Designing a cavity-mediated quantum cphase gate between NV spin qubits in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-05-16 |
| Journal | Physical review. B./Physical review. B |
| Authors | Guido Burkard, V. O. Shkolnikov, D. D. Awschalom |
| Institutions | University of Konstanz, University of Chicago |
| Citations | 16 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Cavity-Mediated Quantum CPHASE Gate in Diamond
Section titled âTechnical Documentation & Analysis: Cavity-Mediated Quantum CPHASE Gate in DiamondâThis document analyzes the requirements and achievements detailed in the research paper, âA cavity-mediated quantum CPHASE gate between NV spin qubits in diamond,â and maps them directly to 6CCVDâs advanced MPCVD diamond material solutions.
Executive Summary
Section titled âExecutive SummaryâThe research validates a theoretical and numerical model for achieving a universal, ultra-fast two-qubit Controlled-Phase (CPHASE) gate using Nitrogen-Vacancy (NV) centers embedded in a common optical cavity within diamond.
- Universal QIP: The CPHASE gate, combined with standard single-qubit operations, forms a universal set for arbitrary quantum computation.
- Ultra-Fast Operation: Gate times ($\tau$) of approximately 200 ns are achieved, nearly three orders of magnitude faster than typical NV spin coherence times ($T_{2} \sim 10$ ”s).
- Material Requirement: Successful implementation relies critically on high-quality diamond substrates suitable for integrated Cavity Quantum Electrodynamics (QED) architectures.
- Critical Q Factor: The scheme requires optical cavities with a quality factor $Q \sim 10^{5}$ to maintain a photon loss rate compatible with the 200 ns gate time.
- Scalability: The architecture is inherently scalable, limited only by the extension of the common optical cavity, enabling coupling between distant NV centers.
- 6CCVD Value Proposition: 6CCVD provides the ultra-low-defect, high-purity Single Crystal Diamond (SCD) required for fabricating high-Q photonic crystal cavities and maximizing NV spin coherence times.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the numerical simulations and physical requirements detailed in the paper:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target Gate Time ($\tau$) | 200 | ns | CPHASE operation speed |
| Required Spin Coherence Time ($T_{2}$) | 10 | ”s | Minimum required coherence time |
| Required Cavity Quality Factor ($Q$) | 105 | Dimensionless | Minimum Q factor for $\tau \sim 200$ ns |
| Maximum Laser-NV Coupling ($g_{L,max}$) | 24 | MHz | Used in numerical simulation |
| NV-Cavity Coupling ($g_{c}$) | 100 | MHz | Used in numerical simulation |
| Laser Detuning ($\delta_{L}$) | 1640 | MHz | Used in numerical simulation |
| Cavity Detuning ($\delta_{c}$) | 400 | MHz | Used in numerical simulation |
| GS Zero-Field Splitting ($D_{gs}$) | 2.88 | GHz | NV ground state property |
| ES Zero-Field Splitting ($D_{es}$) | 1.44 | GHz | NV excited state property |
| Operating Temperature | < 20 | K | Required for excited state level stability |
| Magnetic Field ($B_{0}$) | $\sim 1000$ | G | Near GS level crossing for qubit basis selection |
Key Methodologies
Section titled âKey MethodologiesâThe proposed CPHASE gate relies on specific material integration and operational parameters:
- Substrate Preparation: Utilizing high-quality diamond substrates suitable for embedding NV centers and fabricating integrated optical cavities (e.g., photonic crystals).
- Qubit Basis Selection: Applying a magnetic field ($B_{0} \sim 1000$ G) to achieve near-degeneracy between the $m_{s} = 0$ and $m_{s} = -1$ ground states, which serve as the two-qubit basis.
- Raman Transition Coupling: Employing two identical, off-resonant laser fields ($\omega_{L1}, \omega_{L2}$) to couple the NV spin to the common cavity mode via Raman transitions involving the NV excited states (ES).
- Spin-Dependent Scattering: The gate mechanism relies on the difference in zero-field splittings between the GS and ES, leading to unequal scattering matrix elements for the $m_{s} = 0$ and $m_{s} = -1$ states.
- Adiabatic Control: Implementing laser pulses with long ramp times (e.g., 133 ns FWHM Gaussian convolution) to ensure adiabatic switching, preventing residual population in the excited state after the gate operation.
- Gate Validation: The resulting unitary operation is confirmed to be a CNOT/CPHASE gate through the calculation of Makhlin invariants ($G_{1}=0, G_{2}=1$).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful implementation and scaling of this cavity-mediated quantum gate require diamond materials optimized for both long spin coherence ($T_{2}$) and high-Q optical integration. 6CCVD is uniquely positioned to supply the necessary substrates and customization services.
Applicable Materials
Section titled âApplicable MaterialsâThe requirement for long $T_{2}$ times ($\sim 10$ ”s) and the need to fabricate high-Q photonic crystal cavities directly within the diamond lattice mandate the use of the highest purity, lowest strain material available.
| Material Solution | 6CCVD Grade | Relevance to Research |
|---|---|---|
| Single Crystal Diamond (SCD) | Optical Grade (Ultra-High Purity) | Essential for maximizing $T_{2}$ coherence times by minimizing nitrogen and defect incorporation. Low strain is critical for stable ES levels and high-Q cavity performance. |
| Polycrystalline Diamond (PCD) | N/A | PCD is unsuitable for this application due to high defect density, grain boundaries, and high optical loss, which would destroy the required $Q \sim 10^{5}$. |
| Boron-Doped Diamond (BDD) | N/A | BDD is typically used for electrochemical or thermal applications; the high boron concentration would quench the NV spin coherence. |
Customization Potential for QIP Architectures
Section titled âCustomization Potential for QIP ArchitecturesâThe integration of NV centers with photonic crystal cavities requires precise material engineering and post-growth processing capabilities, all offered by 6CCVD:
- Custom Dimensions: 6CCVD supplies SCD plates and wafers up to 125mm in size, enabling the scalable fabrication of large arrays of coupled NV-cavity systems, as suggested for future architectures.
- Thickness Control: We provide SCD layers from 0.1 ”m up to 500 ”m, allowing researchers to select the optimal thickness for subsequent etching processes required for photonic crystal fabrication.
- Surface Finish: Achieving high-Q factors in integrated cavities requires extremely low surface roughness. 6CCVD offers SCD polishing down to Ra < 1 nm, ensuring minimal scattering loss during cavity fabrication.
- Metalization Services: While the CPHASE gate itself is optical, scalable QIP architectures often require integrated microwave or RF control lines. 6CCVD offers in-house custom metalization (including Au, Pt, Ti, W, Cu) for creating necessary control electrodes or gates.
- Substrate Engineering: For architectures requiring NV centers near the surface, 6CCVD can provide substrates with controlled NV implantation and annealing protocols, or high-quality SCD layers grown on thick substrates (up to 10mm).
Engineering Support
Section titled âEngineering SupportâThe successful replication and extension of this researchâespecially concerning the trade-off between cavity $Q$ factor, detuning ($\delta_{c}$), and gate speedârequires deep material expertise.
6CCVDâs in-house PhD team specializes in the growth and characterization of quantum-grade diamond. We can assist researchers in material selection, optimizing defect density, and minimizing strain for similar Cavity QED and Quantum Gate projects. Our expertise ensures the supplied SCD substrates meet the stringent requirements for long $T_{2}$ coherence and high-fidelity photonic integration.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
While long spin coherence times and efficient single-qubit quantum control\nhave been implemented successfully in nitrogen-vacancy (NV) centers in diamond,\nthe controlled coupling of remote NV spin qubits remains challenging. Here, we\npropose and analyze a controlled-phase (CPHASE) gate for the spins of two NV\ncenters embedded in a common optical cavity and driven by two off-resonant\nlasers. In combination with previously demonstrated single-qubit gates, CPHASE\nallows for arbitrary quantum computations. The coupling of the NV spin to the\ncavity mode is based upon Raman transitions via the NV excited states and can\nbe controlled with the laser intensities and relative phase. We find\ncharacteristic laser frequencies at which the scattering amplitude of a laser\nphoton into the cavity mode is strongly dependent on the NV center spin. A\nscattered photon can be reabsorbed by another selectively driven NV center and\ngenerate a conditional phase (CPHASE) gate. Gate times around 200 ns are within\nreach, nearly three orders of magnitude shorter than typical NV spin coherence\ntimes of around 10 microseconds. The separation between the two interacting NV\ncenters is only limited by the extension of the cavity.\n