On the quantum performance evaluation of two distributed quantum architectures

At a Glance

Metadata	Details
Publication Date	2021-10-13
Journal	Performance Evaluation
Authors	Gayane Vardoyan, Matthew Skrzypczyk, Stephanie Wehner
Institutions	QuTech, Delft University of Technology
Citations	8
Analysis	Full AI Review Included

Quantum Architecture Performance Optimization: Leveraging High-Purity MPCVD Diamond for NV Centers

This technical documentation analyzes the findings of Vardoyan et al. regarding the performance evaluation of distributed quantum architectures based on Nitrogen-Vacancy (NV) centers in diamond. As an expert material scientist and technical sales engineer for 6CCVD, this analysis focuses on connecting the critical material requirements—specifically, maximizing quantum memory lifetimes ($T_1$ and $T_2$)—to 6CCVD’s capabilities in high-purity Single Crystal Diamond (SCD) substrates.

Executive Summary

The research evaluates two quantum network node architectures (Single-Device, SD, and Double-Device, DD) implemented using Nitrogen-Vacancy (NV) centers in diamond, emphasizing the critical role of quantum memory quality in overall system performance.

Platform Focus: The study utilizes the NV center in diamond platform, where electron spins serve as communication qubits and Carbon-13 nuclear spins act as storage qubits.
Performance Metric: Performance is quantified using average gate fidelity ($F_{avg}$) and entanglement fidelity ($F_e$), which are shown to decay exponentially based on qubit waiting times and memory lifetimes ($T_1, T_2$).
Architectural Tradeoffs: The DD architecture generally offers higher $F_{avg}$ when memory quality is identical, but the SD architecture is simpler to implement and more robust in entanglement-heavy applications (e.g., QKD).
Material Criticality: The paper analytically proves that improving the quantum memory lifetime ($T_1$ and $T_2$) of the SD architecture can allow it to outperform a DD architecture with poorer quality memories, highlighting the paramount importance of high-purity diamond substrates.
Modeling Approach: Performance is modeled using Continuous-Time Markov Chains (CTMC) to derive qubit waiting time distributions, which are then integrated with standard quantum noise models (Depolarizing, Dephasing, Amplitude Damping) to calculate average fidelities.
Conclusion for Implementation: For computation-heavy applications, the DD design is suitable, but for high entanglement generation rates (distributed quantum clusters), the SD design with superior memory quality (i.e., high-purity diamond) is preferred.

Technical Specifications

The following hard data points were extracted from the analysis, focusing on the parameters governing quantum memory quality and gate performance in the NV diamond platform.

Parameter	Value	Unit	Context
Minimum Entanglement Fidelity (QKD)	$\ge 0.81$	N/A	Required threshold for basic Quantum Key Distribution.
Memory Lifetime T₁ (High Quality SD)	10	s	Used in simulations to demonstrate SD superiority over DD.
Memory Lifetime T₂ (High Quality SD)	0.01	s	Used in simulations to demonstrate SD superiority over DD.
Memory Lifetime T₁ (Baseline DD)	0.00286	s	Baseline value for DD architecture simulations.
Memory Lifetime T₂ (Baseline DD)	0.001	s	Baseline value for DD architecture simulations.
Electron Spin Depolarizing Probability ($p_G$)	0.02	N/A	Noise parameter for Electron Initialization.
Carbon Spin Rz Depolarizing Probability ($p_G$)	0.001/3	N/A	Noise parameter for Carbon Rz rotations.
Electron-Carbon CNOT Depolarizing Probability ($p_G$)	0.005	N/A	Noise parameter for two-qubit gates.
SD State Transfer Rate ($\mu_m^{(1)}$)	1667	Hz	Corresponds to 600 µs local swap time.
DD State Transfer Rate ($\mu_m^{(2)}$)	700	Hz	Optimistic estimate for inter-device transfer.
Noise Model Used for Fidelity Calculation	Composite Channel ($C_t$)	N/A	Combines Dephasing ($P_t$) and Amplitude Damping ($A_t$).

Key Methodologies

The performance evaluation relies on a rigorous combination of queueing theory and quantum information principles applied to the NV center platform.

Platform Implementation: The architectures are physically realized using Nitrogen-Vacancy (NV) centers in diamond, where the electron spin serves as the communication qubit and surrounding Carbon-13 nuclear spins are used for quantum memory (storage qubits).
Queueing Model: Both SD and DD architectures are modeled as M/HYPO3/1 queueing systems using a Continuous-Time Markov Chain (CTMC) to track outstanding entanglement requests and processing stages (entanglement generation, waiting for move request, moving operation).
Waiting Time Distribution: Analytical expressions for the qubit waiting time distribution ($f_{w}(t)$) are derived from the stationary distribution of the CTMC, assuming negligible computational processing time ($\mu_c = \infty$) in the analytical case.
Quantum Noise Modeling: Quantum state decay during waiting times is characterized by standard noise channels: Depolarizing ($D_t$), Dephasing ($P_t$), and Amplitude Damping ($A_t$), combined into a Composite Channel ($C_t$).
Fidelity Calculation: Average gate fidelity ($F_{avg}$) and entanglement fidelity ($F_e$) are computed by integrating the time-dependent fidelity function $F(N_t, G)$ over the derived waiting time distribution $dw(t)$.
Simulation and Validation: Results are validated using NetSquid, a discrete-event quantum network simulator, which incorporates hardware-validated NV center models to explore regimes where computational time is non-negligible ($\mu_c < \infty$).

6CCVD Solutions & Capabilities

The research clearly establishes that the performance of distributed quantum architectures, particularly the ability of the SD design to compete with or surpass the DD design, hinges entirely on maximizing the quantum memory lifetimes ($T_1$ and $T_2$). This requirement translates directly into a demand for ultra-high-purity, low-strain Single Crystal Diamond (SCD) substrates—6CCVD’s core expertise.

Applicable Materials

To replicate or extend this research, specifically targeting the high-quality memory lifetimes (e.g., $T_1 = 10$ s, $T_2 = 0.01$ s) necessary for robust SD architecture performance, researchers require:

Optical Grade Single Crystal Diamond (SCD): Essential for NV center creation. 6CCVD provides SCD with ultra-low intrinsic nitrogen concentration (< 1 ppb) and minimal lattice defects, which are critical for achieving the long $T_1$ and $T_2$ coherence times required for high-fidelity quantum memory.
High-Purity Polycrystalline Diamond (PCD): While SCD is preferred for NV centers, 6CCVD offers high-quality PCD for applications requiring large-area heat spreading or robust structural support in cryogenic environments.

Customization Potential

The complexity of both SD (local gate sequences, Fig 12) and DD (inter-device teleportation, Fig 13) architectures necessitates highly customized diamond substrates and interfaces.

Research Requirement	6CCVD Capability	Impact on Research
Specific Dimensions/Integration	Custom Dimensions and Thickness Control. Plates/wafers up to 125 mm (PCD). SCD thickness from 0.1 µm to 500 µm, and substrates up to 10 mm.	Enables precise integration of diamond chips into complex optical cavities, microwave setups, and on-chip quantum network nodes.
High-Fidelity Optical Interface	Ultra-Smooth Polishing (Ra < 1 nm for SCD).	Minimizes surface scattering and optical losses, crucial for efficient NV center initialization, readout, and remote entanglement generation ($\mu_e$ rate).
On-Chip Control Lines	Internal Metalization Services (Au, Pt, Pd, Ti, W, Cu).	Supports the fabrication of high-speed microwave/RF control lines directly on the diamond surface, necessary for fast local gates and state transfer operations ($\mu_m$ rates).
Complex Qubit Architectures	Custom Laser Cutting and Shaping.	Allows for the creation of micro-structures (e.g., solid immersion lenses or photonic waveguides) directly in the diamond to enhance photon collection efficiency, a known limitation cited in the paper.

Engineering Support

The analytical framework presented in this paper—linking queueing theory, noise models, and memory lifetimes to fidelity—is highly specialized. 6CCVD’s in-house team of PhD material scientists and quantum engineers can provide crucial support:

Material Selection for Fidelity Targets: We assist researchers in selecting the optimal SCD grade and processing parameters (e.g., specific nitrogen doping for NV creation) to meet target $T_1$ and $T_2$ coherence times, ensuring the material quality supports the desired average gate fidelity ($F_{avg}$) for Distributed Quantum Computing Cluster projects.
Interface Optimization: Our expertise in metalization and polishing ensures that the physical interfaces required for state transfer and networking (e.g., fast $\mu_m$ rates) are implemented with minimal noise overhead.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

Tech Support

Original Source

DOI: https://doi.org/10.1016/j.peva.2021.102242

References

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