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New York Scientific Data Summit (NYSDS)

Quantum Computation and Visualization of Carbon Single and Double Nano-Rings

Joseph Peltroche, Michael McGuigan

Published Jun 1, 2019• 2 citations
Publisher

Abstract

This paper concentrates on computational nanoscience to better understand the properties of different materials of interest. In particular, the material graphene has many interesting properties with promising applications. This project will focus on different carbon nanostructures, including the hexagonal honeycomb lattices of a single graphene sheet. Using visualization, animation, and simulation, the thermodynamic properties and energy spectrum of the different carbon nanostructures, mainly carbon nano-ring of different geometries were investigated. The tight-binding model for interacting and non-interacting systems of bosons and fermions was implemented on Mathematica and IBM-Q's quantum computing platform QISkit for a thorough understanding of these atomic structures.

DOI
10.1109/nysds.2019.8909754

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This paper concentrates on computational nanoscience to better understand the properties of different materials of interest. In particular, the material graphene has many interesting properties with promising applications. This project will focus on different carbon nanostructures, including the hexagonal honeycomb lattices of a single graphene sheet. Using visualization, animation, and simulation, the thermodynamic properties and energy spectrum of the different carbon nanostructures, mainly carbon nano-ring of different geometries were investigated. The tight-binding model for interacting and non-interacting systems of bosons and fermions was implemented on Mathematica and IBM-Q's quantum computing platform QISkit for a thorough understanding of these atomic structures.
We present numerical studies of quantum walks on C60{\text{C}}_{60}C60​ and related graphene structures to investigate their transport properties. Also known as a honeycomb lattice, the lattice formed by carbon atoms in the graphene phase can be rolled up to form nanotubes of various dimensions. Graphene nanotubes have many important applications, some of which rely on their unusual electrical conductivity and related properties. Quantum walks on graphs provide an abstract setting in which to study such transport properties independent of the other chemical and physical properties of a physical substance. They can thus be used to further the understanding of mechanisms behind such properties. We find that nanotube structures are significantly more efficient in transporting a quantum walk than cycles of equivalent size, provided the symmetry of the structure is respected in how they are used. We find faster transport on zigzag nanotubes compared to armchair nanotubes, which is unexpected given that for the actual materials the armchair nanotube is metallic, while the zigzag is semiconducting.
Molecular dynamics simulations are a central computational methodology in materials design for relating atomic composition to mechanical properties. However, simulating materials with atomic-level resolution on a macroscopic scale is infeasible on current classical hardware, even when using the simplest elastic network models (ENMs) that represent molecular vibrations as a network of coupled oscillators. To address this issue, we introduce Quantum Elastic Network Models (QENMs) and utilize the quantum algorithm of Babbush et al. (PRX, 2023), which offers an exponential advantage when simulating systems of coupled oscillators. Here, we extend their algorithm in 2D systems and demonstrate how our method enables the efficient simulation of planar materials. As an example, we apply our algorithm to the task of simulating a 2D graphene sheet. We analyze the complexity for initial-state preparation, Hamiltonian simulation, and measurement of this material, and provide two real-world applications: heat transfer and the out-of-plane rippling effect. We estimate that an atomistic simulation of a graphene sheet on the centimeter scale, classically requiring hundreds of petabytes of memory and prohibitive runtimes, could be encoded and simulated with as few as ∼160\sim 160∼160 logical qubits.
Quantum Monte Carlo (QMC) is one of the most promising methods for solving quantum many-body problems. QMC combines known analytical properties of wave functions, results from other methods, and stochastic techniques, into a powerful tool for investigation of the electronic structure of real materials. Furthermore, the method has a favorable scaling ( O[N3] in the number of electrons), perfect scalability on parallel architectures, and can be applied to a wide range of systems. Our work has focused both on expanding the capabilities of QMC for calculation of quantities beyond energies, such as interatomic forces, and on application of the method to challenging problems in nanostructure materials research. For the calculation of interatomic forces we have implemented a finite difference correlated sampling method. The correlated sampling enables us to avoid the problem of statistical noise in evaluating the energy differences and allows us to obtain forces with an average 1% error. We have analyzed the effect of the method's main approximations on the estimate of the forces, both by theoretical arguments and by performing a variety of tests on small systems. Furthermore, we have used this newly developed method for estimating equilibrium geometries in a problem where other methods have failed. QMC enabled us to treat the electron correlation effects with high accuracy and to provide accurate predictions in a number of interesting applications. In particular, for carbon rings of C4N+2 stoichiometry we have resolved a long-standing problem regarding the competition between the aromaticity and second order Jahn-Teller effects. We have found that the dominant mechanism at small and intermediate sizes, which stabilizes the bond angle and bond length alternated geometries, is the secondorder Jahn-Teller effect while the aromatic isomer is always found to be a transition state. These high accuracy calculations which have involved multi-reference wave functions, extensive variational optimizations, and the use of massively parallel platforms demonstrate clearly the unique capabilities of the QMC approach.
Graphene, a material of extraordinary interest in condensed matter physics due to its unique electronic properties, presents a fundamental challenge: the precise calculation of its band structure. This Master’s Thesis addresses this problem by proposing the use of one of the most widely used algorithms in quantum computing. To achieve this, a tight-binding model is used that describes the electron hopping between the atoms of the single-layer hexagonal lattice that defines graphene. This model is extended to include not only the interactions of each atom in the lattice with adjacent atoms (first neighbors), but also with the next closest atoms (second neighbors), allowing for the capture of more subtle physical effects. The resulting hamiltonian is then prepared for execution in the quantum simulators of IBM’s Qiskit platform. The results under ideal conditions demonstrate that the algorithm reproduces analytical solutions with high fidelity, capturing essential features such as Dirac points, where valence and conduction bands intersect, causing electrons to behave as massless particles, and electron-hole symmetry breaking, which reflects the difference in the energetic behavior of electrons and their absences (holes). However, when introducing a noise model that emulates current quantum processors (inherently noisy, intermediate-scale devices, the socalled NISQ era), a systematic deviation is observed that underscores the limiting impact of the hardware. The study concludes that VQE is a conceptually viable and powerful tool for materials simulation, but its practical application to achieve quantum advantage will critically depend on the development of advanced error mitigation techniques.
The investigation of many-body quantum systems stands as a cornerstone in contemporary physics research. These systems exhibit a richness of phenomena, characterized by the emergence of collective behavior, which leads to the formation of quasi-particle excitations with occasionally unconventional statistics, alongside the occurrence of quantum phase transitions. Their significance extends further as they serve as models for understanding the behavior of real quantum materials, underlining the necessity for their comprehension.In the realm of theoretical physics, exact solutions are often elusive for many-body systems and are limited to a few select cases or toy models. However, real materials are often more complicated with additional dominant interactions beyond solvable limits. Consequently, the study and understanding of generic Hamiltonians necessitate resorting to computational simulations. Utilizing computational resources becomes indispensable, albeit challenging, as the Hilbert space expands exponentially with the number of spins, demanding substantial memory and computational bandwidth.However, recent advancements in quantum computing present a promising avenue for tackling these challenges. Quantum computers offer the potential to simulate many-body quantum systems with minimal overhead, overcoming the limitations of classical computational techniques. Although current quantum computing platforms operate within the confines of the NISQ era -noisy intermediate-scale quantum- they hold immense promise for the exact modelling of many-body systems.In this doctoral research, our objective is to investigate the predictive capabilities of quantum computers through simulating and benchmarking quantum many-body systems relevant to magnetic materials. We showcase three different projects on studying frustrated magnetism: 1) simulating non-equilibrium dynamics of frustrated Ising models on an analog quantum annealer, 2) studying frustrated Rydberg atom quench dynamics on a neutral atom platform, and 3) simulating the Kitaev honeycomb model and probing its topological order on a digital quantum computer. By leveraging the potential of quantum computing in this domain, this research aims to advance both theoretical understanding and practical applications in quantum physics.