Comparing Classical and Quantum Ground State Preparation Heuristics
Abstract: One promising field of quantum computation is the simulation of quantum systems, and specifically, the task of ground state energy estimation (GSEE). Ground state preparation (GSP) is a crucial component in GSEE algorithms, and classical methods like Hartree-Fock state preparation are commonly used. However, the efficiency of such classical methods diminishes exponentially with increasing system size in certain cases. In this study, we investigated whether in those cases quantum heuristic GSP methods could improve the overlap values compared to Hartree-Fock. Moreover, we carefully studied the performance gain for GSEE algorithms by exploring the trade-off between the overlap improvement and the associated resource cost in terms of T-gates of the GSP algorithm. Our findings indicate that quantum heuristic GSP can accelerate GSEE tasks, already for computationally affordable strongly-correlated systems of intermediate size. These results suggest that quantum heuristic GSP has the potential to significantly reduce the runtime requirements of GSEE algorithms, thereby enhancing their suitability for implementation on quantum hardware.
- L. Lin and Y. Tong, Heisenberg-limited ground-state energy estimation for early fault-tolerant quantum computers, PRX Quantum 3, 010318 (2022a).
- P. Echenique and J. L. Alonso, A mathematical and computational review of hartree–fock scf methods in quantum chemistry, Molecular Physics 105, 3057 (2007).
- C. D. Sherrill and H. F. Schaefer III, The configuration interaction method: Advances in highly correlated approaches, in Advances in quantum chemistry, Vol. 34 (Elsevier, 1999) pp. 143–269.
- R. Zhang, G. Wang, and P. Johnson, Computing ground state properties with early fault-tolerant quantum computers, Quantum 6, 761 (2022).
- Z. Ding and L. Lin, Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation, arXiv:2211.11973:absent2211.11973:2211.11973: 2211.11973 (2022).
- Y. Dong, L. Lin, and Y. Tong, Ground-state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices, PRX Quantum 3, 040305 (2022).
- K. Gratsea, C. Sun, and P. D. Johnson, When to reject a ground state preparation algorithm (2022), arXiv:2212.09492 [quant-ph] .
- J. S. Kottmann and A. Aspuru-Guzik, Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation, Physical Review A 105 (2022).
- G. Wang, S. Sim, and P. D. Johnson, State preparation boosters for early fault-tolerant quantum computation, Quantum 6, 829 (2022).
- L. Lin and Y. Tong, Near-optimal ground state preparation, Quantum 4, 372 (2020a).
- N. H. Stair and F. A. Evangelista, Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation, The Journal of Chemical Physics 153, 10.1063/5.0014928 (2020), 104108.
- J. S. Kottmann, Molecular quantum circuit design: A graph-based approach (2022), arXiv:2207.12421 [quant-ph] .
- Y. Saad, Numerical methods for large eigenvalue problems: revised edition (SIAM, 2011).
- N. J. Ross and P. Selinger, Optimal ancilla-free clifford+t approximation of z-rotations (2016), arXiv:1403.2975 [quant-ph] .
- C. Jones, Low-overhead constructions for the fault-tolerant toffoli gate, Phys. Rev. A 87, 022328 (2013).
- L. Lin and Y. Tong, Near-optimal ground state preparation, Quantum 4, 372 (2020b).
- E. Knill, G. Ortiz, and R. D. Somma, Optimal quantum measurements of expectation values of observables, Phys. Rev. A 75, 012328 (2007).
- L. Lin and Y. Tong, Heisenberg-limited ground-state energy estimation for early fault-tolerant quantum computers, PRX Quantum 3, 010318 (2022b).
- W. Kohn, Nobel lecture: Electronic structure of matter—wave functions and density functionals, Rev. Mod. Phys. 71, 1253 (1999).
- A. J. Cohen, P. Mori-Sánchez, and W. Yang, Challenges for density functional theory, Chemical Reviews 112, 289 (2012), pMID: 22191548, https://doi.org/10.1021/cr200107z .
- Orquestra workflow sdk.
- Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023).
- J. S. Kottmann, F. A. Bischoff, and E. F. Valeev, Direct determination of optimal pair-natural orbitals in a real-space representation: The second-order Moller–Plesset energy, The Journal of Chemical Physics 152, 074105 (2020), https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.5141880/15569782/074105_1_online.pdf .
- F. A. Bischoff, Regularizing the molecular potential in electronic structure calculations. I. SCF methods, The Journal of Chemical Physics 141, 184105 (2014), https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.4901021/15487939/184105_1_online.pdf .
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.