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Treespilation: Architecture- and State-Optimised Fermion-to-Qubit Mappings (2403.03992v3)

Published 6 Mar 2024 in quant-ph

Abstract: Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermioinc problem in the qubits of a quantum computer. In this work, we introduce "treespilation," a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings previously introduced by some of the authors. We use this technique to minimise the number of CNOT gates required to simulate chemical groundstates found numerically using the ADAPT-VQE algorithm. We observe significant reductions, up to $74\%$, in CNOT counts on full connectivity and for limited qubit connectivity-type devices such as IBM Eagle and Google Sycamore, we observe similar reductions in CNOT counts. In many instances, the reductions achieved on these limited connectivity devices even surpass the initial full connectivity CNOT count. Additionally, we find our method improves the CNOT and parameter efficiency of QEB- and qubit-ADAPT-VQE, which are, to our knowledge, the most CNOT-efficient VQE protocols for molecular state preparation.

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References (66)
  1. J. Preskill, “Quantum computing in the NISQ era and beyond,” Quantum, vol. 2, p. 79, 2018.
  2. Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, “Evidence for the utility of quantum computing before fault tolerance,” Nature, vol. 618, no. 7965, pp. 500–505, 2023.
  3. A. Morvan et al., “Phase transition in random circuit sampling,” arXiv preprint arXiv:2304.11119, 2023.
  4. E. Rosenberg et al., “Dynamics of magnetization at infinite temperature in a heisenberg spin chain,” arXiv preprint arXiv:2306.09333, 2023.
  5. N. Keenan, N. F. Robertson, T. Murphy, S. Zhuk, and J. Goold, “Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator,” npj Quantum Information, vol. 9, no. 1, p. 72, 2023.
  6. F. Arute et al., “Quantum supremacy using a programmable superconducting processor,” Nature, vol. 574, no. 7779, pp. 505–510, 2019.
  7. H.-S. Zhong et al., “Quantum computational advantage using photons,” Science, vol. 370, no. 6523, pp. 1460–1463, 2020.
  8. Y. Wu et al., “Strong quantum computational advantage using a superconducting quantum processor,” Phys. Rev. Lett., vol. 127, no. 18, p. 180501, 2021.
  9. L. S. Madsen et al., “Quantum computational advantage with a programmable photonic processor,” Nature, vol. 606, no. 7912, pp. 75–81, 2022.
  10. S. Filippov, M. Leahy, M. A. C. Rossi, and G. García-Pérez, “Scalable tensor-network error mitigation for near-term quantum computing,” arXiv preprint arXiv:2307.11740, 2023.
  11. S. Endo, S. C. Benjamin, and Y. Li, “Practical quantum error mitigation for near-future applications,” Phys. Rev. X, vol. 8, no. 3, p. 031027, 2018.
  12. S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, “Hybrid quantum-classical algorithms and quantum error mitigation,” J. Phys. Soc. Jpn., vol. 90, no. 3, p. 032001, 2021.
  13. Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y. Li, J. R. McClean, and T. E. O’Brien, “Quantum error mitigation,” Reviews of Modern Physics, vol. 95, no. 4, p. 045005, 2023.
  14. E. Van Den Berg, Z. K. Minev, A. Kandala, and K. Temme, “Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors,” Nature Physics, pp. 1–6, 2023.
  15. 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, vol. 549, no. 7671, pp. 242–246, 2017.
  16. P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo, S. Filipp, and I. Tavernelli, “Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions,” Phys. Rev. A, vol. 98, no. 2, p. 022322, 2018.
  17. P. J. Ollitrault, A. Kandala, C.-F. Chen, P. K. Barkoutsos, A. Mezzacapo, M. Pistoia, S. Sheldon, S. Woerner, J. M. Gambetta, and I. Tavernelli, “Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor,” Phys. Rev. Research, vol. 2, no. 4, p. 043140, 2020.
  18. V. Lordi and J. M. Nichol, “Advances and opportunities in materials science for scalable quantum computing,” MRS Bulletin, vol. 46, no. 7, pp. 589–595, 2021.
  19. Y. Cao, J. Romero, and A. Aspuru-Guzik, “Potential of quantum computing for drug discovery,” IBM Journal of Research and Development, vol. 62, no. 6, pp. 6–1, 2018.
  20. N. S. Blunt, J. Camps, O. Crawford, R. Izsák, S. Leontica, A. Mirani, A. E. Moylett, S. A. Scivier, C. Sunderhauf, P. Schopf, et al., “Perspective on the current state-of-the-art of quantum computing for drug discovery applications,” Journal of Chemical Theory and Computation, vol. 18, no. 12, pp. 7001–7023, 2022.
  21. S. Maniscalco, E.-M. Borrelli, D. Cavalcanti, C. Foti, A. Glos, M. Goldsmith, S. Knecht, K. Korhonen, J. Malmi, A. Nykänen, et al., “Quantum network medicine: Rethinking medicine with network science and quantum algorithms,” arXiv preprint arXiv:2206.12405, 2022.
  22. A. Fitzpatrick, A. Nykänen, N. W. Talarico, A. Lunghi, S. Maniscalco, G. García-Pérez, and S. Knecht, “A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive,” arXiv preprint arXiv:2212.11405, 2022.
  23. W. Kirby, M. Motta, and A. Mezzacapo, “Exact and efficient Lanczos method on a quantum computer,” Quantum, vol. 7, p. 1018, 2023.
  24. A. Nykänen, A. Miller, W. Talarico, S. Knecht, A. Kovyrshin, M. Skogh, L. Tornberg, A. Broo, S. Mensa, B. C. B. Symons, E. Sahin, J. Crain, I. Tavernelli, and F. Pavošević, “Toward accurate post-Born–Openheimer molecular simulations on quantum computers: An adaptive variational eigensolver with nuclear-electronic frozen natural orbitals,” Journal of Chemical Theory and Computation, vol. 19, no. 24, p. 9269–9277, 2023.
  25. S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, “Quantum computational chemistry,” Reviews of Modern Physics, vol. 92, no. 1, p. 015003, 2020.
  26. 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,” Physics Reports, vol. 986, pp. 1–128, 2022.
  27. M. Cerezo, K. Sharma, A. Arrasmith, and P. J. Coles, “Variational quantum state eigensolver,” npj Quantum Information, vol. 8, no. 1, pp. 1–11, 2022. Number: 1 Publisher: Nature Publishing Group.
  28. G. H. Low and I. L. Chuang, “Hamiltonian simulation by qubitization,” Quantum, vol. 3, p. 163, 2019.
  29. H. Soeparno and A. S. Perbangsa, “Cloud quantum computing concept and development: A systematic literature review,” Procedia Computer Science, vol. 179, pp. 944–954, 2021. 5th International Conference on Computer Science and Computational Intelligence 2020.
  30. H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, “An adaptive variational algorithm for exact molecular simulations on a quantum computer,” Nature Communications, vol. 10, no. 1, p. 3007, 2019.
  31. Y. S. Yordanov, V. Armaos, C. H. Barnes, and D. R. Arvidsson-Shukur, “Qubit-excitation-based adaptive variational quantum eigensolver,” Communications Physics, vol. 4, no. 1, p. 228, 2021.
  32. 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, vol. 2, no. 2, p. 020310, 2021.
  33. Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferová, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik, “Quantum Chemistry in the Age of Quantum Computing,” Chemical Reviews, vol. 119, no. 19, pp. 10856–10915, 2019. Publisher: American Chemical Society.
  34. 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 Information, vol. 9, no. 1, pp. 1–8, 2023. Number: 1 Publisher: Nature Publishing Group.
  35. C. Feniou, M. Hassan, D. Traoré, E. Giner, Y. Maday, and J.-P. Piquemal, “Overlap-ADAPT-VQE: Practical quantum chemistry on quantum computers via overlap-guided compact Ansätze,” Communications Physics, vol. 6, no. 1, pp. 1–11, 2023. Number: 1 Publisher: Nature Publishing Group.
  36. X. Xiao, H. Zhao, J. Ren, W.-h. Fang, and Z. Li, “Physics-constrained hardware-efficient ansatz on quantum computers that is universal, systematically improvable, and size-consistent,” arXiv preprint arXiv:2307.03563, 2023.
  37. G. García-Pérez, M. A. Rossi, B. Sokolov, F. Tacchino, P. K. Barkoutsos, G. Mazzola, I. Tavernelli, and S. Maniscalco, “Learning to measure: Adaptive informationally complete generalized measurements for quantum algorithms,” PRX Quantum, vol. 2, no. 4, p. 040342, 2021.
  38. A. Glos, A. Nykänen, E.-M. Borrelli, S. Maniscalco, M. A. Rossi, Z. Zimborás, and G. García-Pérez, “Adaptive POVM implementations and measurement error mitigation strategies for near-term quantum devices,” arXiv preprint arXiv:2208.07817, 2022.
  39. A. Miller, Z. Zimborás, S. Knecht, S. Maniscalco, and G. García-Pérez, “Bonsai algorithm: Grow your own fermion-to-qubit mappings,” PRX Quantum, vol. 4, p. 030314, 2023.
  40. T. Parella-Dilmé, K. Kottmann, L. Zambrano, L. Mortimer, J. S. Kottmann, and A. Acín, “Reducing entanglement with physically-inspired fermion-to-qubit mappings,” arXiv preprint arXiv:2311.07409, 2023.
  41. P. Jordan and E. Wigner, “Über das Paulische Äquivalenzverbot,” Zeitschrift für Physik, vol. 47, no. 9, pp. 631–651, 1928.
  42. S. B. Bravyi and A. Y. Kitaev, “Fermionic quantum computation,” Annals of Physics, vol. 298, no. 1, pp. 210–226, 2002.
  43. S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, “Tapering off qubits to simulate fermionic Hamiltonians,” arXiv preprint arXiv:1701.08213, 2017.
  44. M. Chiew and S. Strelchuk, “Optimal fermion-qubit mappings,” arXiv preprint arXiv:2110.12792, 2021.
  45. K. Setia and J. D. Whitfield, “Bravyi-Kitaev superfast simulation of electronic structure on a quantum computer,” The Journal of chemical physics, vol. 148, no. 16, p. 164104, 2018.
  46. M. Steudtner and S. Wehner, “Fermion-to-qubit mappings with varying resource requirements for quantum simulation,” New Journal of Physics, vol. 20, no. 6, p. 063010, 2018.
  47. V. Havlíček, M. Troyer, and J. D. Whitfield, “Operator locality in the quantum simulation of fermionic models,” Physical Review A, vol. 95, no. 3, p. 032332, 2017.
  48. R. W. Chien and J. D. Whitfield, “Custom fermionic codes for quantum simulation,” arXiv preprint arXiv:2009.11860, 2020.
  49. M. Steudtner and S. Wehner, “Quantum codes for quantum simulation of fermions on a square lattice of qubits,” Physical Review A, vol. 99, no. 2, p. 022308, 2019.
  50. Z. Jiang, A. Kalev, W. Mruczkiewicz, and H. Neven, “Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning,” Quantum, vol. 4, p. 276, 2020.
  51. A. Vlasov, “Clifford algebras, spin groups and qubit trees,” Quanta, vol. 11, no. 1, pp. 97–114, 2022.
  52. Q. Wang, Z.-P. Cian, M. Li, I. L. Markov, and Y. Nam, “Ever more optimized simulations of fermionic systems on a quantum computer,” arXiv preprint arXiv:2303.03460, 2023.
  53. R. W. Chien and J. Klassen, “Optimizing fermionic encodings for both Hamiltonian and hardware,” arXiv preprint arXiv:2210.05652, 2022.
  54. S. D. Sarma, M. Freedman, and C. Nayak, “Majorana zero modes and topological quantum computation,” npj Quantum Information, vol. 1, no. 1, p. 15001, 2015.
  55. “Why Majoranas are cool: braiding and quantum computation,” 2023. https://topocondmat.org/w2_majorana/braiding.html.
  56. M. Fellner, K. Ender, R. ter Hoeven, and W. Lechner, “Parity quantum optimization: Benchmarks,” Quantum, vol. 7, p. 952, 2023.
  57. K. Setia, S. Bravyi, A. Mezzacapo, and J. D. Whitfield, “Superfast encodings for fermionic quantum simulation,” Physical Review Research, vol. 1, no. 3, p. 033033, 2019. Publisher: American Physical Society.
  58. W. Kirby, B. Fuller, C. Hadfield, and A. Mezzacapo, “Second-quantized fermionic operators with polylogarithmic qubit and gate complexity,” PRX Quantum, vol. 3, no. 2, p. 020351, 2022. Publisher: American Physical Society.
  59. M. Nooijen, “Can the eigenstates of a many-body hamiltonian be represented exactly using a general two-body cluster expansion?,” Phys. Rev. Lett., vol. 84, pp. 2108–2111, 2000.
  60. J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, “Simulation of electronic structure Hamiltonians using quantum computers,” Molecular Physics, vol. 109, no. 5, pp. 735–750, 2011.
  61. G. Aleksandrowicz et al., “Qiskit: An Open-source Framework for Quantum Computing,” Jan. 2019. Language: en.
  62. S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, “t—ket⟩: a retargetable compiler for nisq devices,” Quantum Science and Technology, vol. 6, no. 1, p. 014003, 2020.
  63. V. Vandaele, S. Martiel, and T. G. de Brugière, “Phase polynomials synthesis algorithms for NISQ architectures and beyond,” Quantum Science and Technology, vol. 7, p. 045027, 2022.
  64. Boston, MA: Springer US, 1972.
  65. Y. S. Yordanov, D. R. Arvidsson-Shukur, and C. H. Barnes, “Efficient quantum circuits for quantum computational chemistry,” Physical Review A, vol. 102, p. 062612, 2020.
  66. A. Cowtan, W. Simmons, and R. Duncan, “A generic compilation strategy for the Unitary Coupled Cluster ansatz,” arXiv preprint arXiv:2007.10515, 2020.
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