Quantum-computing study of the electronic structure of crystals - the case study of Si
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2023-01-01 |
| Journal | NANOCOM ⊠|
| Authors | Michal ÄuriĆĄka, Ivana MihĂĄlikovĂĄ, Martin FriĂĄk |
| Institutions | Czech Academy of Sciences, Institute of Physics of Materials, Masaryk University |
| Citations | 1 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Quantum Computing Study of Diamond-Structure Materials
Section titled âTechnical Documentation & Analysis: Quantum Computing Study of Diamond-Structure MaterialsâExecutive Summary
Section titled âExecutive SummaryâThis analysis translates the computational study of diamond-structure Silicon (Si) electronic bands into actionable material requirements for quantum hardware development, emphasizing 6CCVDâs expertise in MPCVD diamond.
- Methodology Validation: The research successfully validated the hybrid Variational Quantum Eigensolver (VQE) algorithm combined with the tight-binding method for calculating the electronic structure of crystalline diamond-lattice materials.
- Computational Platform: Calculations were performed using both quantum computer simulators and a physical IBM Quantum processor (âibm_lagosâ).
- Key Finding (Accuracy): Excellent agreement between classical and quantum results was achieved, provided the iterative optimization parameter (MAXITER) was set sufficiently high (e.g., MAXITER = 100).
- Material Relevance: Although the study focused on Si, the diamond-structure lattice and computational methodology are directly transferable to Single Crystal Diamond (C), the premier platform for solid-state quantum computing (e.g., Nitrogen-Vacancy (NV) centers).
- 6CCVD Value Proposition: 6CCVD provides the ultra-high purity, highly polished Single Crystal Diamond (SCD) substrates necessary to physically realize the quantum systems modeled computationally in this research.
- Engineering Focus: The study highlights the need for precise material control and high-fidelity integration, areas where 6CCVD offers custom dimensions, ultra-low roughness polishing (Ra < 1nm), and integrated metalization services.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the computational study, providing context for material requirements in similar quantum solid-state physics applications.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| On-site Energy (Es) | -4.03 | eV | Tight-binding matrix element for Si s orbitals. |
| Hopping Energy (Vss) | -8.13 | eV | Tight-binding matrix element between Si s orbitals. |
| Minimum Iterations (Simulation) | 20 | Iterations | Required MAXITER for decent accuracy in VQE simulation. |
| High Accuracy Iterations (Hardware) | 100 | Iterations | MAXITER used on the âibm_lagosâ processor for reliable results. |
| Hamiltonian Size | 2x2 | Matrix | Simplified tight-binding model considering only s orbitals. |
| Qubit Requirement | 1 | Qubit | Required for mapping the 2x2 Hamiltonian to the Pauli basis. |
| Crystal Structure Studied | Diamond | N/A | Crystalline structure of Silicon (Si). |
Key Methodologies
Section titled âKey MethodologiesâThe computational approach utilized a hybrid classical-quantum framework optimized for current noisy quantum processors (NISQ era).
- Hamiltonian Formulation: A parametrized Hamiltonian H(k) was constructed using the tight-binding method (Slater and Koster) for the diamond-structure lattice, simplifying the model to include only interactions between s orbitals.
- Qubit Mapping: The 2x2 Hermitian Hamiltonian H(k) was transformed into the qubit space by decomposition using the complete Pauli basis (I, X, Y, Z), requiring only one qubit.
- Algorithm Selection: The Variational Quantum Eigensolver (VQE) was employed to find the ground energy, chosen for its suitability on noisy quantum computers due to its use of shallow (small) quantum circuits.
- State Preparation: The parametrized quantum state utilized the heuristic RyRz variational form, consisting of parametrized Ry and Rz single qubit rotations.
- Optimization: The classical optimization step used the Constrained Optimization by Linear Approximation (COBYLA) method, proceeding iteratively based on the user-defined maximum number of iterations (MAXITER).
- Validation: Results were compared against classical calculations and tested for sensitivity to the MAXITER parameter, confirming that higher iteration counts (up to 100) were necessary for high-fidelity results on real quantum hardware.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe computational study validates a critical method for analyzing the electronic structure of diamond-lattice materials. To transition this theoretical success into practical quantum devices, engineers require the highest quality MPCVD diamond, which 6CCVD specializes in providing.
Applicable Materials for Quantum Hardware
Section titled âApplicable Materials for Quantum HardwareâThe research focuses on the diamond lattice, which is the foundational structure for solid-state quantum platforms utilizing defect centers (e.g., NV, SiV, GeV). Replicating or extending this research into physical devices requires ultra-pure Single Crystal Diamond (SCD).
| Application Requirement | 6CCVD Material Recommendation | Key Capability |
|---|---|---|
| Quantum Defect Hosting | Electronic/Optical Grade SCD | Ultra-low impurity levels (N, B) essential for high T2 coherence times. |
| High Power Electronics | High Purity SCD | Excellent thermal conductivity (up to 2200 W/mK) for heat dissipation. |
| Electrochemical Sensing | Heavy Boron-Doped Diamond (BDD) | Highly conductive, stable electrode material (not directly used in this paper, but relevant for BDD applications). |
| Large Area Integration | PCD Wafers | Custom plates/wafers up to 125mm in diameter for large-scale integration. |
Customization Potential for Quantum Platforms
Section titled âCustomization Potential for Quantum PlatformsâQuantum computing experiments, particularly those involving VQE and tight-binding models, demand materials with highly controlled physical and surface properties. 6CCVD offers comprehensive customization services to meet these stringent requirements:
- Precision Polishing: Achieving the necessary surface quality for high-fidelity quantum experiments is paramount.
- SCD: Polishing to Ra < 1nm (atomic scale smoothness) to minimize surface noise and maximize defect coherence near the surface.
- PCD: Polishing to Ra < 5nm for inch-size polycrystalline wafers.
- Custom Dimensions and Thickness:
- Plates/Wafers: Custom dimensions up to 125mm (PCD).
- Thickness Control: SCD and PCD layers available from 0.1”m (for thin film devices) up to 500”m, and substrates up to 10mm.
- Integrated Metalization: For creating electrodes, gates, or contact pads required for VQE circuit integration (as implied by the need for classical optimization loops).
- Internal Capability: Custom deposition of Au, Pt, Pd, Ti, W, and Cu stacks directly onto the diamond surface.
- Orientation Control: SCD growth on specific crystal orientations (e.g., [100], [111]) to optimize the alignment and performance of quantum defects.
Engineering Support
Section titled âEngineering SupportâThe successful application of VQE to solid-state systems requires deep expertise in both computational physics and material science.
- Consultation: 6CCVDâs in-house PhD team can assist researchers in selecting the optimal diamond material specifications (purity, orientation, thickness) required to physically realize the quantum systems modeled using tight-binding or VQE algorithms.
- Global Logistics: We ensure reliable, global delivery of sensitive materials, offering DDU (default) and DDP shipping options worldwide.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Quantum computing is newly emerging information-processing technology which is foreseen to be exponentially faster than classical supercomputers.Current quantum processors are nevertheless very limited in their availability and performance and many important software tools for them do not exist yet.Therefore, various systems are studied by simulating the run of quantum computers.Building upon our previous experience with quantum computing of small molecular systems (see I. MihĂĄlikovĂĄ et al., Molecules 27 (2022) 597, and I. MihĂĄlikovĂĄ et al., Nanomaterials 2022, 12, 243), we have recently focused on computing electronic structure of periodic crystalline materials.Being inspired by the work of Cerasoli et al. (Phys.Chem.Chem.Phys., 2020, 22, 21816), we have used hybrid variational quantum eigensolver (VQE) algorithm, which combined classical and quantum information processing.Employing tight-binding type of crystal description, we present our results for crystalline diamond-structure silicon.In particular, we focus on the states along the lowest occupied band within the electronic structure of Si and compare the results with values obtained by classical means.While we demonstrate an excellence agreement between classical and quantum-computed results in most of our calculations, we further critically check the sensitivity of our results with respect to computational set-up in our quantum-computing study.A few results were obtained also using quantum processors provided by the IBM.