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arxiv: 2410.18910 · v1 · submitted 2024-10-24 · 🪐 quant-ph · physics.chem-ph· physics.comp-ph

Characterizing conical intersections of nucleobases on quantum computers

Pith reviewed 2026-05-23 19:19 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-phphysics.comp-ph
keywords quantum simulationconical intersectionscytosinenucleobasessuperconducting quantum computerelectronic structurephotostability
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The pith

Superconducting quantum computers can resolve conical intersections in cytosine.

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

The paper shows that a quantum algorithm can locate the near-degenerate electronic states where two surfaces touch in cytosine, a nucleobase. These conical intersections control how the molecule absorbs and dissipates ultraviolet light, which affects the photostability of DNA and RNA. The authors run the Contracted Quantum Eigensolver on actual superconducting hardware and obtain energies and state characters that match exact classical diagonalization within acceptable error. The result matters because classical methods become expensive precisely when states are nearly degenerate, the regime that governs photochemical outcomes in biology.

Core claim

The authors report the first quantum simulation of conical intersections in cytosine, using the Contracted Quantum Eigensolver on a superconducting processor to compute the ground and first excited states at the intersection geometry. Both the Contracted Quantum Eigensolver and Variational Quantum Deflation produce results close to exact diagonalization despite device noise.

What carries the argument

The Contracted Quantum Eigensolver, an ansatz that is exact for many-electron systems in the absence of noise, applied to extract the two lowest states whose surfaces touch at the conical intersection.

If this is right

  • The method supplies state characters and energy gaps at conical intersections that enter models of DNA damage and repair.
  • The same workflow can be repeated for other nucleobases or for geometries away from the intersection.
  • Hybrid quantum-classical runs become feasible for molecules whose active spaces exceed the reach of full classical diagonalization.
  • Noise resilience of the ansatz suggests it can be used for other near-degenerate electronic-structure problems.

Where Pith is reading between the lines

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

  • Extending the calculation to include nuclear motion would test whether the same hardware can capture non-adiabatic dynamics.
  • If the approach scales to larger active spaces, it could address conical intersections in systems where classical multireference methods already struggle.
  • The reported accuracy sets a benchmark for testing future error-mitigation techniques on similar photochemical problems.

Load-bearing premise

The quantum algorithm still separates the nearly degenerate states with enough accuracy on noisy hardware to be chemically useful.

What would settle it

A direct comparison in which the quantum-computed energy gap or state overlap at the cytosine intersection geometry differs from exact diagonalization by more than the reported error bars.

Figures

Figures reproduced from arXiv: 2410.18910 by Brandon Allen, Cameron Cianci, David A. Mazziotti, Irma Avdic, Lea F. Santos, Nam P. Vu, Rishab Dutta, Samuel Warren, Victor S. Batista, Yuchen Wang.

Figure 1
Figure 1. Figure 1: FIG. 1: An illustration of the CQE algorithm at the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Reported minimum energy CI for cytosine. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The convergence plot for (a) VQD and (b) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The 3D CI topography shown with (a) exact [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

Hybrid quantum-classical computing algorithms offer significant potential for accelerating the calculation of the electronic structure of strongly correlated molecules. In this work, we present the first quantum simulation of conical intersections (CIs) in a biomolecule, cytosine, using a superconducting quantum computer. We apply the Contracted Quantum Eigensolver (CQE) -- with comparisons to conventional Variational Quantum Deflation (VQD) -- to compute the near-degenerate ground and excited states associated with the conical intersection, a key feature governing the photostability of DNA and RNA. The CQE is based on an exact ansatz for many-electron molecules in the absence of noise -- a critically important property for resolving strongly correlated states at CIs. Both methods demonstrate promising accuracy when compared with exact diagonalization, even on noisy intermediate-scale quantum computers, highlighting their potential for advancing the understanding of photochemical and photobiological processes. The ability to simulate these intersections is critical for advancing our knowledge of biological processes like DNA repair and mutation, with potential implications for molecular biology and medical research.

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 / 2 minor

Summary. The manuscript claims to present the first quantum simulation of conical intersections in cytosine (a nucleobase) on a superconducting quantum computer. It applies the Contracted Quantum Eigensolver (CQE) — with comparisons to Variational Quantum Deflation (VQD) — to the near-degenerate ground and excited states at the CI geometry, asserting that both methods achieve promising accuracy versus exact diagonalization even on NISQ hardware, thereby demonstrating potential for photochemical and photobiological applications.

Significance. If the quantitative results hold, the work would constitute a notable early demonstration of quantum hardware applied to a biomolecular CI, a feature central to DNA/RNA photostability. The emphasis on an exact (noiseless) ansatz for strongly correlated states is a methodological strength that could help address degeneracy issues, provided noise effects are rigorously bounded.

major comments (2)
  1. [Abstract] Abstract: the assertion of 'promising accuracy' versus exact diagonalization is presented without any numerical metrics, error bars, energy-gap values, or hardware-error comparisons; this is load-bearing for the central claim that CQE resolves the near-degenerate CI states on noisy superconducting hardware.
  2. [Methods/Results] Methods/Results (CQE implementation): because the CQE ansatz is exact only in the noiseless limit, the manuscript must supply a concrete demonstration (e.g., computed gap size at the cytosine CI geometry versus measured hardware error rates or state-vector fidelity) showing that noise does not collapse or mix the degenerate pair beyond utility; absent this bound, the noise-resilience claim remains unverified.
minor comments (2)
  1. All result figures should include direct overlays or tables comparing CQE, VQD, and exact-diagonalization energies with error bars; axis labels and units must be unambiguous.
  2. Clarify the active-space size, qubit mapping, and number of shots used in the superconducting-device experiments so that reproducibility is immediate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting areas where the manuscript can be strengthened. We address each major comment below and will incorporate revisions to improve the clarity and rigor of our claims regarding the quantum simulation of conical intersections in cytosine.

read point-by-point responses
  1. Referee: [Abstract] Abstract: the assertion of 'promising accuracy' versus exact diagonalization is presented without any numerical metrics, error bars, energy-gap values, or hardware-error comparisons; this is load-bearing for the central claim that CQE resolves the near-degenerate CI states on noisy superconducting hardware.

    Authors: We agree that the abstract would benefit from explicit quantitative support for the 'promising accuracy' claim. The revised manuscript will update the abstract to include the specific energy gap values computed via CQE and VQD on hardware, along with their deviations from exact diagonalization and brief comparisons to hardware noise characteristics. revision: yes

  2. Referee: [Methods/Results] Methods/Results (CQE implementation): because the CQE ansatz is exact only in the noiseless limit, the manuscript must supply a concrete demonstration (e.g., computed gap size at the cytosine CI geometry versus measured hardware error rates or state-vector fidelity) showing that noise does not collapse or mix the degenerate pair beyond utility; absent this bound, the noise-resilience claim remains unverified.

    Authors: We acknowledge that an explicit bound relating the CI energy gap to hardware error rates would strengthen the noise-resilience discussion. The manuscript already reports direct energy comparisons to exact diagonalization obtained on the superconducting device, which demonstrate resolvability of the states. In revision we will add a targeted analysis (in the main text or supplementary information) that quantifies the gap size against observed hardware error rates and state fidelities to make this bound explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: standard application of CQE/VQD to cytosine CI with external benchmarks

full rationale

The paper applies the established Contracted Quantum Eigensolver (CQE) and Variational Quantum Deflation (VQD) to compute near-degenerate states at the cytosine conical intersection on superconducting hardware, reporting comparisons to exact diagonalization. The CQE is described as based on an exact ansatz in the noiseless limit, but this is a stated property of the method rather than a derivation within the paper. No load-bearing steps reduce by construction to the paper's own inputs or fitted parameters; no self-citations form a chain that justifies the central simulation result; and the work is benchmarked against independent exact diagonalization. This is a normal application paper with self-contained content against external references.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work relies on standard quantum algorithms and quantum chemistry frameworks with no new free parameters, axioms, or invented entities introduced in the abstract description.

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Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · 1 internal anchor

  1. [1]

    Aspuru-Guzik, A

    A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head- Gordon, Simulated quantum computation of molecular energies, Science 309, 1704 (2005)

  2. [2]

    Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. John- son, M. Kieferov´ a, I. D. Kivlichan, T. Menke, B. Per- opadre, N. P. Sawaya, et al. , Quantum chemistry in the age of quantum computing, Chem. Rev. 119, 10856 (2019)

  3. [3]

    Bauer, S

    B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum algorithms for quantum chemistry and quan- tum materials science, Chem. Rev. 120, 12685 (2020)

  4. [4]

    Simulating Chemistry on Bosonic Quantum Devices

    R. Dutta, D. G. Cabral, N. Lyu, N. P. Vu, Y. Wang, B. Allen, X. Dan, R. G. Corti˜ nas, P. Khazaei, S. E. Smart, et al. , Simulating chemistry on bosonic quantum devices, arXiv preprint arXiv:2404.10214 10.48550/arXiv.2404.10214 (2024)

  5. [5]

    Preskill, Quantum computing in the nisq era and be- yond, Quantum 2, 79 (2018)

    J. Preskill, Quantum computing in the nisq era and be- yond, Quantum 2, 79 (2018)

  6. [6]

    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 (2017)

  7. [7]

    A. E. Russo, K. M. Rudinger, B. C. Morrison, and A. D. Baczewski, Evaluating energy differences on a quantum computer with robust phase estimation, Phys. Rev. Lett. 126, 210501 (2021)

  8. [8]

    H. L. Tang, V. Shkolnikov, G. S. Barron, H. R. Grim- sley, N. J. Mayhall, E. Barnes, and S. E. Economou, qubit-adapt-vqe: An adaptive algorithm for construct- ing hardware-efficient ans¨ atze on a quantum processor, PRX Quantum 2, 020310 (2021)

  9. [9]

    S. H. Sureshbabu, M. Sajjan, S. Oh, and S. Kais, Im- plementation of quantum machine learning for electronic structure calculations of periodic systems on quantum computing devices, J. Chem. Inf. Model. 61, 2667 (2021)

  10. [11]

    P.; Lyu, N.; Wang, C.; Batista, V

    R. Dutta, N. P. Vu, N. Lyu, C. Wang, and V. S. Batista, Simulating electronic structure on bosonic quantum com- puters, arXiv preprint arXiv:2404.10222 (2024)

  11. [12]

    Cianci, L

    C. Cianci, L. F. Santos, and V. S. Batista, Subspace- search quantum imaginary time evolution for excited state computations (2024), arXiv:2407.11182 [quant-ph]

  12. [13]

    Y. Cao, J. Romero, and A. Aspuru-Guzik, Potential of quantum computing for drug discovery, IBM Journal of Research and Development 62, 6:1 (2018)

  13. [14]

    A. M. Smaldone and V. S. Batista, Quantum-to-classical neural network transfer learning applied to drug toxicity prediction, J. Chem. Theory Comput. , 4901

  14. [15]

    Varsano, R

    D. Varsano, R. Di Felice, M. A. Marques, and A. Rubio, A TDDFT study of the excited states of DNA bases and their assemblies, J. Phys. Chem. B 110, 7129 (2006)

  15. [16]

    Teh and J

    H.-H. Teh and J. E. Subotnik, The simplest possible ap- proach for simulating S 0–S1 conical intersections with DFT/TDDFT: Adding one doubly excited configuration, J. Phys. Chem. Lett. 10, 3426 (2019)

  16. [17]

    Marrot and J.-R

    L. Marrot and J.-R. Meunier, Skin dna photodamage and its biological consequences, J. Am. Acad. Dermatol. 58, S139 (2008)

  17. [18]

    H. Kang, K. T. Lee, B. Jung, Y. J. Ko, and S. K. Kim, Intrinsic lifetimes of the excited state of DNA and RNA bases, J. Am. Chem. Soc. 124, 12958 (2002)

  18. [19]

    R. J. Malone, A. M. Miller, and B. Kohler, Singlet 8 excited-state lifetimes of cytosine derivatives measured by femtosecond transient absorption, Photochem. Pho- tobiol. 77, 158 (2003)

  19. [20]

    Sharonov, T

    A. Sharonov, T. Gustavsson, V. Carr´ e, E. Renault, and D. Markovitsi, Cytosine excited state dynamics studied by femtosecond fluorescence upconversion and transient absorption spectroscopy, Chem. Phys. Lett. 380, 173 (2003)

  20. [21]

    Merch´ an and L

    M. Merch´ an and L. Serrano-Andr´ es, Ultrafast internal conversion of excited cytosine via the lowest ππ* elec- tronic singlet state, J. Am. Chem. Soc. 125, 8108 (2003)

  21. [22]

    Blancafort and M

    L. Blancafort and M. A. Robb, Key role of a threefold state crossing in the ultrafast decay of electronically ex- cited cytosine, J. Phys. Chem. A 108, 10609 (2004)

  22. [23]

    Matsika, Three-state conical intersections in nucleic acid bases, J

    S. Matsika, Three-state conical intersections in nucleic acid bases, J. Phys. Chem. A 109, 7538 (2005)

  23. [24]

    K. A. Kistler and S. Matsika, Three-state conical inter- sections in cytosine and pyrimidinone bases, J. Chem. Phys. 128, 215102 (2008)

  24. [25]

    Gonz´ alez-V´ azquez and L

    J. Gonz´ alez-V´ azquez and L. Gonz´ alez, A time- dependent picture of the ultrafast deactivation of keto-cytosine including three-state conical intersections, ChemPhysChem 11, 3617 (2010)

  25. [26]

    Barbatti, A

    M. Barbatti, A. J. Aquino, J. J. Szymczak, D. Nachti- gallova, and H. Lischka, Photodynamical simulations of cytosine: characterization of the ultrafast bi-exponential uv deactivation, Phys. Chem. Chem. Phys. 13, 6145 (2011)

  26. [27]

    Richter, P

    M. Richter, P. Marquetand, J. Gonzalez-Vazquez, I. Sola, and L. Gonz´ alez, Femtosecond intersystem crossing in the DNA nucleobase cytosine, J. Phys. Chem. Lett 3, 3090 (2012)

  27. [28]

    Blaser, M

    S. Blaser, M. A. Trachsel, S. Lobsiger, T. Wiedmer, H.-M. Frey, and S. Leutwyler, Gas-phase cytosine and cytosine-n1-derivatives have 0.1–1 ns lifetimes near the s1 state minimum, J. Phys. Chem. Lett. 7, 752 (2016)

  28. [29]

    M. A. Trachsel, S. Blaser, S. Lobsiger, L. Siffert, H.-M. Frey, L. Blancafort, and S. Leutwyler, Locating cytosine conical intersections by laser experiments and ab initio calculations, J. Phys. Chem. Lett. 11, 3203 (2020)

  29. [30]

    Shahrokh, R

    L. Shahrokh, R. Omidyan, and G. Azimi, Theoretical insights on the excited-state-deactivation mechanisms of protonated thymine and cytosine, Phys. Chem. Chem. Phys. 23, 8916 (2021)

  30. [31]

    D. R. Yarkony, Diabolical conical intersections, Rev. Mod. Phys. 68, 985 (1996)

  31. [32]

    Domcke, D

    W. Domcke, D. Yarkony, and H. K¨ oppel,Conical inter- sections: Electronic structure, dynamics & spectroscopy , Vol. 15 (World Scientific, 2004)

  32. [33]

    B. G. Levine and T. J. Mart´ ınez, Isomerization through conical intersections, Annu. Rev. Phys. Chem. 58, 613 (2007)

  33. [34]

    Matsika and P

    S. Matsika and P. Krause, Nonadiabatic events and coni- cal intersections, Annu. Rev. Phys. Chem.62, 621 (2011)

  34. [35]

    J. C. Tully, Perspective: Nonadiabatic dynamics theory, J. Chem. Phys. 137 (2012)

  35. [36]

    Guo and D

    H. Guo and D. R. Yarkony, Accurate nonadiabatic dy- namics, Phys. Chem. Chem. Phys. 18, 26335 (2016)

  36. [37]

    D. R. Yarkony, C. Xie, X. Zhu, Y. Wang, C. L. Mal- bon, and H. Guo, Diabatic and adiabatic representations: Electronic structure caveats, Comput. Theor. Chem. 1152, 41 (2019)

  37. [38]

    Yalouz, B

    S. Yalouz, B. Senjean, J. G¨ unther, F. Buda, T. E. O’Brien, and L. Visscher, A state-averaged orbital- optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states, Quantum Sci. Technol. 6, 024004 (2021)

  38. [39]

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

  39. [40]

    Wang and D

    Y. Wang and D. A. Mazziotti, Quantum simulation of conical intersections, Phys. Chem. Chem. Phys. 26, 11491 (2024)

  40. [41]

    Koridon, J

    E. Koridon, J. Fraxanet, A. Dauphin, L. Visscher, T. E. O’Brien, and S. Polla, A hybrid quantum algorithm to detect conical intersections, Quantum 8, 1259 (2024)

  41. [42]

    S. Zhao, D. Tang, X. Xiao, R. Wang, Q. Sun, Z. Chen, X. Cai, Z. Li, H. Yu, and W.-H. Fang, Quantum compu- tation of conical intersections on a programmable super- conducting quantum processor, J. Phys. Chem. Lett. 15, 7244

  42. [43]

    Higgott, D

    O. Higgott, D. Wang, and S. Brierley, Variational quan- tum computation of excited states, Quantum 3, 156 (2019)

  43. [44]

    S. E. Smart and D. A. Mazziotti, Quantum solver of con- tracted eigenvalue equations for scalable molecular simu- lations on quantum computing devices, Phys. Rev. Lett. 126, 070504 (2021)

  44. [45]

    S. E. Smart, J.-N. Boyn, and D. A. Mazziotti, Resolving correlated states of benzyne with an error-mitigated con- tracted quantum eigensolver, Phys. Rev. A 105, 022405 (2022)

  45. [46]

    Y. Wang, L. M. Sager-Smith, and D. A. Mazziotti, Quan- tum simulation of bosons with the contracted quantum eigensolver, New J. Phys. 25, 103005 (2023)

  46. [47]

    Warren, Y

    S. Warren, Y. Wang, C. L. Benavides-Riveros, and D. A. Mazziotti, Exact ansatz of fermion-boson systems for a quantum device, Phys. Rev. Lett. 133, 080202 (2024)

  47. [48]

    D. A. Mazziotti, Contracted Schr¨ odinger equation: De- termining quantum energies and two-particle density ma- trices without wave functions, Phys. Rev. A 57, 4219 (1998)

  48. [49]

    D. A. Mazziotti, Anti-hermitian contracted Schr¨ odinger equation: Direct determination of the two-electron re- duced density matrices of many-electron molecules, Phys. Rev. Lett. 97, 143002 (2006)

  49. [50]

    Nakatsuji, Equation for the direct determination of the density matrix, Phys

    H. Nakatsuji, Equation for the direct determination of the density matrix, Phys. Rev. A 14, 41 (1976)

  50. [51]

    C. L. Benavides-Riveros, Y. Wang, S. Warren, and D. A. Mazziotti, Quantum simulation of excited states from parallel contracted quantum eigensolvers, New J. Phys. 26, 033020 (2024)

  51. [52]

    Wang and D

    Y. Wang and D. A. Mazziotti, Electronic excited states from a variance-based contracted quantum eigensolver, Phys. Rev. A , 022814 (2023)

  52. [53]

    Cleve, A

    R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Quantum algorithms revisited, Proc. R. Soc. London A 454, 339 (1998)

  53. [54]

    D. R. Alcoba, L. Lain, A. Torre, T. R. Ayala, O. B. O˜ na, G. E. Massaccesi, J. E. Peralta, and J. I. Melo, Generalized spin in the variance-based wave function optimization method within the doubly occupied con- figuration interaction framework, J. Phys. Chem. A 10.1021/acs.jpca.4c02742 (2024)

  54. [55]

    K. M. Nakanishi, K. Mitarai, and K. Fujii, Subspace- search variational quantum eigensolver for excited states, Phys. Rev. Res. 1, 033062 (2019)

  55. [56]

    Lischka, T

    H. Lischka, T. M¨ uller, P. G. Szalay, I. Shavitt, R. M. 9 Pitzer, and R. Shepard, Columbus—a program system for advanced multireference theory calculations, Wiley Interdiscip. Rev. Comput. Mol. Sci. 1, 191 (2011)

  56. [57]

    Lischka, R

    H. Lischka, R. Shepard, T. M¨ uller, P. G. Szalay, R. M. Pitzer, A. J. Aquino, M. M. Ara´ ujo do Nascimento, M. Barbatti, L. T. Belcher, J.-P. Blaudeau, et al. , The generality of the guga mrci approach in columbus for treating complex quantum chemistry, J. Chem. Phys. 152 (2020)

  57. [58]

    M. R. Manaa and D. R. Yarkony, On the intersection of two potential energy surfaces of the same symmetry. systematic characterization using a lagrange multiplier constrained procedure, J. Chem. Phys. 99, 5251 (1993)

  58. [59]

    Cu´ ellar-Zuquin, A

    J. Cu´ ellar-Zuquin, A. J. Pepino, I. F. Galv´ an, I. Rivalta, F. Aquilante, M. Garavelli, R. Lindh, and J. Segarra- Mart´ ı, Characterising conical intersections in DNA/RNA nucleobases with multiconfigurational wave functions of varying active space size, J. Chem. Theory Comput. 19, 8258 (2024)

  59. [60]

    Qiskit contributors, Qiskit: An open-source framework for quantum computing (2024)

  60. [61]

    Jordan and E

    P. Jordan and E. Wigner, ¨Uber das paulische ¨Aquivalenzverbot, Z. Physik 47, 631–651 (1928)

  61. [62]

    IBM-Quantum, https://quantum-computing.ibm.com/ (2024)

  62. [63]

    S. E. Smart and D. A. Mazziotti, Verifiably exact solu- tion of the electronic schr¨ odinger equation on quantum devices, Phys. Rev. A 109, 022802 (2024)

  63. [64]

    D. A. Mazziotti, Anti-Hermitian part of the contracted Schr¨ odinger equation for the direct calculation of two- electron reduced density matrices, Phys. Rev. A 75, 022505 (2007)

  64. [65]

    D. A. Mazziotti, Exactness of wave functions from two- body exponential transformations in many-body quan- tum theory, Physical Review A 69, 012507 (2004)

  65. [66]

    M. R. Hoffmann and J. Simons, A unitary multiconfig- urational coupled-cluster method: Theory and applica- tions, J. Chem. Phys. 88, 993–1002 (1988)

  66. [67]

    Romero, R

    J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, Strategies for quantum com- puting molecular energies using the unitary coupled clus- ter ansatz, Quantum Sci. Technol. 4, 014008 (2018)

  67. [68]

    Bonet-Monroig, R

    X. Bonet-Monroig, R. Babbush, and T. E. O’Brien, Nearly optimal measurement scheduling for partial to- mography of quantum states, Phys. Rev. X 10, 031064 (2020)

  68. [69]

    Y. Wang, I. Avdic, and D. A. Mazziotti, Shadow ansatz for the many-fermion wave function in scalable molec- ular simulations on quantum computing devices, arXiv preprint arXiv:2408.11026 10.48550/arXiv.2408.11026 (2024)

  69. [70]

    J. C. Spall, Implementation of the simultaneous per- turbation algorithm for stochastic optimization, IEEE Trans. Aerosp. Electron. Syst. 34, 817 (1998)