A benchmarking procedure for quantum networks
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2023-02-25 |
| Journal | npj Quantum Information |
| Authors | Jonas Helsen, Stephanie Wehner |
| Institutions | University of Amsterdam, QuTech |
| Citations | 18 |
| Analysis | Full AI Review Included |
Technical Documentation: Network Benchmarking for Quantum Diamond Systems
Section titled âTechnical Documentation: Network Benchmarking for Quantum Diamond SystemsâExecutive Summary
Section titled âExecutive SummaryâThis document analyzes the proposed Network Benchmarking (NB) protocol, an adaptation of Randomized Benchmarking (RB), designed to characterize the quality of quantum communication links. The research, which utilizes simulations inspired by Nitrogen-Vacancy (NV) center systems in diamond, highlights the critical role of high-fidelity materials in achieving robust quantum networks.
- Core Achievement: Introduction of the Network Benchmarking protocol (two-node and multi-node versions) to efficiently estimate the average fidelity F(Î) of the effective quantum channel modeling a network link.
- Platform Relevance: The numerical simulations specifically model noise characteristics and operational parameters relevant to NV-center quantum processors in diamond.
- Key Result (Two-Node): The protocol yielded a Network Link Fidelity ($f$) of 0.899 ± 0.004 for a teleportation-mediated link, demonstrating high accuracy in realistic noisy environments.
- Multi-Node Utility: The multi-node protocol successfully quantified the exponential decay of network path fidelity, providing a tool for ânetwork discoveryâ and estimating the maximum distance quantum information can travel (fidelity dropped to 0.56 ± 0.02 over six nodes).
- Material Requirement: Achieving high fidelity (T2 coherence times up to 12 ms for 13C memory qubits) necessitates ultra-high purity Single Crystal Diamond (SCD) substrates, the core specialization of 6CCVD.
- Robustness: The protocol is designed to be robust against State Preparation and Measurement (SPAM) errors, a significant advantage for experimental implementation.
Technical Specifications
Section titled âTechnical SpecificationsâThe following data points were extracted from the simulation results and physical parameters used to model the NV-center quantum network environment.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Physical Platform Basis | NV-centers in Diamond | N/A | Inspiration for noise and operational models. |
| Memory Qubit T2 Time | 12 | ms | Relevant coherence time for 13C memory qubits in NV-centers. |
| Quantum Operation Time | 39 | ”s | Assumed duration for native quantum operations on memory qubits. |
| Local Gateset Used | Single-qubit Clifford Group (C1) | N/A | Used for randomized operations G(i). |
| Two-Node Network Link Fidelity ($f$) | 0.899 ± 0.004 | N/A | Result of exponential decay fit (95% confidence interval). |
| Multi-Node Path Fidelity (2 Nodes) | 0.899 ± 0.04 | N/A | Fidelity for the shortest path (A1 â A2). |
| Multi-Node Path Fidelity (6 Nodes) | 0.56 ± 0.02 | N/A | Fidelity decay observed over a six-node linear configuration. |
| Teleportation State Population ($\alpha$) | 0.95 | N/A | Bright state population used in the noisy entangled state model (Eq. 15). |
Key Methodologies
Section titled âKey MethodologiesâThe Network Benchmarking protocol adapts the standard Randomized Benchmarking (RB) procedure to characterize the quality of the quantum channel (Î) connecting nodes.
- State Initialization: A fixed initial state PA is prepared at Node A.
- Randomized Bounce Sequence: The core sequence, or âbounce,â is repeated m times. Each bounce involves:
- Applying a random gate G(i)A (from a unitary two-design set, e.g., Clifford group) at Node A.
- State transfer from A to B (via channel ÎAâB).
- Applying a random gate G(i)B at Node B.
- State transfer back from B to A (via channel ÎBâA).
- Inverse Operation: A final operation G(inv) is applied at Node A. This operation is the inverse of the product of all preceding gates, followed by a randomly chosen ending gate PA â {I, P}.
- Measurement and Post-Processing: The final state is measured using a two-component POVM {E, I - E} to yield outcome b. The outcome is negated if the ending gate PA = P.
- Fidelity Extraction: The mean outcome bm is computed for various sequence lengths m. The resulting data set {bm} is fitted to a single exponential decay curve (bm = A * fm) to extract the Network Link Fidelity f.
- Underlying Assumptions: The protocol relies on Markovianity (noise is independent of history) and assumes a gate-independent noise model for local operations, standard assumptions adopted from the RB literature.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful implementation and extension of the Network Benchmarking protocol, particularly within the NV-center platform, relies fundamentally on high-quality diamond materials. 6CCVD is uniquely positioned to supply the necessary Single Crystal Diamond (SCD) substrates and custom fabrication services required for next-generation quantum network nodes.
Applicable Materials
Section titled âApplicable MaterialsâThe research explicitly models systems based on NV-centers in diamond, which require materials optimized for spin coherence and defect engineering.
| Research Requirement | 6CCVD Material Solution | Technical Specification |
|---|---|---|
| NV-Center Host Material | Optical/Quantum Grade SCD | Ultra-low nitrogen concentration ([N] < 1 ppb) to maximize T2 coherence times (essential for achieving the simulated 12 ms T2). |
| High-Fidelity Surfaces | Polished SCD Wafers | Surface roughness (Ra) < 1 nm, critical for minimizing surface defects and ensuring high-quality optical coupling for entanglement generation. |
| Distributed Computing | Large-Area SCD Substrates | SCD plates available in various sizes, enabling the fabrication of complex, multi-qubit NV-center arrays necessary for scaling up multi-node network architectures. |
| Integrated Components | Boron-Doped Diamond (BDD) | Available for on-chip electrical components, such as integrated electrodes or high-conductivity heat sinks, often required in complex quantum processors. |
Customization Potential
Section titled âCustomization PotentialâReplicating and advancing this research requires precise material engineering beyond standard off-the-shelf wafers. 6CCVD offers full customization to meet the demands of quantum network development.
- Custom Dimensions and Thickness: We provide SCD wafers with thicknesses ranging from 0.1 ”m to 500 ”m, allowing researchers to optimize for specific optical cavity coupling or thermal management requirements. Custom plates/wafers are available up to 125 mm (PCD) and large-area SCD.
- Advanced Metalization Services: Quantum device fabrication frequently requires specific metal stacks for electrodes, microwave lines, or contacts. 6CCVD offers in-house deposition of critical metals, including Titanium (Ti), Platinum (Pt), Gold (Au), Palladium (Pd), Tungsten (W), and Copper (Cu), tailored to the exact geometry of the NV-center device.
- Precision Polishing: Achieving the necessary surface quality for low-loss optical interfaces is guaranteed with our ultra-precise polishing capabilities, ensuring Ra < 1 nm on SCD material.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house team of PhD-level material scientists and engineers specializes in optimizing MPCVD diamond growth for quantum applications.
- Material Selection for NV-Centers: We provide expert consultation on selecting the optimal diamond grade (e.g., isotopic purity, nitrogen concentration) to maximize qubit performance and T2 coherence times for similar quantum network node projects.
- Integration Assistance: Our team assists with material preparation for subsequent device integration steps, including laser cutting, etching, and metal deposition, ensuring compatibility with complex quantum circuit fabrication.
- Global Logistics: We ensure reliable, global delivery of sensitive quantum materials, offering both DDU (Delivery Duty Unpaid) and DDP (Delivery Duty Paid) shipping options.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract We propose network benchmarking: a procedure to efficiently benchmark the quality of a quantum network link connecting quantum processors in a quantum network. This procedure is based on the standard randomized benchmarking protocol and provides an estimate for the fidelity of a quantum network link. We provide statistical analysis of the protocol as well as a simulated implementation inspired by nitrogen-vacancy center systems using Netsquid, a special purpose simulator for noisy quantum networks.