Quantum computation of conical intersections on a programmable superconducting quantum processor (2402.12708v2)
Abstract: Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multi-configurational methods, face computational hurdles in solving the electronic Schr\"odinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems - ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.
- Conical intersections: electronic structure, dynamics & spectroscopy, vol. 15 (World Scientific, 2004).
- Beyond born-oppenheimer: Molecular dynamics through a conical intersection. Annu. Rev. Phys. Chem. 55, 127–158 (2004). PMID: 15117250.
- Isomerization through conical intersections. Annu. Rev. Phys. Chem. 58, 613–634 (2007). PMID: 17291184.
- Matsika, S. Conical Intersections in Molecular Systems, chap. 2, 83–124 (John Wiley & Sons, Ltd, 2007).
- Nonadiabatic events and conical intersections. Annu. Rev. Phys. Chem. 62, 621–643 (2011). PMID: 21219147.
- Levine, B. G. et al. Conical intersections at the nanoscale: Molecular ideas for materials. Annu. Rev. Phys. Chem. 70, 21–43 (2019). PMID: 30633637.
- Shen, L. et al. Role of multistate intersections in photochemistry. J. Phys. Chem. Lett. 11, 8490–8501 (2020).
- Matsika, S. Electronic structure methods for the description of nonadiabatic effects and conical intersections. Chem. Rev. 121, 9407–9449 (2021).
- Yarkony, D. R. Diabolical conical intersections. Rev. Mod. Phys. 68, 985–1013 (1996).
- De Sio, A. et al. Intermolecular conical intersections in molecular aggregates. Nat. Nanotechnol. 16, 63–68 (2021).
- Lischka, H. et al. Multireference approaches for excited states of molecules. Chem. Rev. 118, 7293–7361 (2018).
- Ab initio quantum chemistry using the density matrix renormalization group. J. Chem. Phys. 110, 4127–4130 (1999).
- The density matrix renormalization group in quantum chemistry. Annu. Rev. Phys. Chem. 62, 465–481 (2011).
- Fermion monte carlo without fixed nodes: A game of life, death, and annihilation in slater determinant space. J. Chem. Phys. 131 (2009).
- Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005).
- Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010).
- Simulating chemistry using quantum computers. Annu. Rev. Phys. Chem. 62, 185–207 (2011).
- Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017).
- Cao, Y. et al. Quantum chemistry in the age of quantum computing. Chem. Rev. 119, 10856–10915 (2019).
- Quantum computational chemistry. Rev. Mod. Phys. 92 (2020).
- Quantum algorithms for quantum chemistry and quantum materials science. Chem. Rev. 120, 12685–12717 (2020).
- Emerging quantum computing algorithms for quantum chemistry. Wiley Interdiscip. Rev. Comput. Mol. Sci. e1580 (2021).
- Whitlow, J. et al. Quantum simulation of conical intersections using trapped ions. Nat. Chem. 15, 1509–1514 (2023).
- Valahu, C. H. et al. Direct observation of geometric-phase interference in dynamics around a conical intersection. Nat. Chem. 15, 1503–1508 (2023).
- O’Malley, P. J. J. et al. Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016).
- Motta, M. et al. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nat. Phys. 16, 205–210 (2020).
- Hybrid quantum-classical algorithms and quantum error mitigation. J. Phys. Soc. Japan 90, 032001 (2021).
- Tilly, J. et al. The variational quantum eigensolver: A review of methods and best practices. Phys. Rep. 986, 1–128 (2022).
- Preskill, J. Quantum computing in the nisq era and beyond. Quantum 2, 79 (2018).
- Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5 (2014).
- Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys. Rev. A 95 (2017).
- Hempel, C. et al. Quantum chemistry calculations on a trapped-ion quantum simulator. Phys. Rev. X 8 (2018).
- An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nat. Commun. 10 (2019).
- Variational quantum algorithms for discovering hamiltonian spectra. Phys. Rev. A 99 (2019).
- Arute, F. et al. Hartree-fock on a superconducting qubit quantum computer. Science 369, 1084–1089 (2020).
- Cerezo, M. et al. Variational quantum algorithms. Nature Reviews Physics 3, 625–644 (2021).
- Tang, H. L. et al. Qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansätze on a quantum processor. PRX Quantum 2 (2021).
- Takeshita, T. et al. Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources. Phys. Rev. X 10, 011004 (2020).
- Tilly, J. et al. Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computers. Phys. Rev. Res. 3, 033230 (2021).
- Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys. Rev. A 95, 042308 (2017).
- Colless, J. I. et al. Computation of molecular spectra on a quantum processor with an error-resilient algorithm. Phys. Rev. X 8, 011021 (2018).
- Variational quantum computation of excited states. Quantum 3, 156 (2019).
- Subspace-search variational quantum eigensolver for excited states. Phys. Rev. Res. 1, 033062 (2019).
- Quantum computation of electronic transitions using a variational quantum eigensolver. Phys. Rev. Lett. 122, 230401 (2019).
- Variational quantum packaged deflation for arbitrary excited states. Quantum Engineering 3 (2021).
- Ollitrault, P. J. et al. Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor. Phys. Rev. Res. 2, 043140 (2020).
- Quantum simulation of conical intersections. arXiv preprint arXiv:2401.15565 (2024).
- Quantum computation of molecular response properties. Phys. Rev. Res. 2, 033324 (2020).
- Variational quantum eigensolver for dynamic correlation functions. Phys. Rev. A 104, 032405 (2021).
- Huang, K. et al. Variational quantum computation of molecular linear response properties on a superconducting quantum processor. J. Phys. Chem. Lett. 13, 9114–9121 (2022).
- Sokolov, I. O. et al. Microcanonical and finite-temperature ab initio molecular dynamics simulations on quantum computers. Phys. Rev. Res. 3 (2021).
- Ab initio molecular dynamics on quantum computers. J. Chem. Phys. 154, 164103 (2021).
- Sokolov, I. O. et al. Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents? J. Chem. Phys. 152 (2020).
- Mizukami, W. et al. Orbital optimized unitary coupled cluster theory for quantum computer. Phys. Rev. Res. 2, 033421 (2020).
- Improving the accuracy of variational quantum eigensolvers with fewer qubits using orbital optimization. J. Chem. Theory Comput. 19, 790–798 (2023).
- Complete active space methods for nisq devices: The importance of canonical orbital optimization for accuracy and noise resilience. J. Chem. Theory Comput. 19, 2863–2872 (2023).
- Yalouz, S. et al. A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states. Quantum Sci. Technol. 6, 024004 (2021).
- Fitzpatrick, A. et al. A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive. arXiv preprint arXiv:2212.11405 (2022).
- Omiya, K. et al. Analytical energy gradient for state-averaged orbital-optimized variational quantum eigensolvers and its application to a photochemical reaction. J. Chem. Theory Comput. 18, 741–748 (2022).
- Yalouz, S. et al. Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver. J. Chem. Theory Comput. 18, 776–794 (2022).
- Molecular electronic-structure theory (John Wiley & Sons, 2014).
- About the pauli exclusion principle. Z. Phys. 47, 631 (1928).
- The bravyi-kitaev transformation for quantum computation of electronic structure. J. Chem. Phys. 137, 224109 (2012).
- A general second order complete active space self-consistent-field solver for large-scale systems. Chem. Phys. Lett. 683, 291–299 (2017). Ahmed Zewail (1946-2016) Commemoration Issue of Chemical Physics Letters.
- Sun, Q. et al. Pyscf: the python-based simulations of chemistry framework. Wiley Interdiscip. Rev. Comput. Mol. Sci. 8, e1340 (2018).
- Yan, F. et al. Tunable coupling scheme for implementing high-fidelity two-qubit gates. Phys. Rev. Appl. 10, 054062 (2018).
- Li, X.-G. et al. Mapping a topology-disorder phase diagram with a quantum simulator (2023). eprint 2301.12138.
- Conical intersections and double excitations in time-dependent density functional theory. Mol. Phys. 104, 1039–1051 (2006).
- Tapering off qubits to simulate fermionic hamiltonians. arXiv preprint arXiv:1701.08213 (2017).
- Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. i. the atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023 (1989).
- Powell, M. J. D. A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation, 51–67 (Springer Netherlands, Dordrecht, 1994). URL https://doi.org/10.1007/978-94-015-8330-5_4.
- Measurement optimization in the variational quantum eigensolver using a minimum clique cover. J. Chem. Phys. 152, 124114 (2020).
- McEwen, M. et al. Removing leakage-induced correlated errors in superconducting quantum error correction. Nat. Commun. 12, 1761 (2021).
- scikit-optimize/scikit-optimize (v0.9.0) (2021).
- Wang, R. et al. Leveraging junk information to enhance the quantum error mitigation (2024). eprint arXiv2402.10480.
- Challenges in the use of quantum computing hardware-efficient ansätze in electronic structure theory. J. Phys. Chem. A (2023).
- Physics-constrained hardware-efficient ansatz on quantum computers that is universal, systematically improvable, and size-consistent. arXiv preprint arXiv:2307.03563 (2023).
- Low-cost error mitigation by symmetry verification. Phys. Rev. A 98, 062339 (2018).
- Sagastizabal, R. et al. Experimental error mitigation via symmetry verification in a variational quantum eigensolver. Phys. Rev. A 100, 010302 (2019).
- McClean, J. R. et al. Openfermion: the electronic structure package for quantum computers. Quantum Sci. Technol. 5, 034014 (2020).
- MindQuantum Developer. Mindquantum, version 0.6.0 (2021). URL https://gitee.com/mindspore/mindquantum.
- Exploring network structure, dynamics, and function using networkx. Tech. Rep., Los Alamos National Lab.(LANL), Los Alamos, NM (United States) (2008).
- Zhao, S. K. et al. Probing operator spreading via floquet engineering in a superconducting circuit. Phys. Rev. Lett. 129, 160602 (2022).
- Bao, F. et al. Fluxonium: An alternative qubit platform for high-fidelity operations. Phys. Rev. Lett. 129, 010502 (2022).
- Rol, M. A. et al. Time-domain characterization and correction of on-chip distortion of control pulses in a quantum processor. Appl. Phys. Lett. (2019).
- Sung, Y. et al. Realization of high-fidelity cz and zz𝑧𝑧zzitalic_z italic_z-free iswap gates with a tunable coupler. Phys. Rev. X 11, 021058 (2021).
- Foxen, B. et al. Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms. Phys. Rev. Lett. 125, 120504 (2020).
- Ren, W. et al. Experimental quantum adversarial learning with programmable superconducting qubits. Nature Computational Science 2, 711–717 (2022).