Protocol for Generating Optical Gottesman-Kitaev-Preskill States with Cavity QED
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-04-27 |
| Journal | Physical Review Letters |
| Authors | Jacob Hastrup, Ulrik L. Andersen |
| Institutions | Technical University of Denmark |
| Citations | 39 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: GKP State Generation via Diamond Cavity QED
Section titled âTechnical Documentation & Analysis: GKP State Generation via Diamond Cavity QEDâExecutive Summary
Section titled âExecutive Summaryâ- Core Application: This research proposes a method using Cavity Quantum Electrodynamics (QED) to generate Gottesman-Kitaev-Preskill (GKP) states, which are fundamental non-Gaussian resources for fault-tolerant optical continuous-variable quantum computing.
- Material Platform: The central non-Gaussian element is a 3-level system realizable using solid-state platforms, specifically citing diamond color centers (e.g., Nitrogen-Vacancy (NV) or Silicon-Vacancy (SiV) centers).
- Performance Gap: Achieving the required fault-tolerance level demands > 10 dB of effective squeezing. Current state-of-the-art systems ($C_0 \approx 200$) only yield 4.4 dB (cavity-only) or 5.5 dB (with breeding).
- Material Requirement: To reach the 10 dB threshold, systems require Internal Cooperativity ($C_0$) exceeding 1000 and high Escape Efficiency ($\eta \approx 0.99$), necessitating ultra-high purity, low-loss diamond substrates.
- 6CCVD Value Proposition: 6CCVD specializes in high-purity, low-birefringence Single Crystal Diamond (SCD) with superior surface quality (Ra < 1 nm), providing the ideal foundation for integrating high-cooperativity microcavities and stable, high-fidelity color centers.
- Methodology: The protocol involves iterative reflection of squeezed states off the QED cavity, optionally combined with a cat breeding protocol to significantly reduce the required $C_0$ (from $C_0 \approx 110$ down to $C_0 \approx 25$ for 10 dB squeezing).
Technical Specifications
Section titled âTechnical SpecificationsâThe following data points summarize the performance requirements and achievements detailed in the analysis:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target Effective Squeezing | > 10 | dB | Required for GKP fault-tolerance [6, 7, 23]. |
| State-of-the-Art Internal Cooperativity ($C_0$) | ~200 | Dimensionless | Demonstrated in current diamond/quantum dot systems [29, 32]. |
| Achievable Squeezing (Current $C_0 \approx 200$) | 4.4 | dB | Cavity-only protocol ($N=1$ interaction). |
| Achievable Squeezing (Current $C_0 \approx 200$) | 5.5 | dB | Using cat breeding protocol ($M=2$ rounds). |
| Required $C_0$ for 10 dB Squeezing (Cavity Only) | ~110 | Dimensionless | Requires $N=3$ interactions and Escape Efficiency $\eta = 0.997$. |
| Required $C_0$ for 10 dB Squeezing (Breeding) | ~25 | Dimensionless | Requires $M=3$ breeding rounds and Escape Efficiency $\eta \approx 0.98$. |
| Squeezing Improvement per Peak Doubling | 3 | dB | Achieved by doubling the number of peaks ($N_{peaks}$) in the large $N_{peaks}$ limit. |
| Polishing Requirement | Ra < 1 | nm | Implied requirement for minimizing internal loss ($\kappa_l$) and maximizing Escape Efficiency ($\eta$). |
Key Methodologies
Section titled âKey MethodologiesâThe GKP state generation relies on a highly controlled Cavity QED system and iterative quantum operations:
- QED System Foundation: The system utilizes a single-mode optical cavity containing a 3-level quantum system (e.g., a diamond color center). The cavity resonance is tuned to match the $\vert 1 \rangle \leftrightarrow \vert e \rangle$ transition of the 3-level system.
- Controlled Phase Rotation: The cavity is engineered with a slightly transparent mirror ($\kappa_c$) to couple to an external field. When the quantum system is prepared in a superposition state ($\vert + \rangle$), the reflected optical field experiences a controlled phase rotation ($R_c$).
- Iterative GKP Generation: An initial displaced squeezed vacuum state is input and reflected off the cavity. Repeating this process $N$ times yields an approximate GKP state with $2^N$ peaks.
- Performance Quantification: The quality of the system is defined by the Internal Cooperativity ($C_0 = g^2 / (2\kappa_l \gamma)$) and the Escape Efficiency ($\eta = \kappa_c / \kappa$), where high values are critical for minimizing noise accumulation over multiple interactions.
- Cat Breeding Integration: To mitigate the high $C_0$ demands, the generated squeezed cat states are combined using a cat breeding protocol (Ref. [19]), which involves combining two states on a 50:50 beamsplitter and performing homodyne detection.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâReplicating and advancing this research requires diamond materials optimized for low optical loss, high thermal stability, and precise integration into microcavity structures. 6CCVD provides the necessary material science expertise and fabrication capabilities to meet the stringent demands of high-cooperativity QED systems.
| Research Requirement | 6CCVD Solution & Capability | Technical Advantage for Quantum QED |
|---|---|---|
| High-Fidelity Quantum Emitters | Optical Grade Single Crystal Diamond (SCD) | Ultra-low nitrogen concentration (< 1 ppb) and minimal lattice defects, ensuring stable, high-coherence NV or SiV color centers required for the 3-level system. |
| Maximizing Escape Efficiency ($\eta$) | Precision Polishing (Ra < 1 nm) | SCD surfaces polished to Ra < 1 nm minimize surface scattering ($\kappa_l$) and optical loss, directly enabling the high $\eta$ values (e.g., $\eta \approx 0.99$) required for 10 dB squeezing. |
| Custom Cavity Integration & Thin Films | Custom Thickness Control (0.1 ”m to 500 ”m) | We supply SCD plates and wafers tailored for specific cavity geometries, including ultra-thin membranes (0.1 ”m) for photonic crystal cavities or thick substrates (up to 10 mm) for robust mounting. |
| Microcavity Mirror Fabrication | Advanced Metalization Services | In-house deposition of high-purity metals (Au, Pt, Pd, Ti, W, Cu) for creating high-reflectivity mirrors, electrodes for Stark tuning, or thermal management layers. |
| Scaling and Production | Large-Area PCD Wafers (up to 125 mm) | While SCD is necessary for the QED core, 6CCVD offers large-scale PCD for related quantum photonic components, allowing for future integration and scaling efforts. |
| Global Supply Chain | Global Shipping (DDU/DDP) | Reliable, secure global shipping ensures prompt delivery of sensitive materials to research facilities worldwide. |
Engineering Support
Section titled âEngineering SupportâThe successful implementation of this GKP generation protocol hinges on achieving unprecedented levels of material purity and surface quality to push Internal Cooperativity ($C_0$) above 1000. 6CCVDâs in-house PhD team specializes in material selection and optimization for quantum applications, including defect engineering and surface preparation for high-cooperativity Cavity QED projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Gottesman-Kitaev-Preskill (GKP) states are a central resource for fault-tolerant optical continuous-variable quantum computing. However, their realization in the optical domain remains to be demonstrated. Here we propose a method for preparing GKP states using a cavity QED system that can be realized in several platforms, such as trapped atoms, quantum dots, or diamond color centers. We then further combine the protocol with the previously proposed breeding protocol by Vasconcelos et al. to relax the demands on the quality of the QED system, finding that GKP states with more than 10 dB squeezing could be achieved in near-future experiments.