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Entanglement structures in disordered chains of nitrogen-vacancy centers

MetadataDetails
Publication Date2024-11-15
JournalPhysical review. A/Physical review, A
AuthorsAlexander M. Minke, Andreas Buchleitner, Edoardo G. Carnio
InstitutionsUniversity of Freiburg
Citations1
AnalysisFull AI Review Included

This 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 “electronic bus” 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 σp ≀ 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 ≄ 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 (σp ≀ 0.4 nm) can actually increase the occurrence of desirable W-like entanglement by suppressing destructive interference effects present in perfectly regular chains.

The following parameters define the physical system and the simulation constraints for the NV center chains.

ParameterValueUnitContext
Qubit Register Size (N)4 to 10spinsMaximum chain length simulated
NV Electronic SpinSpin-1particleQubit carrier
Zero-Field Splitting (D)2.87GHzEnergy gap between spin states
Electron Gyromagnetic Ratio (ge”B/ħ)2.8MHz/GUsed for Zeeman splitting calculation
External Magnetic Field (B)30GApplied to suppress hyperfine coupling effects
Rabi Frequency (Ω)15MHzExternal driving field strength
Dipolar Coupling Strength (Jjk)≈ 70kHzFor 10 nm NV separation
Regular NV Separation (rjk)≈ 10nmEquivalent to 28 diamond lattice constants
Diamond Lattice Constant (a)0.3567nmHost material parameter
Weak Disorder Threshold (σp)≀ 0.4nmEntanglement remains robust; often beneficial
Strong Disorder Threshold (σp)≄ 0.8nmLeads to significant structural changes and separability
Entanglement Threshold (Δ)0.01(Unitless)Minimum Entanglement Entropy (EA) required to classify a state as entangled

The study employs a theoretical and numerical approach based on quantum mechanics and information theory to analyze the entanglement properties of the NV chain eigenstates.

  1. 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.
  2. 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 (σp), ranging from 0 nm (regular chain) up to 0.8 nm.
    • 103 random chain realizations are generated for each system size and disorder strength.
  3. 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.
    • Wootters’s Concurrence (Cjk): Used to quantify pairwise bipartite entanglement between any two spins (j and k).
  4. 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.

This 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 “nuclear memory” (long-lived nuclear spins) connected by an “electronic bus” (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.