Unleashed from Constrained Optimization: Quantum Computing for Quantum Chemistry Employing Generator Coordinate Inspired Method
Abstract: Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized eigenvalue problems through the Unitary Coupled Cluster (UCC) excitation generators. Inspired by the generator coordinate method, we employ these UCC excitation generators to construct non-orthogonal, overcomplete many-body bases, projecting the system Hamiltonian into an effective Hamiltonian, which bypasses issues such as barren plateaus that heuristic numerical minimizers often encountered in standard variational quantum eigensolver (VQE). Diverging from conventional quantum subspace expansion methods, we introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the UCC excitation generators. This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization to address complex, strongly correlated quantum chemical systems cost-effectively, setting the stage for more advanced quantum simulations in chemistry.
- J. Raymond and R. E. Blankenship, Coordination Chemistry Reviews 252, 377 (2008), the Role of Manganese in Photosystem II.
- I. Shavitt and R. Bartlett, Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory, Cambridge Molecular Science (Cambridge University Press, 2009).
- T. Albash and D. A. Lidar, Rev. Mod. Phys. 90, 015002 (2018).
- A. Trabesinger, Nat. Phys. 8, 263 (2012).
- R. M. Parrish and P. L. McMahon, arXiv preprint arXiv:1909.08925 (2019).
- O. Kyriienko, npj Quantum Inf. 6, 1 (2020).
- K. Seki and S. Yunoki, PRX Quantum 2, 010333 (2021).
- K. Kowalski and B. Peng, J. Chem. Phys. 153, 201102 (2020).
- D. L. Hill and J. A. Wheeler, Physical Review 89, 1102 (1953).
- J. J. Griffin and J. A. Wheeler, Phys. Rev. 108, 311 (1957).
- P. Ring and P. Schuck, The nuclear many-body problem (Springer Science & Business Media, 2004).
- J. L. Egido, Physica Scripta 91, 073003 (2016).
- H. Fukutome, Progress of Theoretical Physics 65, 809 (1981).
- K. Jankowski and J. Paldus, International Journal of Quantum Chemistry 18, 1243 (1980).
- Qiskit contributors, “Qiskit: An open-source framework for quantum computing,” (2023), qiskit version 0.45.0.
- K. Kowalski and N. P. Bauman, Phys. Rev. Lett. 131, 200601 (2023).
- M. Zheng, B. Peng, A. Li, X. Yang, and K. Kowalski, “QuGCM,” https://github.com/pnnl/QuGCM (2022).
- H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, “adapt-vqe,” https://github.com/mayhallgroup/adapt-vqe (2022).
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