Dynamical Decoupling of a Geometric Qubit
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2019-11-01 |
| Journal | Physical Review Applied |
| Authors | Yuhei Sekiguchi, Yusuke Komura, Hideo Kosaka, Yuhei Sekiguchi, Yusuke Komura |
| Institutions | Yokohama National University |
| Citations | 18 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Geometric Qubit Decoupling in Diamond
Section titled âTechnical Documentation & Analysis: Geometric Qubit Decoupling in DiamondâThis document analyzes the research demonstrating extended coherence time in a geometric qubit utilizing Nitrogen-Vacancy (NV) centers in diamond, and outlines how 6CCVDâs advanced MPCVD diamond materials and customization capabilities directly support the replication and scaling of this quantum technology.
Executive Summary
Section titled âExecutive Summaryâ- Core Achievement: Demonstration of robust dynamical decoupling (DD) for a geometric qubit based on the spin-1 electron system of a Nitrogen-Vacancy (NV) center in diamond.
- Record Coherence Time: The technique extends the coherence time ($T_2$) of the geometric qubit up to 1.9 ms at room temperature, a value limited primarily by the spin relaxation time ($T_1 \sim 2.6$ ms).
- Error Suppression Mechanism: Error accumulation and population leakage to the ancillary state are spontaneously suppressed by introducing a specific frequency detuning ($\Delta$) during the DD sequence.
- High Fidelity: The additional error per decoupling gate ($\epsilon_{\text{gate}}$) was minimized to $0.03 \pm 0.03%$, enabling the successful operation of 128 high-fidelity gates.
- Material Requirement: The experiment relies on high-purity, low-strain Type-IIa diamond hosting a single $^{14}$N NV center, emphasizing the critical role of the substrate material quality.
- Application: This method provides a crucial route toward realizing holonomic quantum memory and robust quantum sensors capable of operating under ambient conditions.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental demonstration of geometric dynamical decoupling:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Coherence Time ($T_2$) | 1.9 | ms | Achieved with 128 decoupling gates at room temperature. |
| Spin Relaxation Time ($T_1$) | $\sim 2.6$ | ms | Limits the maximum observed $T_2$. |
| Operating Temperature | Room | °C | Ambient conditions. |
| Number of Decoupling Gates ($N$) | Up to 128 | Gates | Fidelity maintained across all gates. |
| Additional Error per Gate ($\epsilon_{\text{gate}}$) | $0.03 \pm 0.03$ | % | Error suppressed by frequency detuning ($\Delta$). |
| Fundamental Error ($\epsilon_0$) | $10.2 \pm 0.6$ | % | Includes state preparation and measurement error. |
| Rabi Frequency ($\Omega$) | $(2\pi) \times 25$ | MHz | Used for the geometric bit-flip gate. |
| Frequency Detuning ($\Delta$) | $(2\pi) \times 130$ | kHz | Introduced to lift degeneracy and suppress leakage. |
| Geomagnetic Field Compensation | $\sim 0.045$ | mT | External magnetic field applied to achieve zero static field. |
| Zero Field Splitting Fluctuation | 74 | kHz/K | Temperature dependence of ZFS, used for thermometry. |
| Temperature Fluctuation | $\pm 0.2$ | K | Corresponds to $\pm 15$ kHz detuning shift. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment successfully implemented geometric dynamical decoupling by carefully controlling the NV center environment and microwave pulse sequence:
- Material Basis: A single NV center (Nitrogen $^{14}$N and a vacancy) was utilized in Type-IIa diamond with natural abundance of Carbon $^{13}$C at room temperature.
- Magnetic Field Compensation: An external permanent magnet was used to carefully compensate the geomagnetic field ($\sim 0.045$ mT), maximizing the electron spin coherence time under a zero static magnetic field.
- Qubit Definition: The geometric qubit was defined using the degenerate $|m_s = \pm 1\rangle$ states of the NV spin-1 electron system, operating within a V-shaped SU(3) three-level structure.
- Gate Implementation: Geometric bit-flip gates were performed using x-polarized microwave pulses at a Rabi frequency ($\Omega$) of $(2\pi) \times 25$ MHz.
- Detuning Introduction: A frequency detuning ($\Delta = (2\pi) \times 130$ kHz) was introduced to lift the degeneracy between the qubit space and the ancillary $|0\rangle$ state, preventing population leakage.
- Decoupling Sequence: The geometric bit-flip gates were periodically operated in a decoupling sequence (up to $N=128$ gates), ensuring the gate interval time ($\tau$) was non-resonant with the detuning ($\tau \neq 2\pi n / \Delta$) to average out angle errors.
- Coherence Analysis: The pure coherence time ($T_2^{\text{pure}}$) was derived from the observed coherence time ($T_2$) and the relaxation time ($T_1$), demonstrating a power scaling consistent with the non-Markovian nature of the nuclear spin bath.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the critical need for ultra-high purity, low-strain diamond substrates to achieve long coherence times necessary for scalable quantum computing and sensing. 6CCVD is uniquely positioned to supply the materials and customization required to replicate and advance this work.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the high-fidelity results achieved in this paper, researchers require diamond with minimal impurities and strain, equivalent to Type-IIa quality.
| Requirement | 6CCVD Solution | Technical Specification |
|---|---|---|
| High Purity Substrate | Optical Grade Single Crystal Diamond (SCD) | Ultra-low nitrogen concentration (< 1 ppb) to minimize decoherence from substitutional nitrogen ($^{14}$N). |
| Low Spin Bath Density | Isotopically Purified SCD | Available with Carbon $^{13}$C depletion (< 0.1%) to suppress inhomogeneous broadening caused by the $^{13}$C nuclear spin bath, potentially extending $T_2$ far beyond the reported 1.9 ms. |
| High-Density NV Arrays | Polycrystalline Diamond (PCD) | For scaling up integrated quantum devices, 6CCVD offers PCD wafers up to 125 mm in diameter, suitable for large-area NV implantation and sensing arrays. |
Customization Potential
Section titled âCustomization PotentialâThe integration of NV centers into practical quantum devices often requires precise geometry and surface engineering, areas where 6CCVD excels:
- Custom Dimensions and Thickness: We provide SCD plates in custom sizes and thicknesses ranging from 0.1 ”m (for surface NV studies) up to 500 ”m (for bulk NV studies, as used here). Substrates up to 10 mm thick are available for high-power optical applications.
- Ultra-Low Roughness Polishing: Achieving high-fidelity optical readout and minimizing surface noise is paramount. 6CCVD guarantees Ra < 1 nm polishing on SCD and Ra < 5 nm on inch-size PCD, ensuring optimal interfaces for microwave and optical coupling.
- Custom Metalization Services: Future integrated quantum circuits will require on-chip microwave delivery structures. 6CCVD offers in-house deposition of standard and custom metal stacks (Au, Pt, Pd, Ti, W, Cu) for fabricating high-Q microwave resonators and contact pads directly onto the diamond surface.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD team can assist researchers in optimizing material selection for similar Holonomic Quantum Memory and High-Sensitivity Quantum Sensing projects:
- Material Optimization: Consultation on selecting the optimal diamond orientation (e.g., [100] or [111]) and purity level to maximize $T_1$ and $T_2$ coherence times for specific NV creation methods (e.g., in-situ growth or post-growth ion implantation).
- Thermal Management: Providing substrates with high thermal conductivity, essential for managing heat generated by high-power microwave pulses or green laser initialization, especially when scaling up gate operations.
- Global Logistics: We offer reliable global shipping (DDU default, DDP available) to ensure rapid delivery of specialized quantum-grade diamond materials worldwide.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Quantum bits or qubits naturally decohere by becoming entangled with uncontrollable environments. Dynamical decoupling is thereby required to disentangle qubits from an environment by periodically reversing the qubit bases, but this causes rotation error to accumulate. Whereas a conventional qubit is rotated within the SU(2) two-level system, a geometric qubit defined in the degenerate subspace of a V-shaped SU(3) three-level system is geometrically rotated via the third ancillary level to acquire a geometric phase. We here demonstrate that, simply by introducing detuning, the dynamical decoupling of the geometric qubit on a spin triplet electron in a nitrogen-vacancy center in diamond can be made to spontaneously suppress error accumulation. The geometric dynamical decoupling extends the coherence time of the geometric qubit up to 1.9 ms, limited by the relaxation time, with 128 decoupling gates at room temperature. Our technique opens a route to holonomic quantum memory for use in various quantum applications requiring sequential operations