Quantum Computation Based on Photons with Three Degrees of Freedom

At a Glance

Metadata	Details
Publication Date	2016-05-13
Journal	Scientific Reports
Authors	M. X. Luo, Hui-Ran Li, Hong Lai, Xiaojun Wang
Institutions	Dublin City University, Southwest University
Citations	10
Analysis	Full AI Review Included

Technical Documentation & Analysis: Quantum Computation via 3-DoF Photons in Diamond NV Centers

Executive Summary

This research demonstrates a significant advancement in quantum computing by proposing hybrid Controlled-NOT (CNOT) gates utilizing photons encoded with three independent degrees of freedom (DoFs), mediated by Nitrogen-Vacancy (NV) centers in diamond.

Core Achievement: Implementation of universal quantum logic gates (CNOT) on photonic systems where each photon acts as a 3-qubit system (polarization DoF and two spatial DoFs).
Material Foundation: The scheme relies critically on the long room-temperature coherence time and unique optical properties of the negatively charged NV center embedded in high-quality diamond photonic crystal cavities.
Gate Mechanism: CNOT operations are realized by exploiting optical circular birefringence induced by the NV center coupled to a Whispering-Gallery Mode (WGM) microresonator.
Performance Metrics: Theoretical fidelity for the CNOT gates exceeds 98.4% when the cavity-NV cooperativity (C) is $\ge 50$ and the relative detuning ($\delta\omega/\kappa$) is low.
Scalability: This 3-DoF encoding method provides a useful way to reduce quantum simulation resources, potentially saving two-thirds of the resources required for large qubit systems (e.g., Shor’s algorithm).
6CCVD Relevance: Replication and extension of this work require ultra-high purity, low-strain Single Crystal Diamond (SCD) material, which 6CCVD provides with custom dimensions and surface finishing (Ra < 1nm) essential for high-Q cavity integration.

Technical Specifications

The following hard data points define the physical requirements and performance targets for the NV-cavity system used in the CNOT gate implementation.

Parameter	Value	Unit	Context
NV Center Ground State Splitting	2.88	GHz	Magnetic sublevel splitting
NV Center Spontaneous Decay Rate ($\gamma$)	$2 \times 15$	MHz	Zero Phonon Line (ZPL) is 4% of total emission
Excitation Pulse Duration	2	ns	Must be shorter than the emission timescale
Required Cooperativity (C) for >82.6% Fidelity	$\ge 18$	Dimensionless	Minimum requirement for high-fidelity gates
Required Cooperativity (C) for >98.4% Fidelity	$\ge 50$	Dimensionless	Target for ultra-high fidelity gates
Cavity Damping Rate ($\kappa$)	1 or 10	GHz	Used in high-fidelity calculations
Relative Detuning ($\delta\omega/\kappa$)	$\approx 0.1$	Dimensionless	Required for optimal phase control
Input Photon Wavelength ($\lambda$)	$2\lambda_p$	N/A	Degenerate wavelength from BBO SPDC

Key Methodologies

The proposed quantum computation scheme relies on precise material engineering and controlled optical interactions within the diamond-cavity system.

SPDC Photon Source: Photons are generated using Spontaneous Parametric Down-Conversion (SPDC) via two Type-I $\beta$-barium-borate (BBO) crystal slabs, creating correlated photons with polarization and spatial degrees of freedom.
3-DoF Encoding: Each photon is encoded as a 3-qubit state using its polarization (Left/Right, L/R) and two spatial modes (Internal/External cone, I/E; and Left/Right mode, l/r).
NV Center Integration: A negatively charged NV center is embedded in a diamond lattice coupled to a Microtoroidal Resonator (MTR) supporting a Whispering-Gallery Mode (WGM).
Optical Selection Rule: The NV center is used as an auxiliary resource, realizing A-type optical transitions between the ground state spin triplet ($m_s=0, \pm 1$) and the excited state $|A_2\rangle$.
CNOT Gate Realization: CNOT gates are implemented by leveraging the optical circular birefringence induced by the NV center, which imparts a controlled phase shift (0 or $\pi$) on the reflected photon depending on the NV spin state.
High Cooperativity Requirement: Achieving high fidelity requires maintaining high cooperativity ($C = 2g^2/(\gamma\kappa)$), necessitating high-Q cavities and strong coupling ($g$) between the NV center and the cavity mode.
Deterministic Operation: The auxiliary NV center is disentangled via measurement, allowing for deterministic CNOT operations across the various combinations of polarization and spatial DoFs.

6CCVD Solutions & Capabilities

This research highlights the critical need for high-quality, engineered diamond materials to serve as the host for stable NV centers and the platform for integrated photonic circuits. 6CCVD is uniquely positioned to supply the necessary materials and customization services to replicate and advance this work.

Applicable Materials

To achieve the required long coherence times and high coupling strengths ($C \ge 50$), the research demands diamond with minimal strain and defects.

Primary Material: Optical Grade Single Crystal Diamond (SCD)
- Justification: Our MPCVD SCD offers ultra-low nitrogen and defect concentrations, minimizing decoherence sources and maximizing the room-temperature coherence time ($T_2$) of the NV centers. This purity is essential for stable quantum operation.
Alternative/Doped Material: Boron-Doped Diamond (BDD)
- Potential Extension: While not used in this specific scheme, BDD substrates are available for researchers exploring electrically controlled NV centers or integrated diamond electronics.

Customization Potential

The integration of diamond into MTRs and photonic crystal cavities requires precise dimensional control and high-quality surface preparation. 6CCVD’s custom capabilities directly address these engineering challenges.

Research Requirement	6CCVD Custom Capability	Technical Specification
Host for Photonic Crystal Fabrication	Custom SCD Thickness	SCD wafers available from 0.1µm to 500µm, ideal for thin-film membrane fabrication.
High-Q Cavity Coupling (MTR/WGM)	Ultra-Smooth Polishing	SCD surfaces polished to Ra < 1nm, minimizing optical scattering losses and maximizing cavity Q-factors necessary for high cooperativity (C).
Large-Scale Integration Platform	Custom Dimensions	Plates and wafers available up to 125mm (PCD) and custom sizes for SCD, supporting scalable device prototyping.
Electrical Control Interface	Custom Metalization	In-house deposition of metals (Au, Pt, Ti, W, Cu) for creating electrical contacts or integrated waveguides necessary for advanced NV control.
Substrate Support	Thick Substrates	SCD substrates available up to 10mm thickness for robust handling during complex micro-fabrication processes.

Engineering Support

The successful implementation of hybrid quantum gates requires deep expertise in both material science and quantum optics.

Material Selection: 6CCVD’s in-house PhD engineering team can assist researchers in selecting the optimal SCD grade (purity, orientation, and thickness) to maximize NV center yield and performance for similar diamond-based quantum computation projects.
Fabrication Consultation: We provide technical consultation on surface preparation and metalization schemes compatible with subsequent micro-fabrication steps (e.g., etching diamond membranes for photonic crystals).
Global Logistics: We offer reliable global shipping (DDU default, DDP available) to ensure prompt delivery of custom materials worldwide, supporting international research collaborations.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

Tech Support

Original Source

DOI: https://doi.org/10.1038/srep25977