Non-adiabatic quantum dynamics with fermionic subspace-expansion algorithms on quantum computers
Abstract: We introduce a novel computational framework for excited-states molecular quantum dynamics simulations driven by quantum computing-based electronic-structure calculations. This framework leverages the fewest-switches surface-hopping method for simulating the nuclear dynamics, and calculates the required excited-state transition properties with different flavors of the quantum subspace expansion and quantum equation-of-motion algorithms. We apply our method to simulate the collision reaction between a hydrogen atom and a hydrogen molecule. For this system, we critically compare the accuracy and efficiency of different quantum subspace expansion and equation-of-motion algorithms and show that only methods that can capture both weak and strong electron correlation effects can properly describe the non-adiabatic effects that tune the reactive event.
- A. Ralli, M. I. Williams, and P. V. Coveney, A Scalable Approach to Quantum Simulation via Projection-based Embedding, arXiv 10.48550/arXiv.2203.01135 (2022).
- K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett. 119, 10.1103/PhysRevLett.119.180509 (2017).
- H. G. A. Burton, Accurate and gate-efficient quantum ansätze for electronic states without adaptive optimisation, arXiv 10.48550/arXiv.2312.09761 (2024).
- T.-C. Yen, R. A. Lang, and A. F. Izmaylov, Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer, J. Chem. Phys. 151, 164111 (2019).
- O. Higgott, D. Wang, and S. Brierley, Variational quantum computation of excited states, Quantum 3, 156 (2019).
- Q.-X. Xie, S. Liu, and Y. Zhao, Orthogonal state reduction variational eigensolver for the excited-state calculations on quantum computers, J. Chem. Theory Comput. 18, 3737 (2022).
- R. Carobene, S. Barison, and A. Giachero, Sequence of penalties method to study excited states using VQE, Quantum Sci. Technol. 8, 035014 (2023).
- N. H. Stair, R. Huang, and F. A. Evangelista, A multireference quantum Krylov algorithm for strongly correlated electrons, J. Chem. Theory Comput. 16, 2236 (2020).
- C. L. Cortes and S. K. Gray, Quantum krylov subspace algorithms for ground- and excited-state energy estimation, Phys. Rev. A 105, 022417 (2022).
- I. Tavernelli, E. Tapavicza, and U. Rothlisberger, Nonadiabatic coupling vectors within linear response time-dependent density functional theory, J. Chem. Phys. 130, 124107 (2009).
- P. Jordan and E. P. Wigner, About the Pauli exclusion principle, Z. Phys 47, 14 (1928).
- E. Wigner, On the Quantum Correction For Thermodynamic Equilibrium, Phys. Rev. 40, 749 (1932).
- Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023).
- J. C. Tully, Molecular dynamics with electronic transitions, J. Chem. Phys. 93, 1061 (1990).
- S. Parker, Mudslide (2020).
- L. González and R. Lindh, Quantum chemistry and dynamics of excited states (John Wiley & Sons, 2020).
- M. D. Prasad, S. Pal, and D. Mukherjee, Some aspects of self-consistent propagator theories, Phys. Rev. A 31, 1287 (1985).
- D. J. Rowe, Equations-of-Motion Method and the Extended Shell Model, Rev. Mod. Phys. 40, 153 (1968).
- Z. Szekeres, A. Szabados, M. Kallay, and P. R. Surjan, On the “killer condition” in the equation-of-motion method: ionization potentials from multi-reference wave functions, Phys. Chem. Chem. Phys. 3, 696 (2001).
- Y. Kim and A. I. Krylov, Two algorithms for excited-state quantum solvers: Theory and application to EOM-UCCSD, J. Phys. Chem. A 127, 6552 (2023).
- S. P. Webb, T. Iordanov, and S. Hammes-Schiffer, Multiconfigurational Nuclear-Electronic Orbital Approach: Incorporation of Nuclear Quantum Effects in Electronic Structure Calculations, J. Chem. Phys. 117, 4106 (2002).
- C. M. Marian, Spin-orbit coupling and intersystem crossing in molecules, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2, 187 (2012).
- F. Mertins and J. Schirmer, Algebraic propagator approaches and intermediate-state representations. I. The biorthogonal and unitary coupled-cluster methods, Phys. Rev. A 53, 2140 (1996).
- S. Hirata and M. Head-Gordon, Time-dependent density functional theory within the Tamm–Dancoff approximation, Chem. Phys. Lett. 314, 291 (1999).
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