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.
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.
Understanding strongly correlated systems is essential for advancing quantum chemistry and materials science, yet conventional methods like Density Functional Theory (DFT) often fail to capture their complex electronic behavior. To address these limitations, we develop a hybrid quantum-classical framework that integrates Multiconfigurational Self-Consistent Field (MCSCF) with the Variational Quantum Eigensolver (VQE). Our initial benchmarks on water dissociation enabled the systematic optimization of key computational parameters, including ansatz selection, active space construction, and error mitigation. Building on this, we extend our approach to investigate the interactions between graphene analogues and water, demonstrating that our framework produces binding energies consistent with high-accuracy quantum methods. Furthermore, we apply this methodology to predict the binding energies of transition metals (Fe, Co, Ni) on both pristine and defective graphene analogues, revealing strong charge transfer effects and pronounced multireference character─phenomena often misrepresented by standard DFT. In contrast to many existing quantum algorithms that are constrained to small molecular systems, our framework achieves chemically accurate predictions for larger, strongly correlated systems such as metal-graphene complexes. This advancement highlights the capacity of hybrid quantum-classical approaches to address complex electronic interactions and demonstrates a practical route toward realizing quantum advantage for real-world materials applications in the Noisy Intermediate-Scale Quantum (NISQ) era.
Band crossings in electronic band structures play an important role in determining the electronic, topological, and transport properties in solid-state systems, making them central to both condensed matter physics and materials science. The emergence of noisy intermediate-scale quantum (NISQ) processors has sparked great interest in developing quantum algorithms to compute band structure properties of materials. While significant research has been reported on computing ground state and excited state energy bands in the presence of noise that breaks the degeneracy, identifying the symmetry at crossing points using quantum computers is still an open question. In this work, we propose a method for identifying the symmetry of bands around crossings and anti-crossings in the band structure of bilayer graphene with two distinct configurations on a NISQ device. The method utilizes eigenstates at neighbouring k points on either side of the touching point to recover the local symmetry by implementing a character-checking quantum circuit that uses ancilla qubit measurements for a probabilistic test. We then evaluate the performance of our method under a depolarizing noise model, using four distinct matrix representations of symmetry operations to assess its robustness. Finally, we demonstrate the reliability of our method by correctly identifying the correct band crossings of AA-stacked bilayer graphene around K point, using the character-checking circuit implemented on a noisy IBM quantum processor ibm_marrakesh.
Abstract Variational Quantum Eigensolver (VQE) and its extension, Variational Quantum Deflation (VQD), have emerged as promising algorithms for computing ground and excited state energy eigenvalues of Hamiltonians, particularly in quantum physics, chemistry, and materials science. Recently, the VQE and VQD algorithms were implemented to calculate the electronic band structure described by the tight-binding Hamiltonian. Despite their success for simple models, scalability remains a challenge due to the need for a large number of circuit executions, limited qubit coherence times, and low gate fidelities. In this work, we implemented the VQE and VQD algorithms for tight-binding models of diamond and zincblende crystal structures (Sn, C, Si, Ge, AlP, AlAs, AlSb, and GaP) using a quantum computer simulator. We investigate the scalability challenges, focusing on the significant overhead caused by a large number of quantum circuit executions required to find the energy eigenvalues. Our analysis highlights the substantial amount of both measurement and optimization overheads in VQD, particularly as the number of excited states increases. Based on our findings, we critically discuss the implications of implementing VQD on current noisy intermediate-scale quantum (NISQ) devices.
Abstract Quantum computing offers transformative potential for simulating real-world materials, providing a powerful platform to investigate complex quantum systems across quantum chemistry and condensed matter physics. In this work, we leverage this capability to simulate the Hubbard model on a six-site graphene hexagon using Qiskit, employing the Iterative Quantum Phase Estimation (IQPE) and adiabatic evolution algorithms to determine its ground-state properties. Our results show that a single Slater determinant is sufficient to initialize IQPE and accurately recover ground-state energies (GSEs) in small-scale Hubbard systems. In noiseless simulations, IQPE converges within a few iterations to exact GSEs, while adiabatic simulations yield charge and spin densities and correlation functions in excellent agreement with exact diagonalization. However, deploying IQPE and adiabatic evolution on today's noisy quantum hardware remains highly challenging. To investigate these limitations in IQPE, we use the Qiskit Aer simulator with a custom noise model tailored to the characteristics of IBM's real hardware. This model includes realistic depolarizing gate errors, thermal relaxation, and readout noise, allowing us to explore how these factors degrade simulation accuracy. Further, we implement the IQPE algorithm on IBM's ibm_strasbourg and ibm_fez devices for a reduced three-site Hubbard model, enabling direct comparison between simulated and real hardware noise. While ibm_fez runs closely match exact results, discrepancies highlight the gap between modeled and physical noise. This study demonstrates both the IQPE's potential and current limitations for simulating strongly correlated systems under realistic conditions.
Moore’s law has been the milestone for electronics improvement, and the cause for the exponential growth in our computational abilities and for reaching nanoscale electron devices. At such dimensions, classical simulation tools must be substituted by quantum ones. Such substitution implies to tackle new fundamental problems. First, the many-body problem makes (almost) impossible the exact simulation of many particles scenarios. Second, the measurement problem is especially relevant in high-frequency scenarios where multi-time measurements are mandatory. Alternatively to the orthodox theory, Bohmian mechanics emerges as a quantum theory which is specially well-equipped for the simulation of high-frequency characteristic of quantum electron devices. The Bohmian theory provides the conditional wave function that guides particles with well-defined positions. In this thesis, I explored quantum transport using Bohmian mechanics, putting special emphasis to graphene, a 2D material with linear bandstructure, which is expected to play an important role in the next future electronics. Differently from other materials, graphene obeys the bispinor Dirac equation, electrons behave as massless particles, exhibiting exotic behaviors, such as the Klein Tunneling effect. During the thesis, the quantum BITLLES simulator has been improved to correctly model electron nanodevices with either linear (by the inclusion of the complex bispinor Dirac equation) or parabolic bandstructures in either ballistic or dissipative (by the inclusion of the complete positive Bohmian scattering approach) systems. Thus, the BITLLES has become the candidate for substituting the versatile semiclassical Monte Carlo approach in the quantum regime, while keeping the versatility to predict DC, AC and noise performances. As practical applications, during the thesis, unexpected scattering probabilities in a Hong-Ou-Mandel experiment were predicted. In addition, different current-voltage characteristics were analyzed. Finally, a new limit (due to the discrete nature of charge) for ultra-small logic applications working at THz frequencies was predicted.
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.