Implementation of Quantum Machine Learning for Electronic Structure Calculations of Periodic Systems on Quantum Computing Devices

Abstract

Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve quantum many-body systems and have demonstrated accurate electronic structure calculations of lattice models, molecular systems, and recently periodic systems. A hybrid approach using restricted Boltzmann machines and a quantum algorithm to obtain the probability distribution that can be optimized classically is a promising method due to its efficiency and ease of implementation. Here, we implement the benchmark test of the hybrid quantum machine learning on the IBM-Q quantum computer to calculate the electronic structure of typical two-dimensional crystal structures: hexagonal-boron nitride and graphene. The band structures of these systems calculated using the hybrid quantum machine learning approach are in good agreement with those obtained by the conventional electronic structure calculations. This benchmark result implies that the hybrid quantum machine learning method, empowered by quantum computers, could provide a new way of calculating the electronic structures of quantum many-body systems.

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

“…Periodic systems in general have received scanty attention as far as quantum algorithms are concerned. Only two reports exists 43,45 both of which have simulated just the valence band in graphene and hexagonal Boron Nitride (h-BN). Further extension of this algorithm can be made to compute operators using Hellmann-Feynmann method, 87 to characterize the influence of noise on the algorithm and to see it being extended to study other interesting phenomenon on 2D materials like spin-orbit interaction due to inversion symmetry breaking 49,88 and Rashba splitting in polar TMDCs 89 or even effect of strain.…”

“…To reduce the effect of noise on the sampling probabilities we employ the same noise mitigation procedure as has been used by the authors recently. 45,71 For the 'RBM-qasm' and 'RBM-cl' simulations, the maximum number of iterations within which well-converged results to be discussed below were obtained is ≤ 30,000 either with a warm-start or randomly initialized parameter set depending on the case. The 'RBM-IBMQ' simulations were performed in batches with maximum iteration ≤ 700 for each run to reduce job queue.…”

“…44 Furthermore unlike most reports on quantum machine learning and quantum computing in general which have studied molecular systems only, we extend the algorithm on important periodic systems quantum simulation of which have just begun to gain attention. 43,45 Of particular importance in this category are 2D materials like monolayer transition metal di-chalcogenides (TMDCs) which are hitherto unexplored on a quantum computer. These materials have been shown to possess tunable band-gap for many novel applications.…”

Quantum Computation of Reactions on Surfaces Using Local Embedding

“…30 Apart from approaches that rely on ab initio calculations, other quantum machine learning techniques were applied to the determination of properties of a periodic system. 31,32 In most of the studies listed above, there is a common thread of selecting a small subsystem from the full system since modeling the latter is prohibitive. The sub-system can then be treated more accurately with quantum algorithms.…”

Simulating the electronic structure of spin defects on quantum computers

“…symmetry verification [56], quasi-probability methods [53,54], or stochastic error mitigation [57]. An alternative strategy to complexity reduction is the use of model Hamiltonians, e.g., Hubbard, Heisenberg [35][36][37][38][39][40][41][42][43][44] or tight-binding Hamiltonians [45][46][47].…”