Computing molecular excited states on a D-Wave quantum annealer (original) (raw)
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Quantum annealers are an alternative approach to quantum computing which make use of the adiabatic theorem to efficiently find the ground state of a physically realizable Hamiltonian. Such devices are currently commercially available and have been successfully applied to several combinatorial and discrete optimization problems. However, the application of quantum annealers to problems in chemistry remains a relatively sparse area of research due to the difficulty in mapping molecular systems to the Ising model Hamiltonian. In this paper we review two different methods for finding the ground state of molecular Hamiltonians using Ising model-based quantum annealers. In addition, we compare the relative effectiveness of each method by calculating the binding energies, bond lengths, and bond angles of the H + 3 and H 2 O molecules and mapping their potential energy curves. We also assess the resource requirements of each method by determining the number of qubits and computation time required to simulate each molecule using various parameter values. While each of these methods is capable of accurately predicting the ground state properties of small molecules, we find that they are still outperformed by modern classical algorithms and that the scaling of the resource requirements remains a challenge.
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Scientific Reports, 2022
In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.
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Quantum annealing devices have been subject to various analyses in order to classify their usefulness for practical applications. While it has been successfully proven that such systems can in general be used for solving combinatorial optimization problems, they have not been used to solve chemistry applications. In this paper we apply a mapping, put forward by Xia et al. [25], from a quantum chemistry Hamiltonian to an Ising spin glass formulation and find the ground state energy with a quantum annealer. Additionally we investigate the scaling in terms of needed physical qubits on a quantum annealer with limited connectivity. To the best of our knowledge, this is the first experimental study of quantum chemistry problems on quantum annealing devices. We find that current quantum annealing technologies result in an exponential scaling for such inherently quantum problems and that new couplers are necessary to make quantum annealers attractive for quantum chemistry.
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A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the original problem. Thus, low-lying excited-state energies can be calculated using existing hybrid-quantum classical techniques and variational algorithm(s) for determining ground-state. The method is shown to be fully valid for the H2 molecule. In addition, conditions for the method's success are discussed in terms of classes of Hamiltonians.
Electronic Structure Calculations using Quantum Computing
arXiv (Cornell University), 2023
The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue, we present a hybrid Classical-Quantum computational procedure that uses the Variational Quantum Eigensolver (VQE) algorithm. By mapping the quantum system to a set of qubits and utilising a quantum circuit to prepare the ground state wavefunction, our algorithm offers a streamlined process requiring fewer computational resources than classical methods. Our algorithm demonstrated similar accuracy in rigorous comparisons with conventional electronic structure methods, such as Density Functional Theory and Hartree-Fock Theory, on a range of molecules while utilising significantly fewer resources. These results indicate the potential of the algorithm to expedite the development of new materials and technologies. This work paves the way for overcoming the computational challenges of electronic structure calculations. It demonstrates the transformative impact of quantum computing on advancing our understanding of complex quantum systems.
Molecular dynamics in electronically excited states using time-dependent density functional theory
Molecular Physics, 2005
We describe two different implementations of time-dependent density functional theory (TDDFT) for use in excited state molecular dynamics simulations. One is based on the linear response formulation (LR-TDDFT), whereas the other uses a time propagation scheme for the electronic wave functions (P-TDDFT). Photo-induced cis-trans isomerization of C¼C, C¼N and N¼N double bonds is investigated in three model compounds, namely the 2,4-pentadiene-1-iminium cation (PSB), formaldimine and diimide. For formaldimine and diimide, the results obtained with both schemes are in agreement with experimental data and previously reported theoretical results. Molecular dynamics simulations yield new insights into the relaxation pathways in the excited state. For PSB, which is a model system for the retinal protonated Schiff base involved in the visual process, the forces computed from the LR-TDDFT S 1 surface lead to an increased bond length alternation and, consequently, to single bond rotation. On the contrary, P-TDDFT dynamics lead to a decreased bond length alternation, in agreement with CASPT2 and restricted open-shell Kohn-Sham (ROKS) calculations.
Chemical Physics Letters, 2007
Time-dependent density functional theory (TDDFT) is combined with the correlation-corrected vibrational self-consistent field method to calculate the fundamental vibrational frequencies of the electronic excited states of diatomic, triatomic, and tetraatomic molecules. Equation of motion coupled-cluster calculations are also carried out for comparison. TDDFT is shown to provide the harmonic and anharmonic frequencies for various excited states with reasonable accuracy by using hybrid functionals, except that several vibrational modes such as hydrogen atom stretching exhibit sizable discrepancies due to the lack of orbital relaxation process in TDDFT.
Journal of Chemical Theory and Computation, 2011
Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response TammÀDancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/ 6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).
Time-dependent density functional theory employing optimized effective potentials
The Journal of Chemical Physics, 2002
Exchange-only ab initio ͑parameter-free͒ time-dependent density functional calculations for the vertical excitation energies of atoms and polyatomic molecules are performed by employing optimized effective potentials ͑OEP's͒ and their corresponding adiabatic exchange kernels for the first time. Accurate OEP's are obtained by a novel linear-combination-of-atomic-orbital ͑LCAO͒ algorithm ͓R. Colle and R. K. Nesbet, J. Phys. B 34, 2475 ͑2001͔͒ in which a potential is represented as a sum of a seed potential having the correct Ϫ1/r asymptotic behavior and a small and rapidly decaying correction, the latter being approximated accurately by a linear combination of Gaussian functions. The time-dependent OEP ͑TDOEP͒ methods with and without the Tamm-Dancoff approximation are implemented by using a trial-vector algorithm, which allows us to avoid the storage or manipulation of transformed two-electron integrals or the diagonalization of large matrices. No approximation is made to TDOEP, besides the adiabatic approximation to the exchange kernel, the LCAO expansion of the orbitals and potentials, and occasionally the Tamm-Dancoff approximation. The vertical excitation energies of the beryllium atom and the nitrogen and water molecules calculated by TDOEP are compared with those obtained from time-dependent density functional theory ͑TDDFT͒ employing conventional local or gradient-corrected functionals, configuration interaction singles ͑CIS͒, time-dependent Hartree-Fock ͑TDHF͒ theory, similarity-transformed equation-of-motion coupled-cluster with single and double substitutions, and experiments. TDOEP, which neglects electron correlation while treating the exchange contribution rigorously within the Kohn-Sham DFT framework, performs equally well as, or even appreciably better than, CIS or TDHF. The slightly better performance of TDOEP might be attributed to the local nature of the exchange potentials that allows the bare orbital energy differences to approximate excitation energies well. Nevertheless, TDDFT employing local or gradient-corrected functionals outperforms TDOEP for low-lying valence excited states, implying that the former somehow accounts for electron correlation effectively, whereas for high-lying and Rydberg excited states, the latter performs better than the former. By combining the desirable features of OEP and local or gradient-corrected exchange-correlation potentials, we arrive at a simple asymptotic correction scheme to the latter. TDDFT with the asymptotic correction yields uniformly accurate excitation energies for both valence and Rydberg excited states.