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 |
Executive Summary
Section titled âExecutive SummaryâThe research introduces Network Benchmarking (NB), a robust and efficient procedure adapted from Randomized Benchmarking (RB) to characterize the quality of quantum network links.
- Core Value Proposition: NB provides an estimate of the average fidelity (F) of the effective quantum channel (Î) modeling a quantum network link, independent of state preparation and measurement (SPAM) errors.
- Protocol Mechanism: The procedure involves performing sequences of random quantum operations (âbouncesâ) and measuring the decay of the average outcome (bm).
- Fidelity Extraction: The data fits a single exponential decay curve, bm = A * fm, where f is the network link fidelity.
- Protocol Versions: Two versions are proposed: a two-node protocol for single link characterization, and a multi-node protocol that functions as a quantum analog of the classical âpingâ operation to assess path quality.
- Simulation Results: Simulations based on Nitrogen-Vacancy (NV) center systems (using the NetSquid simulator) confirmed the protocolâs effectiveness, yielding a link fidelity of 0.899 ± 0.004 for a two-node link.
- Statistical Efficiency: When cost is measured by the number of state transmissions (which grows linearly with sequence length m), NB achieves additive estimation accuracy (variance V(r) = O(r)), sufficient for current low-fidelity network regimes.
Technical Specifications
Section titled âTechnical SpecificationsâThe following specifications are derived from the numerical simulations and theoretical analysis, primarily using an NV-center inspired noise model.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Simulated Network Link Fidelity (2 nodes) | 0.899 ± 0.004 | N/A | Teleportation-mediated link (95% Studentized confidence interval) |
| Simulated Network Path Fidelity (6 nodes) | 0.56 ± 0.02 | N/A | Linear configuration path decay (95% Studentized confidence interval) |
| Qubit Dephasing Time (T2) | 12 | ms | 13C memory qubits in NV-center model |
| Native Quantum Operation Time | 39 | ”s | Local gate application time (NV-center model) |
| Teleportation State Bright Population (α) | 0.95 | N/A | Resource state ÏAB used for link emulation |
| Required Gateset | Unitary Two-Design | N/A | Minimum requirement for the set of random operations G (e.g., Clifford group) |
| Statistical Accuracy (Infidelity r = 1 - f) | Additive (O(r)) | N/A | Achieved accuracy when cost is proportional to the number of state transmissions |
Key Methodologies
Section titled âKey MethodologiesâThe Network Benchmarking procedure is based on randomized sequences of operations and state transfers between nodes.
- State Initialization: A quantum state (PA) is prepared at the starting node (A).
- Bounce Sequence: The protocol executes m bounces, where each bounce consists of:
- Applying a random gate G(1) at Node A.
- Transferring the state from A to B (via channel ÎAâB).
- Applying a random gate G(2) at Node B.
- Transferring the state back from B to A (via channel ÎBâA).
- Inverse Operation: After m bounces, a final gate G(inv) is applied at Node A. G(inv) is constructed as the inverse of the product of all preceding random gates, plus a final ending gate PA.
- Measurement: The final state is measured using a two-component POVM {E, 1 - E}. The binary outcome (b) is recorded and negated if the ending gate PA was the Pauli X-gate (a post-processing trick).
- Data Averaging: The procedure is repeated Nm times for a fixed sequence length m to calculate the mean outcome bm.
- Fidelity Fitting: The set of mean outcomes {bm} across varying lengths m is fitted to the exponential decay model bm = A * fm to extract the network link fidelity f.
- Multi-Node Extension: The protocol is generalized for K nodes (A1âŠAK) by performing random operations at all intermediate nodes during the forward and backward state transfer path.
Commercial Applications
Section titled âCommercial ApplicationsâNetwork Benchmarking is a critical tool for the engineering and operational management of emerging quantum networks.
- Quantum Internet Infrastructure: Provides the necessary certification tool to verify that quantum links meet required fidelity thresholds, crucial for advancing network stages (e.g., from Quantum Memory Network stage onward).
- Network Diagnostics and Routing: The multi-node protocol serves as a high-fidelity, quantum-aware âpingâ operation, allowing network management software to dynamically assess the quality of communication paths for routing decisions.
- Hardware Development and Optimization: Allows engineers developing quantum processing nodes (e.g., NV-centers, ion traps) to isolate and characterize the performance of the communication channel (teleportation or direct transmission) separate from local gate and SPAM errors.
- Distributed Quantum Computing: Essential for quantifying the reliability of state transfer operations, which are fundamental building blocks for distributed quantum algorithms and networked quantum computation.
- Quantum Communication Protocols: Can be adapted to benchmark other quality parameters, such as the unitarity or the fidelity of specific interleaved operations, aiding in the development of robust communication protocols.
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.