Computing static molecular properties using variational quantum eigensolver

Matheus da Silva Fonseca, Caio Moraes Porto, Nicolás A. C. Carpio +4 more

Arthur G. Rattew, Shaohan Hu, Marco Pistoia +2 more

Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6\times$ shallower and use up to $12\times$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6\times$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.

Beekhuis, Gijs

Arthur G. Rattew, Shaohan Hu, Marco Pistoia +2 more

Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6\times$ shallower and use up to $12\times$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6\times$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.

S. Surya Prakash, P. Banu Priya, Sudarshan Someneni +2 more

Amanda Marques de Lima, Erico S. Teixeira, Eivson Darlivam Rodrigues de Aguiar Silva +1 more

ABSTRACT The variational quantum eigensolver (VQE) is a relevant method for simulating molecular systems on near‐term quantum computers. While its primary application is the estimation of ground‐state energies, VQE also produces the one‐particle reduced density matrix (1‐RDM), from which other relevant molecular properties can be obtained. The accuracy of these properties depends on the reliability and convergence of the 1‐RDM, which is not guaranteed by energy‐only optimization. Thus, two new algorithms were introduced: VQE* that incorporates the RMSD of consecutive 1‐RDM as a convergence criterion and VQE‐LD that modifies the cost function by adding to the energy a term involving the RMSD of 1‐RDM weighted by a proper factor. These algorithms were tested for protonated methane, CH, at equilibrium and four dissociation geometries, with the k‐UpCCGSD (4,4)‐ and GateFabric (2,2)‐active space ansätze . For k‐UpCCGSD, whose energies are already close to CASCI(4,4), improvements were mainly observed in density‐dependent properties such as electron density, dipole moments, and Mulliken charges. For GateFabric, which initially displayed larger energy deviations, both approaches significantly improved the energy accuracy and the quality of the 1‐RDM. Overall, our findings show that the convergence of the energy and of the 1‐RDM provides a simple yet effective strategy to improve the accuracy of energies and molecular properties in variational quantum algorithms.