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Efficient quantum information-inspired ansatz for variational quantum eigensolver algorithm: Applications to atomic systems

Abdul Kalam1,2,*, Prasenjit Deb1,†, Akitada Sakurai3,‡, B. K. Sahoo4, V. S. Prasannaa1,2,§, and B. P. Das1,2,5,∥

  • *Contact author: ak6994231@gmail.com
  • †Contact author: devprasen@gmail.com
  • ‡Contact author: akitada.sakurai@oist.jp
  • §Contact author: srinivasaprasannaa@gmail.com
  • ∥Contact author: bhanu.das@tcgcrest.org

Phys. Rev. Research 8, 023272 – Published 11 June, 2026

DOI: https://doi.org/10.1103/kmb5-nkqz

Abstract

We present a quantum information-inspired ansatz for the variational quantum eigensolver and demonstrate its efficacy in calculating ground-state energies of atomic systems. Instead of adopting a heuristic approach, we start with an approximate multiqubit target state and utilize two quantum information-theoretic quantities, i.e., von Neumann entropy and quantum mutual information, to construct our ansatz. The quantum information encoded in the target state helps us design unique blocks and identify qubit pairs that exhibit maximal quantum correlations within the multi-qubit system, thereby enabling us to deterministically place two-qubit entanglers in the suitably constructed parametrized quantum circuit. We find that our approach offers the advantage of reduced circuit depth compared to the physics-inspired unitary coupled-cluster (UCC) ansatz, while yielding accurate results. To test the performance of our ansatz, we apply it to compute ground-state energies of atomic systems in the relativistic regime. Our results show that for up to 12-qubits (12-spinorbitals) noiseless calculations, our ansatz yields energies within chemical accuracy (∼1.6 mhartree) relative to the complete active space configuration interaction values, while utilizing only a few blocks that contain in the best case 98% fewer two-qubit gates when compared with the UCC ansatz in the singles and doubles approximation.

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References (62)

  1. A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Simulated quantum computation of molecular energies, Science 309, 1704 (2005).
  2. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Commun. 5, 4213 (2014).
  3. Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferová, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, et al., Quantum chemistry in the age of quantum computing, Chem. Rev. 119, 10856 (2019).
  4. S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92, 015003 (2020).
  5. N. Baskaran, A. S. Rawat, A. Jayashankar, D. Chakravarti, K. Sugisaki, S. Roy, S. B. Mandal, D. Mukherjee, and V. Prasannaa, Adapting the Harrow-Hassidim-Lloyd algorithm to quantum many-body theory, Phys. Rev. Res. 5, 043113 (2023).
  6. C. Cade, L. Mineh, A. Montanaro, and S. Stanisic, Strategies for solving the Fermi-Hubbard model on near-term quantum computers, Phys. Rev. B 102, 235122 (2020).
  7. Y. Shen, X. Zhang, S. Zhang, J.-N. Zhang, M.-H. Yung, and K. Kim, Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure, Phys. Rev. A 95, 020501 (2017).
  8. C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, et al., Quantum chemistry calculations on a trapped-ion quantum simulator, Phys. Rev. X 8, 031022 (2018).
  9. P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo, et al., Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions, Phys. Rev. A 98, 022322 (2018).
  10. S. Guo, J. Sun, H. Qian, M. Gong, Y. Zhang, F. Chen, Y. Ye, Y. Wu, S. Cao, K. Liu, et al., Experimental quantum computational chemistry with optimized unitary coupled cluster ansatz, Nat. Phys. 20, 1240 (2024).
  11. L. Zhao, J. Goings, K. Shin, W. Kyoung, J. I. Fuks, J.-K. Kevin Rhee, Y. M. Rhee, K. Wright, J. Nguyen, J. Kim, et al., Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers, npj Quantum Inf. 9, 60 (2023).
  12. Q. Gao, G. O. Jones, M. Motta, M. Sugawara, H. C. Watanabe, T. Kobayashi, E. Watanabe, Y.-y. Ohnishi, H. Nakamura, and N. Yamamoto, Applications of quantum computing for investigations of electronic transitions in phenylsulfonyl-carbazole TADF emitters, npj Comput. Mater. 7, 70 (2021).
  13. J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, et al., The variational quantum eigensolver: A review of methods and best practices, Phys. Rep. 986, 1 (2022).
  14. P. Chawla, Shweta, K. Swain, T. Patel, R. Bala, D. Shetty, K. Sugisaki, S. B. Mandal, J. Riu, J. Nogué, et al., Relativistic variational-quantum-eigensolver calculations of molecular electric dipole moments on quantum hardware, Phys. Rev. A 111, 022817 (2025).
  15. A. P. Singh, K. Sugisaki, S. Prasannaa, B. K. Sahoo, B. P. Das, and Y. Nakamura, Experimental computations of atomic properties on a superconducting quantum processor, Phys. Rev. A 110, 062620 (2024).
  16. H. L. Tang, V. Shkolnikov, G. S. Barron, H. R. Grimsley, N. J. Mayhall, E. Barnes, and S. E. Economou, Qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansätze on a quantum processor, PRX Quantum 2, 020310 (2021).
  17. Y. S. Yordanov, V. Armaos, C. H. Barnes, and D. R. Arvidsson-Shukur, Qubit-excitation-based adaptive variational quantum eigensolver, Commun. Phys. 4, 228 (2021).
  18. P. Chawla, D. Shetty, P. B. Tsemo, K. Sugisaki, J. Riu, J. Nogue, D. Mukherjee, and V. Prasannaa, VQE calculations on a NISQ era trapped ion quantum computer using a multireference unitary coupled cluster ansatz: Application to the BeH2 insertion problem, arXiv:2504.07037.
  19. M. Motta and J. E. Rice, Emerging quantum computing algorithms for quantum chemistry, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 12, e1580 (2022).
  20. K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, et al., Noisy intermediate-scale quantum algorithms, Rev. Mod. Phys. 94, 015004 (2022).
  21. K. Sugisaki, T. Kato, Y. Minato, K. Okuwaki, and Y. Mochizuki, Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: A case study of the C2v quasi-reaction pathway of beryllium insertion into a H2 molecule, Phys. Chem. Chem. Phys. 24, 8439 (2022).
  22. Y. Nam, J.-S. Chen, N. C. Pisenti, K. Wright, C. Delaney, D. Maslov, K. R. Brown, S. Allen, J. M. Amini, J. Apisdorf, et al., Ground-state energy estimation of the water molecule on a trapped-ion quantum computer, npj Quantum Inf. 6, 33 (2020).
  23. C. Ying, B. Cheng, Y. Zhao, H.-L. Huang, Y.-N. Zhang, M. Gong, Y. Wu, S. Wang, F. Liang, J. Lin, et al., Experimental simulation of larger quantum circuits with fewer superconducting qubits, Phys. Rev. Lett. 130, 110601 (2023).
  24. 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 (London) 549, 242 (2017).
  25. A. Kandala, K. Temme, A. D. Córcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Error mitigation extends the computational reach of a noisy quantum processor, Nature (London) 567, 491 (2019).
  26. D. S. Abrams and S. Lloyd, Simulation of many-body Fermi systems on a universal quantum computer, Phys. Rev. Lett. 79, 2586 (1997).
  27. D. S. Abrams and S. Lloyd, Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors, Phys. Rev. Lett. 83, 5162 (1999).
  28. J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz, Quantum Sci. Technol. 4, 014008 (2019).
  29. J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Simulation of electronic structure Hamiltonians using quantum computers, Mol. Phys. 109, 735 (2011).
  30. F. A. Evangelista, Alternative single-reference coupled cluster approaches for multireference problems: The simpler, the better, J. Chem. Phys. 134, 224102 (2011).
  31. B. Cooper and P. J. Knowles, Benchmark studies of variational, unitary and extended coupled cluster methods, J. Chem. Phys. 133, 234102 (2010).
  32. R. J. Bartlett and M. Musiał, Coupled-cluster theory in quantum chemistry, Rev. Mod. Phys. 79, 291 (2007).
  33. L. Leone, S. F. Oliviero, L. Cincio, and M. Cerezo, On the practical usefulness of the hardware efficient ansatz, Quantum 8, 1395 (2024).
  34. L. Ratini, C. Capecci, F. Benfenati, and L. Guidoni, Wave function adapted Hamiltonians for quantum computing, J. Chem. Theory Comput. 18, 899 (2022).
  35. A. G. Rattew, S. Hu, M. Pistoia, R. Chen, and S. Wood, A domain-agnostic, noise-resistant, hardware-efficient evolutionary variational quantum eigensolver, arXiv:1910.09694.
  36. S. Sim, P. D. Johnson, and A. Aspuru-Guzik, Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, Adv. Quantum Technol. 2, 1900070 (2019).
  37. J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nat. Commun. 9, 4812 (2018).
  38. Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connecting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022).
  39. L. Cadi Tazi and A. J. Thom, Folded spectrum VQE: A quantum computing method for the calculation of molecular excited states, J. Chem. Theory Comput. 20, 2491 (2024).
  40. C. Cao, H. Yano, and Y. O. Nakagawa, Accelerated variational quantum eigensolver with joint Bell measurement, Phys. Rev. Res. 6, 013205 (2024).
  41. M. M. Wilde, Quantum Information Theory (Cambridge University Press, UK, 2013).
  42. N. V. Tkachenko, J. Sud, Y. Zhang, S. Tretiak, P. M. Anisimov, A. T. Arrasmith, P. J. Coles, L. Cincio, and P. A. Dub, Correlation-informed permutation of qubits for reducing ansatz depth in the variational quantum eigensolver, PRX Quantum 2, 020337 (2021).
  43. D. Materia, L. Ratini, C. Angeli, and L. Guidoni, Quantum information driven ansatz (QIDA): Shallow-depth empirical quantum circuits from quantum chemistry, J. Phys. Chem. A 128, 8533 (2024).
  44. D. Materia, L. Ratini, C. Angeli, and L. Guidoni, Quantum information reveals that orbital-wise correlation is essentially classical in natural orbitals, J. Chem. Phys. 161, 244108 (2024).
  45. Z.-J. Zhang, T. H. Kyaw, J. S. Kottmann, M. Degroote, and A. Aspuru-Guzik, Mutual information-assisted adaptive variational quantum eigensolver, Quantum Sci. Technol. 6, 035001 (2021).
  46. I. P. Grant, Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation (Springer, New York, 2007).
  47. I. Lindgren and J. Morrison, Atomic Many-Body Theory (Springer Science & Business Media, Berlin, 2012), Vol. 3.
  48. J. T. Seeley, M. J. Richard, and P. J. Love, The Bravyi-Kitaev transformation for quantum computation of electronic structure, J. Chem. Phys. 137, 224109 (2012).
  49. See Supplemental Material at http://link.aps.org/supplemental/10.1103/kmb5-nkqz for relevant details of our numerical results.
  50. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  51. L. Bassman Oftelie, R. Van Beeumen, E. Younis, E. Smith, C. Iancu, and W. A. de Jong, Constant-depth circuits for dynamic simulations of materials on quantum computers, Mater. Theory 6, 13 (2022).
  52. K. Dyall, I. Grant, and S. Wilson, The Dirac equation in the algebraic approximation. II. Extended basis set calculations for hydrogenic atoms, J. Phys. B 17, 1201 (1984).
  53. S. Battaglia, D. Bouet, A. Lecoq, S. Evangelisti, N. Faginas-Lago, T. Leininger, and A. Lombardi, Distributed Gaussian orbitals for molecular calculations: Application to simple systems, Mol. Phys. 118, 1615646 (2020).
  54. S. Huzinaga, Basis sets for molecular calculations, Comput. Phys. Rep. 2, 281 (1985).
  55. A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, et al., Quantum computing with Qiskit, arXiv:2405.08810.
  56. H. G. A. Burton, D. Marti-Dafcik, D. P. Tew, and D. J. Wales, Exact electronic states with shallow quantum circuits from global optimisation, npj Quantum Inf. 9, 75 (2023).
  57. D. Kraft, A Software Package for Sequential Quadratic Programming, Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt Köln: Forschungsbericht (Wiss. Berichtswesen d. DFVLR, Germany, 1988).
  58. I. G. Ryabinkin, T.-C. Yen, S. N. Genin, and A. F. Izmaylov, Qubit coupled cluster method: A systematic approach to quantum chemistry on a quantum computer, J. Chem. Theory Comput. 14, 6317 (2018).
  59. R. D’Cunha, T. D. Crawford, M. Motta, and J. E. Rice, Challenges in the use of quantum computing hardware-efficient ansatze in electronic structure theory, J. Phys. Chem. A 127, 3437 (2023).
  60. S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, t|ket〉: A retargetable compiler for NISQ devices, Quantum Sci. Technol. 6, 014003 (2021).
  61. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  62. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76, 722 (1996).

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