Quantum chemistry calculations using energy derivatives on quantum computers

Azad, Utkarsh; Singh, Harjinder

doi:10.1016/j.chemphys.2022.111506

Cited by 9 publications

(4 citation statements)

References 28 publications

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“…Molecular properties can be accessed by estimating energy gradients with respect to a given perturbation . Analytical expressions, that are less expensive and more precise than finite difference techniques, have been derived in the context of ground-state VQE in refs − . In this section, we turn toward the question of the analytical evaluation of the individual-state nuclear energy gradient with the SA-OO-VQE algorithm (which will be noted |Ψ I ⟩, with I = 0, 1, ...).…”

Section: Theorymentioning

confidence: 99%

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

Yalouz

Koridon

Senjean

et al. 2022

J. Chem. Theory Comput.

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We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH 2 NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

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Section: Theorymentioning

confidence: 99%

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

Yalouz

Koridon

Senjean

et al. 2022

J. Chem. Theory Comput.

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“…When computing energy derivatives, there will generally be contributions due to derivatives of the state with respect to the nuclear coordinates. This can be seen for example in the expression for second-order derivatives [18]:…”

Section: Computing Accurate Energy Derivativesmentioning

confidence: 99%

“…Here, a quantum circuit is optimized in order to minimize the expectation value of a molecular Hamiltonian with respect to the output state of the circuit, yielding an approximation of the ground-state energy. Similar algorithms have been proposed to calculate other electronic properties such as excited-state energies [12][13][14][15], equilibrium geometries [16], dipole transition amplitudes [17], transition states [18], and molecular dynamics [19]. It has also been shown that computing first-and second-order energy derivatives of ground and excited state energies can be performed using variational methods [6,18,20].…”

Section: Introductionmentioning

confidence: 99%

“…Similar algorithms have been proposed to calculate other electronic properties such as excited-state energies [12][13][14][15], equilibrium geometries [16], dipole transition amplitudes [17], transition states [18], and molecular dynamics [19]. It has also been shown that computing first-and second-order energy derivatives of ground and excited state energies can be performed using variational methods [6,18,20]. Second-order energy deriva- * jack.ceroni@mail.utoronto.ca tives can be used to characterize the vibrational structure of molecules, which allows for the prediction of chemical properties such as vibronic spectra [21], simulating local mode dynamics [22,23] and electron transport [24], and computing thermodynamic observables [25].…”

Section: Introductionmentioning

confidence: 99%

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Tailgating quantum circuits for high-order energy derivatives

Ceroni¹,

Delgado²,

Jahangiri³

et al. 2022

Preprint

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To understand the chemical properties of molecules, it is often important to study derivatives of energies with respect to nuclear coordinates or external fields. Quantum algorithms for computing energy derivatives have been proposed, but only limited work has been done to address the specific challenges that arise in this context, where calculations are more complicated and involve more stringent requirements on accuracy compared to single-point energy calculations. In this work, we introduce a technique to improve the performance of variational quantum circuits calculating energy derivatives. The method, which we refer to as tailgating, is an adaptive procedure that selects gates based on their gradient with respect to the expectation value of Hamiltonian derivatives. These gates are then added at the end of a quantum circuit originally designed to calculate ground-or excited-state energies. A distinguishing feature of this approach is that the appended gates do not need to be optimized: their parameters can be set to zero and varied only for the purpose of computing energy derivatives, via calculating derivatives with respect to circuit parameters. We support the validity of this method by establishing sufficient conditions for a circuit to compute accurate energy gradients. This is achieved through a connection between energy derivatives and eigenstates of Taylor approximations of the Hamiltonian. We illustrate the advantages of the tailgating approach by performing simulations calculating the vibrational modes of beryllium hydride and water: quantities that depend on second-order energy derivatives.

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Contemporary Quantum Computing Use Cases: Taxonomy, Review and Challenges

Singh

Bhangu

2022

Arch Computat Methods Eng

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Quantum chemistry calculations using energy derivatives on quantum computers

Cited by 9 publications

References 28 publications

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

Tailgating quantum circuits for high-order energy derivatives

Contemporary Quantum Computing Use Cases: Taxonomy, Review and Challenges

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