Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
Pauline J. Ollitrault, Abhinav Kandala, Chun-Fu Chen, Panagiotis Kl. Barkoutsos, Antonio Mezzacapo, Marco Pistoia, Sarah Sheldon, Stefan Woerner, Jay M. Gambetta, Ivano Tavernelli
The computation of molecular excitation energies is essential for predicting photo-induced reactions of chemical and technological interest.While the classical computing resources needed for this task scale poorly, quantum algorithms emerge as promising alternatives.In particular, the extension of the variational quantum eigensolver algorithm to the computation of the excitation energies is an attractive option.However, there is currently a lack of such algorithms for correlated molecular systems that is amenable to near-term, noisy hardware.In this work, we propose an extension of the well-established classical equation of motion approach to a quantum algorithm for the calculation of molecular excitation energies on noisy quantum computers.In particular, we demonstrate the efficiency of this approach in the calculation of the excitation energies of the LiH molecule on an IBM Quantum computer.
The computation of molecular excitation energies is essential for predicting photo-induced reactions of chemical and technological interest.While the classical computing resources needed for this task scale poorly, quantum algorithms emerge as promising alternatives.In particular, the extension of the variational quantum eigensolver algorithm to the computation of the excitation energies is an attractive option.However, there is currently a lack of such algorithms for correlated molecular systems that is amenable to near-term, noisy hardware.In this work, we propose an extension of the well-established classical equation of motion approach to a quantum algorithm for the calculation of molecular excitation energies on noisy quantum computers.In particular, we demonstrate the efficiency of this approach in the calculation of the excitation energies of the LiH molecule on an IBM Quantum computer.
The computation of molecular excitation energies is essential for predicting photo-induced reactions of chemical and technological interest. While the classical computing resources needed for this task scale poorly, quantum algorithms emerge as promising alternatives. In particular, the extension of the variational quantum eigensolver algorithm to the computation of the excitation energies is an attractive option. However, there is currently a lack of such algorithms for correlated molecular systems that is amenable to near-term, noisy hardware. In this work, we propose an extension of the well-established classical equation of motion approach to a quantum algorithm for the calculation of molecular excitation energies on noisy quantum computers. In particular, we demonstrate the efficiency of this approach in the calculation of the excitation energies of the LiH molecule on an IBM Quantum computer.
Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate-scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ans\"atze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. We introduce the excited qubit-excitation-based adaptive (e-QEB-ADAPT)-VQE protocol to calculate molecular-excited-state energies. The e-QEB-ADAPT-VQE constructs efficient problem-tailored ans\"atze by iteratively appending evolutions of qubit excitation operators. The e-QEB-ADAPT-VQE also improves on previous ADAPT-VQE protocol in that it is designed to be independent on the choice of initial reference state. We perform classical numerical simulations for LiH and BeH2 to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ans\"atze that require at least an order of magnitude fewer cnot gates than standard fixed unitary coupled-cluster ans\"atze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ans\"atze for excited molecular states than other ADAPT-VQE protocols.
Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ansatze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. In this paper, we introduce the ``excited iterative qubit-excitation-based variational quantum eigensolver'' (e-IQEB-VQE) protocol to calculate molecular excited state energies. The e-IQEB-VQE constructs efficient problem-tailored ansatze by iteratively appending evolutions of qubit excitation operators. The e-IQEB-VQE is an adaptation of the IQEB-VQE protocol, designed to be less dependent on the choice of an initial reference state. We perform classical numerical simulations for LiH and BeH2 to benchmark the performance of the IQEB-VQE. We demonstrate that the e-IQEB-VQE can construct highly accurate ansatze that require at least an order of magnitude fewer CNOTs than standard fixed UCC ansatze, such as the UCCSD and the GUCCSD.
High Resolution Image Download MS PowerPoint Slide The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same or quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H 2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.
The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.
Knowing the ground state energies of molecules and atoms gives scientists critical insight into these particles' behavior in reactions, thermodynamic and molecular properties, and excitation energies.However, due to the quantum mechanical nature of particles, finding the ground state of a system is intractable, both mathematically and experimentally.Computational methods are utilized to estimate the ground state energies.As we approach the limits of classical computers, quantum computers are viewed as promising alternatives that present a bright future for computational chemistry.In this paper, I review classical and quantum algorithms/methods for computational chemistry.Then, I discuss the current topics in using quantum computers for computational chemistry by analyzing the performance of the Variational Quantum Eigensolver (VQE) in different contexts on IBM's noisy quantum computer simulator, "QasmSimulator," and one of IBM's quantum computers, ibmq_belem.This review presents a theoretical and practical view of quantum computational chemistry.It allows the reader to learn the theory behind the algorithms and implement them with the guidance of the presented code and its detailed explanations.The purpose of this paper is to leave the reader with the necessary theory and adequate programming reference to implement the algorithms in various contexts.