VanQver: the variational and adiabatically navigated quantum eigensolver

Abstract

The accelerated progress in manufacturing noisy, intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving computationally challenging problems. The important limitations common among all NISQ computing technologies are the absence of error correction and the short coherence time, which limit the computational power of these systems. Shortening the required time of a single run of a quantum algorithm is essential for reducing environment-induced errors and for the efficiency of the computation. We have investigated the ability of a variational version of adiabatic state preparation (ASP) to generate an accurate state more efficiently compared to existing adiabatic methods. The standard ASP method uses a time-dependent Hamiltonian, connecting the initial Hamiltonian with the final Hamiltonian. In the current approach, a navigator Hamiltonian is introduced which has a non-zero amplitude only in the middle of the annealing process. Both the initial and navigator Hamiltonians are determined using variational methods. A Hermitian cluster operator, inspired by coupled-cluster theory and truncated to single and double excitations/de-excitations, is used as a navigator Hamiltonian. A comparative study of our variational algorithm (VanQver) with that of standard ASP, starting with a Hartree-Fock Hamiltonian, is presented. The results indicate that the introduction of the navigator Hamiltonian significantly improves the annealing time required to achieve chemical accuracy by two to three orders of magnitude. The efficiency of the method is demonstrated in the ground-state energy estimation of molecular systems, namely, H 2 , P4, and LiH. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft New J. Phys. 22 (2020) 053023 S Matsuura et aldifficulty faced in these experiments is in executing operations without losing relevant quantum coherence. Whereas quantum error correction will make it possible to perform an unlimited number of operations, the required resources are large, well beyond the capabilities of current hardware. Therefore, the development of methods that require less-stringent quantum coherence is essential for near-term quantum devices. A subset of the authors of the present work have previously investigated the idea of combining problem decomposition techniques in conjunction with quantum computing approaches [13]. Quantum-classical hybrid algorithms, such as the variational quantum eigensolver (VQE) [14][15][16], are suitable from this perspective. In addition to the algorithm requiring a shorter coherence time, the VQE has demonstrated robustness against systematic control errors [6,7,10].Thus far, most of the experiments that have made use of the VQE and phase estimation algorithms (PEA) [17,18] have been performed within the framework of gate model quantum computation. An alternative framework is adiabatic quantum computation (AQC) [19][20][2...

Quantum computational chemistry

“…It is difficult to know the size of the gap along the entire adiabatic path a priori, restricts our ability to perform ASP in the minimum amount of time. One possible method for reducing the annealing time required is to introduce additional 'driving' Hamiltonians, as was numerically investigated by Matsuura et al (2018). Although Eq.…”

Variational optimization of the quantum annealing schedule for the Lechner-Hauke-Zoller scheme

“…We have adapted the variational method of Refs. [27,28] to the determination of optimal annealing schedule of the constraint term in the LHZ scheme for quantum annealing in the diabatic regime. Numerical studies of small-size systems with random (spin glass) and non-random (ferromagnetic) interactions reveal that non-monotonic schedules with a single local minimum lead to significant improvements in the ground-state fidelity in almost all cases.…”

“…One of the promising approaches to diabatic annealing is a variational method recenlty proposed by Matsuura et al [27,28], in which one iteratively improves the time dependence of coefficients in the Hamiltonian to minimize the energy expectation value. This is an idea inspired by variational quantum eigensolver [29,30], a quantum-classical hybrid algorithm, to find the eigenstate of a quantum system in the noisy near-term quantum device.…”

“…Given these developments, we follow Refs. [27,28] and adapt the method to the LHZ scheme toward performance enhancement under diabatic conditions. We numerically show that variational optimization of the annealing schedule of the constraint term in the LHZ scheme leads to a significant improvement of performance measured by the residual energy and ground-state fidelity using small-scale examples of a simple ferromagnet and the spin glass problem.…”

Dominant Reaction Pathways by Quantum Computing

“…In recent years, progress has been made on designing quantum annealing algorithms for chemistry and biology applications [6][7][8][9][10][11]. Yet, only a few applications of quantum computation to classical molecular sampling problems have been reported to date [12,13].…”