers, and L. P. Yatsenko, J Chem Phys125, 014301 (2006)

    work page 2006

  14. [14]

    R. D. Levine,Quantum mechanics of molecular rate processes(Courier Dover Publications, 2011)

    work page 2011

  15. [15]

    Bergmann, H

    K. Bergmann, H. Theuer, and B. W. Shore, Reviews of Modern Physics70, 1003 (1998)

    work page 1998

  16. [16]

    Fano, Reviews of Modern Physics29, 74 (1957)

    U. Fano, Reviews of Modern Physics29, 74 (1957)

    work page 1957

  17. [17]

    B. W. Shore, Manipulating Quantum Structures Using Laser Pulses, by Bruce W. Shore, Cambridge, UK: Cambridge University Press, 20111(2011)

    work page 2011

  18. [18]

    N. V. Viatnov, T. Halfmann, B. W. Shore, and K. Bergmann, Annual Review of Physical Chemistry52, 763 (2001)

    work page 2001

  19. [19]

    G. P. Berman, G. D. Doolen, R. Mainieri, and V. I. Tsifrinovich,Introduction to quantum computers(World Scientific, 1998)

    work page 1998

  20. [20]

    D. H. Hailu, Results in Optics18, 100789 (2025), ISSN 2666-9501, URLhttps://www.sciencedirect.com/ science/article/pii/S2666950125000173

    work page 2025

  21. [21]

    Allen and J

    L. Allen and J. H. Eberly,Optical resonance and two-level atoms(Wiley, 1975)

    work page 1975

  22. [22]

    K. Blum,Density Matrix Theory and Applications, Springer Series on Atomic, Optical, and Plasma Physics (Springer Berlin Heidelberg, 2012), ISBN 9783642205613, URLhttps://books.google.com/books?id= o0Bofi3_ZI0C

    work page 2012

  23. [23]

    Breuer and F

    H. Breuer and F. Petruccione,The Theory of Open Quantum Systems(OUP Oxford, 2007)

    work page 2007

  24. [24]

    Cohen-Tannoudji, J

    C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg,Optical Bloch Equations (John Wiley & Sons, Ltd, 1998), chap. 5, pp. 353–405, ISBN 9783527617197, https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527617197.ch5, URLhttps://onlinelibrary. wiley.com/doi/abs/10.1002/9783527617197.ch5

    work page doi:10.1002/9783527617197.ch5 1998

  25. [25]

    Mukamel,Principles of Nonlinear Optical Spectroscopy, Oxford Series on Optical and Imaging Sciences (Oxford University Press, 1999)

    S. Mukamel,Principles of Nonlinear Optical Spectroscopy, Oxford Series on Optical and Imaging Sciences (Oxford University Press, 1999)

    work page 1999

  26. [26]

    M. A. Nielsen and I. L. Chuang,Quantum computation and quantum information(Cambridge University Press, 2010), 10th ed. 19

    work page 2010

  27. [27]

    Hiluf, Journal of Physics: Conference Series987, 012033 (2018)

    D. Hiluf, Journal of Physics: Conference Series987, 012033 (2018)

    work page 2018

  28. [28]

    Hioe and C

    F. Hioe and C. Carroll, Physical Review A32, 1541 (1985)

    work page 1985

  29. [29]

    Dattoli and A

    G. Dattoli and A. Torre, Il Nuovo Cimento B106, 1247 (1991)

    work page 1991

  30. [30]

    P. K. Aravind, J. Opt. Soc. Am. B3, 1025 (1986)

    work page 1986

  31. [31]

    F. T. Hioe and J. H. Eberly, Phys. Rev. Lett.47, 838 (1981)

    work page 1981

  32. [32]

    Hioe and J

    F. Hioe and J. Eberly, Physical Review A25, 2168 (1982)

    work page 1982

  33. [33]

    Hioe, Physical Review A28, 879 (1983)

    F. Hioe, Physical Review A28, 879 (1983)

    work page 1983

  34. [34]

    R. P. Feynman, F. L. Vernon Jr, and R. W. Hellwarth, Journal of applied physics28, 49 (1957)

    work page 1957

  35. [35]

    F. B. W. H. M. Packard, Physical Review70, 474 (1946)

    work page 1946

  36. [36]

    Dattoli, M

    G. Dattoli, M. Richetta, and A. Torre, Journal of mathematical physics29, 2586 (1988)

    work page 1988

  37. [37]

    Alhassid and R

    Y. Alhassid and R. D. Levine, The Journal of Chemical Physics67, 4321 (1977)

    work page 1977

  38. [38]

    Alhassid and R

    Y. Alhassid and R. D. Levine, Phys. Rev. A18, 89 (1978)

    work page 1978

  39. [39]

    Dattoli, P

    G. Dattoli, P. D. Lazzaro, and A. Torre, Phys. Rev. A35, 1582 (1987)

    work page 1987

  40. [40]

    Komarova, F

    K. Komarova, F. Remacle, and R. D. Levine, The Journal of Chemical Physics155, 204110 (2021)

    work page 2021

  41. [41]

    Cohen-Tannoudji, B

    C. Cohen-Tannoudji, B. Diu, and F. Laloe,Quantum Mechanics, Volume 1(Wiley, 1991), ISBN 9780471164333

    work page 1991

  42. [42]

    Pfeifer,The Lie Algebras SU(n): An introduction(Birkhäuser Basel, 2003)

    W. Pfeifer,The Lie Algebras SU(n): An introduction(Birkhäuser Basel, 2003)

    work page 2003

  43. [43]

    F. T. Hioe, Phys. Rev. A28, 879 (1983)

    work page 1983

  44. [44]

    Komarova, H

    K. Komarova, H. Gattuso, R. D. Levine, and F. Remacle, Frontiers in Physics8(2020)

    work page 2020

  45. [45]

    Komarova, H

    K. Komarova, H. Gattuso, R. D. Levine, and F. Remacle, The Journal of Physical Chemistry Letters11, 6990 (2020)

    work page 2020

  46. [46]

    S. G. Schirmer and A. I. Solomon, Physical Review A70, 022107 (2004)

    work page 2004

  47. [47]

    Alexander, G

    J. Alexander, G. Dold, O. W. Kennedy, M. Šim˙ enas, J. O’Sullivan, C. W. Zollitsch, S. Welinski, A. Ferrier, E. Lafitte-Houssat, T. Lindström, et al., Phys. Rev. B106, 245416 (2022), URLhttps://link.aps.org/ doi/10.1103/PhysRevB.106.245416

    work page doi:10.1103/physrevb.106.245416 2022

  48. [48]

    F. Beil, J. Klein, and T. Halfmann, Photonics Nanostruct.7, 32 (2009), ISSN 1569-4410

    work page 2009

  49. [49]

    F. Beil, T. Halfmann, F. Remacle, and R. Levine, Physical Review A83, 033421 (2011)

    work page 2011

  50. [50]

    Heinze, A

    G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Physical Review A81, 011401 (2010)

    work page 2010

  51. [51]

    Remacle and R

    F. Remacle and R. D. Levine, Eur. Phys. J. D42, 49 (2007)

    work page 2007

  52. [52]

    L. K. Grover, inProceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing(Asso- ciation for Computing Machinery, New York, NY, USA, 1996), STOC ’96, pp. 212–219, ISBN 0897917855, URLhttps://doi.org/10.1145/237814.237866

    work page doi:10.1145/237814.237866 1996

  53. [53]

    Farhi and S

    E. Farhi and S. Gutmann, Phys. Rev. A58, 915 (1998)

    work page 1998

  54. [54]

    Remacle and R

    F. Remacle and R. Levine, Physical Review A73, 033820 (2006)

    work page 2006

  55. [55]

    Physical Review A33(5), 2913–2927 (1986)

    L. Viola and S. Lloyd, Phys. Rev. A58, 2733 (1998), URLhttps://link.aps.org/doi/10.1103/PhysRevA. 58.2733

    work page doi:10.1103/physreva 1998

  56. [56]

    Cincio, K

    L. Cincio, K. Rudinger, M. Sarovar, and P. J. Coles, PRX Quantum2, 010324 (2021), URLhttps://link. aps.org/doi/10.1103/PRXQuantum.2.010324

    work page doi:10.1103/prxquantum.2.010324 2021

  57. [57]

    P. W. Shor, Phys. Rev. A52, R2493 (1995), URLhttps://link.aps.org/doi/10.1103/PhysRevA.52. R2493

    work page doi:10.1103/physreva.52 1995

  58. [58]

    A. M. Steane, Phys. Rev. Lett.77, 793 (1996), URLhttps://link.aps.org/doi/10.1103/PhysRevLett. 77.793

    work page doi:10.1103/physrevlett 1996