Experimental Protection of Two-Qubit Quantum Gates against Environmental Noise by Dynamical Decoupling
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2015-09-10 |
| Journal | Physical Review Letters |
| Authors | Jingfu Zhang, Dieter Suter |
| Institutions | TU Dortmund University |
| Citations | 42 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Protected 2-Qubit Gates in NV Diamond
Section titled āTechnical Documentation & Analysis: Protected 2-Qubit Gates in NV DiamondāExecutive Summary
Section titled āExecutive SummaryāThis research successfully demonstrates the protection of 2-qubit quantum gates in a hybrid Nitrogen-Vacancy (NV) center system using Dynamical Decoupling (DD). The findings validate the feasibility of high-fidelity quantum operations in diamond-based registers, directly aligning with 6CCVDās expertise in high-purity MPCVD diamond materials.
- Core Achievement: Implementation of a protected Controlled Rotation (CR) 2-qubit gate in an NV center, combining the electron spin (control) and the nitrogen nuclear spin (target).
- Decoherence Mitigation: Dynamical Decoupling (DD) was applied to the rapidly decohering electron spin in parallel with the long-duration nuclear spin gate operation.
- Performance Gain: The electron spin dephasing time (Tā) was dramatically extended from approximately 34 Āµs (unprotected) to 2.4 ms (protected), approaching the longitudinal relaxation limit (Tā ā 3.5 ms).
- Material Requirement: The experiment relied on a high-purity, Ā¹Ā²C enriched diamond substrate to minimize environmental noise from native Ā¹Ā³C nuclear spins, a critical material specification offered by 6CCVD.
- Scalability: The demonstrated protocol is applicable to arbitrary 2-qubit gates and is scalable to larger quantum registers and other hybrid quantum systems.
- Fidelity: A gate fidelity of F = 0.90 was achieved for the identity operation ($\theta=0$), limited primarily by longitudinal relaxation and experimental imperfections.
Technical Specifications
Section titled āTechnical SpecificationsāThe following hard data points were extracted from the experimental protocol and results:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Operating Environment | Room Temperature | Ā°C | Standard operational environment. |
| Substrate Type | Ā¹Ā²C Enriched Diamond | N/A | Used to minimize Ā¹Ā³C nuclear spin decoherence. |
| Magnetic Field Strength (B) | ~87 | G | Applied along the NV symmetry axis. |
| Zero-Field Splitting (D) | 2.87 | GHz | Intrinsic NV center property. |
| Electron Spin Tā (Unprotected) | ~34 | Āµm | Dephasing time without DD pulses. |
| Electron Spin Tā (Protected) | ~2.4 | ms | Extended dephasing time, limited by Tā. |
| Longitudinal Relaxation Time (Tā) | ~3.5 | ms | Measured relaxation limit. |
| DD Pulse Rabi Frequency (MW) | ~11 | MHz | Used for hard Ļ-pulses on the electron spin. |
| Nuclear Spin Rabi Frequency (Ī©/2Ļ) | 5.60 to 9.05 | kHz | Range for target qubit transitions (long gate duration). |
| Maximum Gate Fidelity (F) | 0.90 | N/A | Measured for the identity gate ($\theta=0$). |
Key Methodologies
Section titled āKey MethodologiesāThe experiment successfully combined material purity, defect engineering, and advanced pulse sequences to achieve high-fidelity quantum control:
- Material Foundation: A high-purity, isotopically enriched Ā¹Ā²C diamond sample was selected to suppress the decoherence channel caused by the native Ā¹Ā³C nuclear spin bath.
- Qubit System Definition: The NV center was utilized as a hybrid 2-qubit register: the electron spin (S=1) served as the control qubit (Qubit 1), and the nitrogen nuclear spin (I=1) served as the target qubit (Qubit 2).
- Gate Selection: The Controlled Rotation (CR) gate was implemented, chosen because the slow Rabi frequency of the nuclear spin results in a long gate duration, making it highly susceptible to electron spin decoherence.
- Dynamical Decoupling (DD) Sequence: Hard Ļ-pulses (MW pulses) were applied to the electron spin (Qubit 1) in parallel with the RF pulses driving the nuclear spin rotation (Qubit 2).
- Synchronization and Segmentation: The control field driving the nuclear spin gate was split into segments inserted into the delays of the DD sequence. These segments were carefully adjusted to account for the DD pulses interchanging the computational basis states (|0) ā |1)).
- Readout Protocol: Quantum state tomography was performed on the control qubit (electron spin) after the gate operation. Readout required a selective MW pulse to transfer the nuclear spin information back to the electron spin for measurement.
6CCVD Solutions & Capabilities
Section titled ā6CCVD Solutions & Capabilitiesā6CCVD is uniquely positioned to supply the high-specification MPCVD diamond materials required to replicate, extend, and scale this critical quantum computing research. Our capabilities directly address the need for ultra-high purity, isotopic control, and integrated device fabrication.
| Research Requirement | 6CCVD Applicable Materials & Services | Technical Value Proposition |
|---|---|---|
| Ultra-Low Decoherence Substrate (Need for Ā¹Ā²C enrichment) | Optical Grade Single Crystal Diamond (SCD). We offer ultra-low nitrogen concentration (< 1 ppb) and can provide high isotopic purity (e.g., 99.999% Ā¹Ā²C enrichment) upon custom order. | Guarantees minimal spin bath noise (e.g., Ā¹Ā³C), essential for achieving and exceeding the millisecond Tā coherence times demonstrated in this work. |
| Precise Wafer Dimensions (Required for device integration) | Custom Dimensions and Thickness Control. SCD wafers available from 0.1 Āµm up to 500 Āµm thick. Substrates available up to 10 mm thick. | Allows engineers to select the optimal thickness for maximizing NV center creation depth, minimizing strain, and integrating into specific microwave resonator geometries. |
| High-Fidelity Control Integration (Need for MW/RF contacts) | Integrated Metalization Services. We offer in-house deposition of standard contacts including Au, Pt, Pd, Ti, W, and Cu. | Enables rapid prototyping and fabrication of high-frequency coplanar waveguides (CPW) directly on the diamond surface, crucial for delivering the 11 MHz Rabi frequency DD pulses. |
| Surface Quality (Essential for low-loss optical readout) | Ultra-Smooth Polishing. SCD surfaces are polished to an industry-leading roughness of Ra < 1 nm. | Minimizes surface defects that can introduce decoherence or scattering losses during laser initialization and optical readout steps. |
| Scaling and Advanced Protocols (Generalizing to KDD sequences) | Expert Engineering Support. 6CCVDās in-house PhD team specializes in material selection, defect engineering (NV creation), and crystal orientation for advanced quantum sensing and computing projects. | Provides authoritative guidance on optimizing material specifications (e.g., strain management, specific doping profiles) necessary for implementing complex, multi-qubit DD sequences like KDD [25]. |
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting of the electronic and nuclear spins of a nitrogen-vacancy center in diamond. The results show that processing is compatible with protection: The dephasing time was extended almost to the limit given by the longitudinal relaxation time of the electron spin.
Tech Support
Section titled āTech SupportāOriginal Source
Section titled āOriginal SourceāReferences
Section titled āReferencesā- 2000 - Quantum Computation and Quantum Information
- 2008 - Quantum Computing: A Short Course from Theory to Experiment