Quantum Repeaters with Encoding on Nitrogen-Vacancy-Center Platforms
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-08-16 |
| Journal | Physical Review Applied |
| Authors | Yumang Jing, Mohsen Razavi |
| Institutions | University of Leeds |
| Citations | 5 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Encoded Quantum Repeaters on NV Center Platforms
Section titled âTechnical Documentation & Analysis: Encoded Quantum Repeaters on NV Center PlatformsâSource Paper: Jing, Y. & Razavi, M. (2022). Quantum repeaters with encoding on nitrogen-vacancy center platforms. arXiv:2105.14122v2.
Executive Summary
Section titled âExecutive SummaryâThis research validates the feasibility and performance advantages of using encoded Quantum Repeaters (QRs) based on Nitrogen-Vacancy (NV) centers in diamond for long-distance Quantum Key Distribution (QKD).
- Core Application: Deterministic QKD over long distances (up to 2000 km simulated) using three-qubit repetition codes on NV center platforms.
- Material Requirement: Ultra-high purity Single Crystal Diamond (SCD) is essential to achieve the long electron ($T_e$) and nuclear ($T_n$) spin coherence times required for practical operation ($T_e$ up to 100 ms, $T_n$ up to 10 s).
- Performance Benchmark: Encoded protocols (P1, P2) significantly outperform uncoded protocols (P3, P4) at distances > 100 km, demonstrating the necessity of error detection/correction for scalable quantum networks.
- Optimal Structure: Protocol 2 (partially encoded entanglement) offers the highest normalized secret key rate across most practical parameter regimes, requiring fewer physical resources (NV centers) than the fully encoded Protocol 1.
- Critical Parameters: Key rate is highly sensitive to CNOT gate error probability ($\beta$) and coupling efficiency ($\eta_c$), necessitating high-fidelity material and device integration (e.g., microcavities).
- 6CCVD Value Proposition: 6CCVD provides the foundational ultra-pure SCD material and specialized processing (polishing, custom dimensions, metalization) required to fabricate high-coherence NV center devices and integrated quantum chips.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters were used in the numerical simulations to determine the performance of the encoded QR protocols:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Total Distance (Ltot) | 100, 300, 500, 2000 | km | Simulated QKD network range. |
| Electron Spin Coherence Time (Te) | 10, 100 | ms | Achievable/Improved values for NV centers. |
| Nuclear Spin Coherence Time (Tn) | 1, 10 | s | Achievable/Improved values for NV centers. |
| CNOT Gate Error Probability ($\beta$) | $10^{-3}$ to $10^{-1}$ | Dimensionless | Simulated range of operational error. |
| Measurement Error Probability ($\delta$) | $10^{-4}$ | Dimensionless | Fixed value for electron spin measurement. |
| Coupling Efficiency ($\eta_c$) | 0.3, 0.4, 0.5 | Dimensionless | ZPL photon emission/collection efficiency (requires microcavity integration). |
| Optical Fiber Attenuation Length (Latt) | 22 | km | Standard telecom fiber parameter. |
| Speed of Light in Channel (c) | $2 \times 10^{5}$ | km/s | Used for calculating transmission time (T0). |
| Electron-Electron Entanglement Time (Ts) | 5 | ”s | Timing of internal operations. |
Key Methodologies
Section titled âKey MethodologiesâThe protocols rely on deterministic two-qubit operations within NV centers, utilizing the electron spin (optical interface) and nuclear spin (long-term memory).
- Entanglement Distribution (Elementary Link):
- A two-mode entanglement distribution scheme is assumed, where the polarization of a single photon is entangled with the electron spin of the NV center at nodes A and B.
- A partial Bell-State Measurement (BSM) is performed on the photons in the middle of the link.
- Upon successful herald, the electron spin state is mapped and stored onto the corresponding nuclear spin memory.
- Encoded Entanglement Generation (P1, P2):
- Three Bell pairs are generated per encoded link.
- A transversal remote CNOT gate (requiring an auxiliary entangled link between electron spins) is used to generate the encoded entangled state: $|\Phi^{+}\rangle_{AB} = \frac{1}{\sqrt{2}}(|00\rangle_{AB} + |11\rangle_{AB})$.
- Entanglement Swapping (ES):
- Additional Bell pairs are distributed between the electron spins of two separate NV centers (co-located or remote).
- Deterministic BSMs (X and Z operator measurements) are performed on the nuclear and electron spins within each NV center, enabled by CNOT gates and electron spin measurements.
- Decoherence Modeling:
- Decoherence is modeled using a depolarizing channel, accounting for the average waiting time ($T_1$ and $T_2$) required for successful entanglement generation and swapping across the repeater chain.
- QKD Performance Calculation:
- The secret key rate (R) is calculated based on the success probability ($P_s$) and the total time ($T_1 + T_2$), normalized by the number of NV centers used. Post-selection based on error detection is used to boost the key rate.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the critical need for high-quality diamond material and advanced device integration to realize practical encoded quantum repeaters. 6CCVD is uniquely positioned to supply the foundational materials and specialized processing required to meet these stringent specifications.
Applicable Materials
Section titled âApplicable MaterialsâThe core requirement for achieving $T_e$ up to 100 ms and $T_n$ up to 10 s is extremely low defect density and high isotopic purity in the host diamond.
| Research Requirement | 6CCVD Solution | Technical Justification |
|---|---|---|
| Ultra-pure Diamond Host | Optical Grade Single Crystal Diamond (SCD) | Our MPCVD SCD is grown with extremely low nitrogen and substitutional defect concentrations, minimizing decoherence sources and maximizing spin coherence times ($T_e$, $T_n$). |
| Cavity Integration | Custom Polished SCD Plates (Ra < 1 nm) | High-fidelity microcavity integration (required for ZPL enhancement up to 46%) demands atomically smooth surfaces. Our SCD polishing achieves Ra < 1 nm, ideal for subsequent nanofabrication (etching, bonding). |
| Spin Control | Custom Doping (Nitrogen/Boron) | Precise control over NV center density and location is crucial. We offer controlled nitrogen incorporation during growth, or Boron-Doped Diamond (BDD) for integrated electrodes/sensors. |
Customization Potential
Section titled âCustomization PotentialâThe implementation of deterministic two-qubit gates and the integration of NV centers into microcavities require highly customized diamond substrates and processing.
- Custom Dimensions and Thickness: The paper implies the need for small, high-quality chips for integration into microcavities and cryostats. 6CCVD provides SCD plates from 0.1 ”m up to 500 ”m thick and PCD wafers up to 125 mm for large-scale integration platforms.
- Metalization for Control: Deterministic CNOT and controlled phase gates rely on microwave and radio frequency signals. 6CCVD offers in-house metalization services (Ti, Pt, Au, Cu, W, Pd) for depositing high-quality contact pads and transmission lines directly onto the diamond surface, enabling deterministic spin manipulation.
- Substrate Engineering: For advanced architectures (like those implied by Protocol 2âs resource efficiency), 6CCVD can provide custom laser cutting and shaping of SCD substrates to facilitate complex 3D integration or specific optical coupling geometries.
Engineering Support
Section titled âEngineering SupportâThe transition from theoretical modeling (like the $\beta$ and $\delta$ error rates used here) to practical implementation requires expert material optimization.
- Coherence Time Optimization: 6CCVDâs in-house PhD team specializes in optimizing MPCVD growth recipes to maximize $T_e$ and $T_n$ in NV centers, directly addressing the most sensitive parameters identified in the paper (Fig. 5).
- Defect Management: We assist researchers in selecting the optimal diamond grade to balance NV creation efficiency with background defect reduction, ensuring the material foundation supports the required $10^{-4}$ measurement error probability ($\delta$).
- Global Supply Chain: We ensure reliable, DDU/DDP global shipping of sensitive quantum materials, supporting international collaborations like those cited in the research.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (NV) centers in diamond as quantum memories. NV centers offer a two-qubit register, corresponding to their electron and nuclear spins, which makes it possible to perform deterministic two-qubit operations within one NV center. For quantum repeater applications, we, however, need to do joint operations on two separate NV centers. Here, we study two NV-center based repeater structures that enable such deterministic joint operations. One structure offers less consumption of classical communication, at the cost of more computation overhead, whereas the other one relies on a fewer number of physical resources and operations. We assess and compare their performance for the task of secret key generation under the influence of noise and decoherence with current and near-term experimental parameters. We quantify the regimes of operation, where one structure outperforms the other, and find the regions where encoded quantum repeaters offer practical advantages over their non-encoded counterparts.