Entanglement structures in disordered chains of nitrogen-vacancy centers
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2024-11-15 |
| Journal | Physical review. A/Physical review, A |
| Authors | Alexander M. Minke, Andreas Buchleitner, Edoardo G. Carnio |
| Institutions | University of Freiburg |
| Citations | 1 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research investigates the feasibility and robustness of creating scalable, connected qubit registers using chains of Nitrogen-Vacancy (NV) centers self-assembled along one-dimensional defects in diamond.
- Core Value Proposition: The study confirms that chains of up to 10 dipole-coupled NV electron spins exhibit strong N-partite entanglement, enabling them to function as a robust âelectronic busâ for connecting long-lived nuclear spin memories.
- High Connectivity: The vast majority of the Hamiltonian eigenstates are found to be N-partite entangled, particularly those closer to the center of the energy spectrum and in longer chains (N > 6).
- Disorder Resilience: The connectivity of the qubit register is highly resilient to weak positional disorder (Gaussian width Ïp †0.4 nm), which is crucial given the random nature of defect assembly.
- Entanglement Structures: Cluster and GHZ-like entanglement structures become increasingly dominant as system size increases, while W-like and Path structures decrease in frequency for N â„ 7.
- Fabrication Implications: The findings support the use of diamond dislocations (e.g., 30° partial dislocations) as templates for self-assembling connected NV chains, offering a potential path to higher-yield multi-qubit fabrication than traditional ion implantation.
- Disorder Benefit: Weak disorder (Ïp †0.4 nm) can actually increase the occurrence of desirable W-like entanglement by suppressing destructive interference effects present in perfectly regular chains.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters define the physical system and the simulation constraints for the NV center chains.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit Register Size (N) | 4 to 10 | spins | Maximum chain length simulated |
| NV Electronic Spin | Spin-1 | particle | Qubit carrier |
| Zero-Field Splitting (D) | 2.87 | GHz | Energy gap between spin states |
| Electron Gyromagnetic Ratio (ge”B/ħ) | 2.8 | MHz/G | Used for Zeeman splitting calculation |
| External Magnetic Field (B) | 30 | G | Applied to suppress hyperfine coupling effects |
| Rabi Frequency (Ω) | 15 | MHz | External driving field strength |
| Dipolar Coupling Strength (Jjk) | â 70 | kHz | For 10 nm NV separation |
| Regular NV Separation (rjk) | â 10 | nm | Equivalent to 28 diamond lattice constants |
| Diamond Lattice Constant (a) | 0.3567 | nm | Host material parameter |
| Weak Disorder Threshold (Ïp) | †0.4 | nm | Entanglement remains robust; often beneficial |
| Strong Disorder Threshold (Ïp) | â„ 0.8 | nm | Leads to significant structural changes and separability |
| Entanglement Threshold (Δ) | 0.01 | (Unitless) | Minimum Entanglement Entropy (EA) required to classify a state as entangled |
Key Methodologies
Section titled âKey MethodologiesâThe study employs a theoretical and numerical approach based on quantum mechanics and information theory to analyze the entanglement properties of the NV chain eigenstates.
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System Modeling and Reduction:
- NV centers are assumed to align along a 1D defect (z-axis) in diamond.
- The electronic spin-1 system is restricted to the {|0>, |-1>} subspace, forming a two-level qubit system via resonant external driving (Rabi frequency Ω = 15 MHz).
- The full Hamiltonian is simplified using the secular approximation, focusing only on the magnetic dipolar coupling (Hdipolar) between the electron spins, which governs the slowest dynamics.
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Disorder Implementation:
- Positional disorder is simulated by drawing the position of each spin (rj) from a Gaussian distribution centered on the ideal lattice position.
- Disorder strength is controlled by the standard deviation (Ïp), ranging from 0 nm (regular chain) up to 0.8 nm.
- 103 random chain realizations are generated for each system size and disorder strength.
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Entanglement Quantification Metrics:
- Entanglement Entropy (EA): Used to quantify N-partite entanglement. If EA > Δ (0.01) for all bipartitions, the state is N-partite entangled.
- Woottersâs Concurrence (Cjk): Used to quantify pairwise bipartite entanglement between any two spins (j and k).
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Automated Entanglement Classification:
- A custom scheme classifies the eigenstates based on the patterns of EA and Cjk, mapping them to graph structures:
- W-like: Non-zero EA and non-zero Cjk for all pairs (fully connected graph).
- GHZ-like: Non-zero EA but vanishing Cjk for all pairs (N-partite entangled, but no pairwise connection).
- Path: Non-zero EA, with non-zero Cjk forming a linear path through all nodes.
- Cluster: Non-zero EA, where the concurrence graph splits into two or more disjoint subgraphs.
- A custom scheme classifies the eigenstates based on the patterns of EA and Cjk, mapping them to graph structures:
Commercial Applications
Section titled âCommercial ApplicationsâThis research directly supports the development of scalable quantum hardware, particularly within the solid-state quantum computing sector utilizing diamond defects.
- Scalable Quantum Computing: Provides the theoretical basis for building connected, multi-qubit registers (N > 4) using NV centers, overcoming the limited scalability of single-NV architectures.
- Hybrid Quantum Architecture: Enables the realization of a ânuclear memoryâ (long-lived nuclear spins) connected by an âelectronic busâ (fast, coupled electronic spins), mirroring successful trapped-ion architectures.
- Fault-Tolerant Qubit Fabrication: The demonstrated resilience to positional disorder (up to 0.4 nm) relaxes the stringent spatial precision requirements for defect placement, potentially increasing the yield and throughput of quantum device manufacturing.
- Quantum Control Optimization: The classification of eigenstates (W-like, GHZ-like, Cluster) informs the design of optimal quantum control sequences (e.g., optimal control schemes) necessary to implement specific quantum gates (like two-qubit gates) using the entangled energy landscape.
- Solid-State Quantum Simulation: The system serves as a highly controllable platform for simulating complex 1D spin chain physics, including the effects of disorder on entanglement and thermalization.
View Original Abstract
A recent study [Phys. Rev. B 17 174111 (2022)] has hypothesized the assembly, along a specific type of one-dimensional defects of diamond, of chains of nitrogen-vacancy (NV) centers, potentially enabling the creation of qubit registers via their dipole-coupled electron spins. Here we investigate the connectivity of chains of up to ten coupled spins, mediated by the bi- and multipartite entanglement of their eigenstates. Rather conveniently, for regularly spaced spins the vast majority of the eigenstates displays strong connectivity, especially towards the center of the spectrum and for longer chains. Furthermore, positional disorder can change, and possibly reduce, the connectivity of the register, but seldom suppresses it.