Long-range photon-mediated gate scheme between nuclear spin qubits in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2016-01-04 |
| Journal | Physical review. B./Physical review. B |
| Authors | Adrian Auer, Guido Burkard |
| Institutions | University of Konstanz |
| Citations | 11 |
| Analysis | Full AI Review Included |
Technical Documentation: Photon-Mediated Quantum Gates in Diamond NV Centers
Section titled âTechnical Documentation: Photon-Mediated Quantum Gates in Diamond NV Centersâ6CCVD Analysis of arXiv:1507.08468v1: Long-range photon-mediated gate scheme between nuclear spin qubits in diamond
Executive Summary
Section titled âExecutive SummaryâThis research proposes a theoretical framework for implementing a universal controlled-Z (CZ) quantum gate between two distant nitrogen nuclear spin qubits embedded in NV centers within diamond. The scheme leverages virtual cavity photon exchange mediated by external lasers.
- Ultra-Fast Gate Speed: The predicted gate operation time ($T_{\text{CZ}}$) is below 100 nanoseconds (ns), achieving speeds four orders of magnitude faster than the measured nuclear spin decoherence time ($T_2 \approx 5 \text{ ms}$).
- Long-Range Coupling: The mechanism enables deterministic coupling between distant NV centers, a fundamental requirement for scalable quantum information processing.
- Mechanism: The gate relies on nuclear-spin dependent scattering of laser photons into a common optical cavity mode, facilitated by the hyperfine interaction difference ($\delta A$) between the NV ground and excited states.
- Material Requirement: Successful implementation demands ultra-high quality Single Crystal Diamond (SCD) integrated with high-Q optical cavities.
- Q-Factor Demand: Achieving fast gate times ($T_{\text{CZ}} \approx 20 \text{ ns}$) requires cavity quality factors ($Q$) in the range of $10^6$ to $10^7$.
- Isotope Versatility: The scheme is validated for both the intrinsic nitrogen isotopes: ${}^{14}\text{N}$ (Spin I=1) and ${}^{15}\text{N}$ (Spin I=1/2).
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points are extracted from the analysis, highlighting the critical physical parameters required for the proposed quantum gate.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Predicted Gate Time ($T_{\text{CZ}}$) | < 100 | ns | Universal Controlled-Z (CZ) gate |
| Required Cavity Q-Factor | $10^6$ - $10^7$ | Dimensionless | For $T_{\text{CZ}} \approx 20 \text{ ns}$ operation |
| Nuclear Spin Decoherence Time ($T_2$) | $\approx 5$ | ms | Measured at room temperature |
| Magnetic Field (B) | 120 | G | Used for theoretical calculations |
| Electron Gyromagnetic Ratio ($\gamma_{\text{e}}/2\pi$) | 2.803 | MHz/G | NV electron spin parameter |
| ${}^{14}\text{N}$ Nuclear Spin (I) | 1 | Dimensionless | Qubit candidate |
| ${}^{15}\text{N}$ Nuclear Spin (I) | 1/2 | Dimensionless | Qubit candidate |
| ${}^{14}\text{N}$ Ground State Hyperfine ($A_{\text{gs}}/2\pi$) | -2.2 | MHz | Longitudinal coupling |
| ${}^{15}\text{N}$ Excited State Hyperfine ($A_{\text{es}}/2\pi$) | 61 | MHz | Longitudinal coupling |
| Laser Rabi Frequency ($\Omega/2\pi$) | 100 - 400 | MHz | Used for coupling strength calculations (Fig. 3) |
| Energy Gap (Ground to Excited State, $E_{\text{g}}$) | 1.945 | eV | NV orbital transition energy |
Key Methodologies
Section titled âKey MethodologiesâThe theoretical implementation of the long-range CZ gate relies on advanced quantum optics and perturbation theory applied to the NV-cavity system.
- System Modeling: The combined system of a single NV center, an optical cavity, and an external laser field is described using a time-dependent Hamiltonian $H(t)$, incorporating electron ($H_{\text{e}}$), nuclear ($H_{\text{n}}$), and hyperfine ($H_{\text{hf}}$) interactions.
- Hyperfine Dependence: The analysis leverages the significant difference ($\delta A$) in hyperfine coupling between the NV ground and excited states (excited state coupling is $\approx 20$ times stronger). This difference forms the basis of the nuclear-spin dependent scattering effect.
- Schrieffer-Wolff (SW) Transformation (First Pass): A SW transformation is applied to eliminate the intermediate virtual transition to the excited state, resulting in an effective ground-state Hamiltonian $H^{(\text{gs})}$. This step isolates the nuclear-spin dependent scattering process.
- Two-Qubit Extension: The model is extended to two distant NV centers (NV 1 and NV 2) coupled to a common cavity mode, each driven by an individual laser.
- Schrieffer-Wolff Transformation (Second Pass): A second SW transformation is applied to eliminate the virtual cavity photon mode, decoupling the nuclear spin degree of freedom from the cavity field.
- Effective Hamiltonian Derivation: This yields an effective Hamiltonian $H_{\text{eff}}$ containing the two-qubit interaction term $H_{\text{int}} = -g_{12}|11\rangle\langle 11|$, where $g_{12}$ is the effective coupling strength.
- Gate Implementation: The universal CZ gate is implemented by setting the interaction time $T_{\text{CZ}} = \pi/g_{12}$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe realization of this ultra-fast quantum gate scheme requires diamond materials with exceptional purity, precise surface quality, and integrated fabrication capabilities. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond substrates and engineering services.
| Research Requirement | 6CCVD Solution & Capability | Technical Advantage for Quantum Applications |
|---|---|---|
| Ultra-High Purity Substrates (Essential for long $T_2$ coherence) | Optical Grade Single Crystal Diamond (SCD) | Provides the lowest native defect density and highest chemical purity, crucial for maximizing the nuclear spin coherence time ($T_2$) well beyond the required 5 ms. |
| Integrated High-Q Cavities (Requires smooth surfaces, $Q \ge 10^6$) | Precision Polishing (Ra < 1 nm for SCD) | Ultra-smooth surfaces are mandatory for minimizing optical scattering losses, enabling the fabrication of high-Q photonic crystal cavities in bulk diamond, as referenced in the paper. |
| Custom Device Geometry (For coupling and strain control) | Custom Dimensions and Thickness (SCD up to 500 ”m thick; Plates/wafers up to 125 mm PCD) | Allows engineers to specify exact wafer dimensions and thicknesses required for deep etching, focused ion beam (FIB) structuring, and integration into specific optical setups. |
| Electrical/Magnetic Control (Requires electrodes for B-field and Rabi driving $\Omega$) | In-House Custom Metalization (Au, Pt, Pd, Ti, W, Cu) | Enables the deposition of high-quality, low-loss metal contacts and micro-wires directly onto the diamond surface for precise control of external magnetic fields and microwave excitation. |
| Isotopic Control (For ${}^{14}\text{N}$ or ${}^{15}\text{N}$ qubits) | Custom Material Doping and Growth | While the paper focuses on intrinsic N, 6CCVD can provide substrates with controlled nitrogen incorporation or isotopically enriched diamond (e.g., low ${}^{13}\text{C}$ content) to further extend $T_2$ coherence times. |
Applicable Materials
Section titled âApplicable MaterialsâTo replicate or extend this research into a functional device, researchers require:
- Optical Grade Single Crystal Diamond (SCD): Necessary for hosting isolated, high-coherence NV centers and supporting high-Q optical structures.
- Custom Thickness SCD: To optimize the coupling efficiency between the NV centers and the integrated photonic cavity mode.
Customization Potential
Section titled âCustomization Potentialâ6CCVD offers full customization critical for scaling this quantum architecture:
- Precision Laser Cutting: For creating specific chip sizes and geometries required for mounting and optical alignment.
- Multi-Layer Metalization Stacks: We provide complex metal stacks (e.g., Ti/Pt/Au) tailored for robust electrical contacts and superconducting circuits if required for cryogenic operation.
- Substrate Preparation: We deliver substrates with specified crystallographic orientation and low surface roughness (Ra < 1 nm) essential for subsequent lithography and etching processes used in cavity fabrication.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house team of PhD material scientists and engineers specializes in MPCVD growth parameters optimized for quantum applications. We provide authoritative support for material selection, defect engineering, and surface preparation necessary for NV-based quantum computing and quantum memory projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Defect centers in diamond are exceptional solid-state quantum systems that\ncan have exceedingly long electron and nuclear spin coherence times. So far,\nsingle-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a\nnitrogen-vacancy (NV) center electron spin, and entanglement between nearby\nnitrogen nuclear spins have been demonstrated. Here, we develop a scheme to\nimplement a universal two-qubit gate between two distant nitrogen nuclear\nspins. Virtual excitation of an NV center that is embedded in an optical cavity\ncan scatter a laser photon into the cavity mode; we show that this process\ndepends on the nuclear spin state of the nitrogen atom. If two NV centers are\nsimultaneously coupled to a common cavity mode and individually excited,\nvirtual cavity photon exchange can mediate an effective interaction between the\nnuclear spin qubits, conditioned on the spin state of both nuclei, which\nimplements a universal controlled-$\textit{Z}$ gate. We predict operation times\nbelow 100 nanoseconds, which is several orders of magnitude faster than the\ndecoherence time of nuclear spin qubits in diamond.\n