Equation-of-Motion Theory to Calculate Accurate Band Structures with a Quantum Computer

Abstract

Band structure is a cornerstone to understand the electronic properties of materials. Accurate band structure calculations using a high-level quantum chemistry theory can be computationally very expensive. It is promising to speed up such calculations with a quantum computer. In this study, we present a quantum algorithm for band structure calculations based on the equation-of-motion (EOM) theory. First, we introduce a new variational quantum eigensolver algorithm named ADAPT-C for ground-state quantum simulation of solids, where the wave function is built adaptively from a complete set of anti-Hermitian operators. Then, on top of the ADAPT-C ground state, quasiparticle energies and the band structure can be calculated using the EOM theory in a quantum-subspaceexpansion style, where the projected excitation operators guarantee that the killer condition is satisfied. As a proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band structures of silicon and diamond using a quantum computer simulator.

Ground and excited states from model-space quantum imaginary time evolution for strongly correlated systems

“…In passing, that FS-QLanczos is able to capture two excited states can be attributed to the use of the folded-spectrum propagator Eq. (11), which projects the non-dominant states at a slower rate, thus holding the information about other excited states nearby the target one.…”

“…Many of them are based on the variational quantum eigensolver (VQE) [6], which, using classical computers, optimizes parameters in a fixed quantum circuit. VQE has been extensively studied for molecules [7][8][9] and recently extended to solid states [10][11][12].…”

Quantum Version of the k‐NN Classifier Based on a Quantum Sorting Algorithm

“…In 1982, Richard Feynman and Paul Benioff showed that a classical computer is not capable of simulating a quantum system without a disproportionate amount of resources, [6] opening the door for multiple potential applications in chemistry and material science. [7][8][9][10] To date, several examples of the superiority of quantum computing over classical computing have been given, [11] being Shor's factorization algorithm [12] and Grover's search algorithm [13] two of the most famous examples. Furthermore, algorithms to achieve quantum advantage in noisy intermediate-scale quantum (NISQ) computers have also been proposed.…”

Quantum version of the k-NN classifier based on a quantum sorting algorithm

“…In essence, quantum computing is a new way of computing that takes advantage of collective properties of quantum systems, such as superposition and entanglement, to perform concrete calculations faster than a regular or classical computer. In 1982, Richard Feynman and Paul Benioff showed that a classical computer is not capable of simulating a quantum system without a disproportionate amount of resources [6], opening the door for multiple potential applications in chemistry and material science [7][8][9][10]. To date, several examples of the superiority of quantum computing over classical computing have been given [11], being Shor's factorization algorithm [12] and Grover's search algorithm [13] two of the most famous examples.…”