Opportunities for Long-Range Magnon-Mediated Entanglement of Spin Qubits via On- and Off-Resonant Coupling
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-10-21 |
| Journal | PRX Quantum |
| Authors | Masaya Fukami, Denis R. Candido, David D. Awschalom, Michael E. Flatté, Masaya Fukami |
| Institutions | Eindhoven University of Technology, University of Chicago |
| Citations | 90 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Core Achievement: Predicted strong, long-distance (> 2 ”m) entanglement between Nitrogen-Vacancy (NV) spin qubits mediated by magnon modes in Yttrium Iron Garnet (YIG) nanostructures.
- Scalability Solution: This magnon-mediated coupling provides a pathway for scalable two-qubit gates over optically resolvable micron distances, overcoming a major challenge for solid-state quantum computing platforms.
- High Performance (YIG Bar): Optimized YIG bar geometry yields exceptional performance, including single-magnon cooperativity (C) exceeding 104 under on-resonant conditions.
- High Fidelity Gate: The off-resonant virtual-magnon exchange protocol achieves high fidelity (F â 0.95 at 70 mK) and is robust against thermal magnon fluctuations up to T â 150 mK.
- Fast Gate Operation: The on-resonant transduction protocol offers faster gate operation but requires lower temperatures and extremely low Gilbert damping (α †10-7) to outperform the virtual-magnon exchange.
- Gate to Decoherence Ratio (GDR): Predicted useful entangling gates with GDR > 700 for NV centers separated by 2.2 ”m in the YIG bar system.
- Methodology: Results are based on a realistic Hamiltonian formalism incorporating dipole and exchange interactions, simulated using the Lindblad master equation at finite temperatures.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV-NV Separation (Max Useful) | > 2.2 | ”m | Distance for useful entangling gate |
| Required Operating Temperature (T) | †150 | mK | Maximum temperature for useful entanglement |
| NV Center Coherence Time (T2*) | 1 | ms | Used in simulation |
| NV Zero-Field Splitting (DNV) | 2Ï x 2.877 | GHz | NV center property |
| YIG Saturation Magnetization (Ms) | 245.8 | mT/”0 | YIG material property |
| YIG Bar Thickness (d) | 5 | nm | Optimized geometry example |
| YIG Bar Length (l) | 3 | ”m | Optimized geometry example |
| Single-Magnon Cooperativity (C) | â„ 104 | Dimensionless | YIG bar, on-resonant coupling |
| Gate to Decoherence Ratio (GDR) | > 700 | Dimensionless | YIG bar, 2.2 ”m separation, off-resonant |
| Effective NV-NV Coupling (geff) | 2Ï x 90 | kHz | YIG bar, 2.2 ”m separation, off-resonant |
| Virtual-Magnon Fidelity (F) | 0.95 | Dimensionless | T = 70 mK, off-resonant protocol |
| Transduction Fidelity (F) | 0.81 | Dimensionless | T = 70 mK, on-resonant protocol |
| Gilbert Damping (α) | 10-5 | Dimensionless | Value used for primary simulations |
Key Methodologies
Section titled âKey Methodologiesâ- Dipole-Exchange Magnon Formalism: Employed a complete Hamiltonian formalism to describe dipole-exchange magnons in YIG nanostructures, accounting for both magnetic dipole and quantum exchange interactions.
- Magnon Mode Diagonalization: Diagonalized the magnon Hamiltonian for two geometriesâinfinitely long YIG waveguides and finite YIG barsâusing the Bogoliubov transformation to obtain normal magnon modes and frequencies.
- NV-Magnon Coupling Calculation: Derived the NV-magnon coupling strength (g”) by applying the Bogoliubov transformation to the interaction Hamiltonian, focusing on the lowest energy magnon band (n, m) = (0, 0).
- Effective NV-NV Hamiltonian: Used the Schrieffer-Wolff transformation to derive the effective NV-NV interaction (geff) for the off-resonant virtual-magnon exchange protocol.
- Lindblad Master Equation Simulation: Simulated the time evolution of the hybrid system (two NV centers and one magnon mode) at finite temperatures (T †300 mK) using the Lindblad master equation.
- Protocol Comparison: Compared two entanglement protocolsâon-resonant transduction (Jaynes-Cummings model) and off-resonant virtual-magnon exchangeâby evaluating entanglement negativity, Bell inequality violation, and fidelity under varying Gilbert damping (α) and coherence times (T2*).
Commercial Applications
Section titled âCommercial Applicationsâ- Quantum Computing (Qubit Interconnects): The primary application is enabling scalable, fault-tolerant quantum computers by providing fast, high-fidelity, long-range (micron scale) two-qubit gates between solid-state spin qubits (NV centers).
- On-Chip Quantum Networks: Magnon waveguides serve as efficient, low-loss quantum buses for connecting distant quantum nodes on a single chip, essential for building integrated quantum processors.
- Hybrid Quantum Systems: Provides optimized design parameters (YIG dimensions, NV placement) for integrating diamond-based spin qubits with ferromagnetic materials, accelerating the development of hybrid quantum architectures.
- Cryogenic Magnonics Research: The work guides experimental efforts in ultra-low temperature (millikelvin) magnonics, particularly in optimizing YIG film quality (low Gilbert damping) necessary for quantum coherence applications.
- Quantum Sensing and Relaxometry: The detailed analysis of NV spin coupling to magnetic fringe fields and magnon-induced decoherence informs the design of high-sensitivity NV-based magnetometers operating near ferromagnetic films.
View Original Abstract
The ability to manipulate entanglement between multiple spatially separated qubits is essential for quantum-information processing. Although nitrogen-vacancy (NV) centers in diamond provide a promising qubit platform, developing scalable two-qubit gates remains a well-known challenge. To this end, magnon-mediated entanglement proposals have attracted attention due to their long-range spin-coherent propagation. Optimal device geometries and gate protocols of such schemes, however, have yet to be determined. Here we predict strong long-distance (>ÎŒm) NV-NV coupling via magnon modes with cooperativities exceeding unity in ferromagnetic bar and waveguide structures. Moreover, we explore and compare on-resonant transduction and off-resonant virtual-magnon exchange protocols, and discuss their suitability for generating or manipulating entangled states at low temperatures (T 150mK) under realistic experimental conditions. This work will guide future experiments that aim to entangle spin qubits in solids with magnon excitations.