Quantum tomography of an entangled three-qubit state in silicon
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-06-07 |
| Journal | Nature Nanotechnology |
| Authors | Kenta Takeda, Akito Noiri, Takashi Nakajima, Jun Yoneda, Takashi Kobayashi |
| Institutions | RIKEN Center for Emergent Matter Science |
| Citations | 101 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Quantum Entanglement in Silicon Qubits
Section titled âTechnical Documentation & Analysis: Quantum Entanglement in Silicon QubitsâThis document analyzes the research paper, âQuantum tomography of an entangled three-spin state in silicon,â focusing on material requirements, experimental limitations, and how 6CCVDâs advanced MPCVD diamond solutions can address these challenges or provide superior alternative platforms for scalable quantum computing.
Executive Summary
Section titled âExecutive SummaryâThe research successfully demonstrates the operation and characterization of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state in a silicon quantum dot array, achieving a state fidelity of 88.0%. This achievement is a critical step toward implementing quantum error correction in silicon-based architectures.
Key takeaways and 6CCVDâs value proposition:
- Achievement: Generation of genuine multipartite entanglement (GHZ state) in a solid-state silicon platform, validating the potential for multiqubit quantum algorithms.
- Core Limitation Identified: The fidelity and coherence times ($T_2$ echo) are limited primarily by magnetic noise (from $^{29}$Si nuclear spins) and charge noise.
- Proposed Solution (Paper): The authors suggest using isotopically enriched $^{28}$Si/SiGe material to reduce magnetic noise.
- 6CCVD Strategic Alternative: 6CCVD specializes in high-purity, isotopically controlled Single Crystal Diamond (SCD), which offers intrinsically superior nuclear spin noise suppression (C-13 concentration control) and is the foundation for high-coherence solid-state qubits (e.g., NV centers).
- Fabrication Synergy: The device relies on complex metalization (Ti/Co/Al micro-magnets) and precise gate structures, capabilities directly offered by 6CCVDâs custom fabrication services.
- Scalability Path: The results confirm the need for ultra-low noise materials, positioning 6CCVDâs SCD as a leading alternative platform for achieving the necessary coherence for scalable quantum error correction.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental results, highlighting key performance metrics and operating conditions:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| GHZ State Fidelity ($F_{GHZ}$) | 0.880 ± 0.007 | Dimensionless | Measured via quantum state tomography. |
| Single-Qubit Fidelity (Q3) | 99.91 | % | Highest fidelity achieved via randomized benchmarking. |
| Average Bell State Fidelity | 94.1 | % | Benchmark for two-qubit CZ gate quality (Q2 and Q3). |
| $T_1$ Relaxation Time (Q1) | 4.30 ± 0.08 | ms | Longest relaxation time measured. |
| $T_2$ Inhomogeneous Dephasing (Q1) | 1.82 ± 0.08 | ”s | Limited by 4.7% $^{29}$Si nuclear spins. |
| $T_2$ echo Hahn Echo Time (Q3) | 45.8 ± 0.4 | ”s | Extended coherence time using echo sequence. |
| External Magnetic Field ($B_{\text{ext}}$) | 0.5275 | T | Applied in-plane to create Zeeman splitting. |
| Zeeman Splitting | ~18 | GHz | Corresponds to $B_{\text{ext}}$. |
| Base Electron Temperature | 40 | mK | Operating temperature in dry dilution refrigerator. |
| Charge Noise $S(f=1 \text{ Hz})$ | 0.2 | ”eV/âHz | Effective low-frequency charge noise measured. |
| Exchange Coupling $J_{12}$ (ON) | 2.8 | MHz | Nominal value controlled by gate voltage pulses. |
| Exchange Coupling $J_{23}$ (ON) | 12.5 | MHz | Nominal value controlled by gate voltage pulses. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment utilized advanced semiconductor fabrication and cryogenic measurement techniques to isolate and control the three-qubit system:
- Substrate Fabrication: Triple quantum dot array fabricated on an isotopically natural, undoped Si/SiGe heterostructure wafer.
- Gate Architecture: Three layers of overlapping aluminum gates were nanofabricated to control confinement potential (plunger and barrier gates).
- Ohmic Contacts: Phosphorus ion implantation was used to create ohmic contacts.
- Magnetic Field Gradient: A cobalt micro-magnet stack (Ti/Co/Al films with thicknesses of 10/250/20 nm) was placed on top of the quantum dot array to enable fast, addressable Electric-Dipole Spin Resonance (EDSR).
- Qubit Control: Single-qubit control achieved via EDSR; two-qubit entanglement achieved via controlled phase (CZ) gates utilizing fast gate voltage pulses to control exchange coupling ($J_{ij}$).
- Noise Mitigation: A decoupled CZ gate sequence (incorporating $\pi$ pulses) was implemented to decouple quasi-static single-qubit phase noise (low-frequency nuclear magnetic and charge noises).
- Measurement: Charge sensing performed using radio-frequency reflectometry (181.5 MHz resonance frequency) connected to a charge sensor quantum dot for single-shot spin readout.
- Characterization: Quantum state tomography was performed using 27 combinations of pre-rotations, averaging 2,000 single-shot readout outcomes per combination, followed by maximum likelihood estimation.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe challenges faced in achieving higher fidelity in Si/SiGe spin qubitsâspecifically, the limitations imposed by nuclear spin noise and charge noiseâare precisely the areas where 6CCVDâs expertise in high-purity MPCVD diamond provides a powerful alternative or complementary solution.
Applicable Materials for Quantum Coherence
Section titled âApplicable Materials for Quantum CoherenceâThe paper explicitly notes that fidelity is limited by magnetic noise from $^{29}$Si nuclear spins. Diamond, particularly isotopically purified Single Crystal Diamond (SCD), is the premier solid-state material for minimizing nuclear spin noise, enabling exceptional coherence times necessary for fault-tolerant quantum computing.
| 6CCVD Material | Application Relevance to Quantum Qubits | Key Advantage |
|---|---|---|
| High-Purity SCD (Optical Grade) | Ideal substrate for creating high-coherence Nitrogen-Vacancy (NV) centers, a proven platform for multipartite entanglement (Ref [15]). | Near-zero nuclear spin noise (C-13 < 1 ppm available) leading to $T_2$ coherence times in the millisecond range. |
| Isotopically Purified SCD | Direct solution to the noise problem identified in the paper, offering a platform where the host lattice is virtually nuclear-spin-free. | Enables intrinsic long-lived spin coherence, bypassing the need for complex echo sequences to mitigate environmental noise. |
| Boron-Doped Diamond (BDD) | Potential for highly conductive gate structures or integrated electrodes in diamond-based quantum devices. | High conductivity and chemical inertness, suitable for cryogenic environments and complex device integration. |
| Polycrystalline Diamond (PCD) | Cost-effective, large-area substrates (up to 125mm) for high-throughput sensor arrays or integrated photonics components. | Scalability and large dimensions for hybrid quantum systems. |
Customization Potential for Advanced Device Fabrication
Section titled âCustomization Potential for Advanced Device FabricationâThe Si/SiGe device utilized complex, multi-layer metal structures (Al gates, Ti/Co/Al micro-magnets) and precise dimensions. 6CCVD offers comprehensive custom fabrication services essential for replicating or advancing such complex quantum architectures:
- Custom Metalization Stacks: 6CCVD offers in-house deposition of critical metals including Ti, W, Pt, Au, Pd, and Cu. We can replicate the Ti/Co/Al micro-magnet stack (10/250/20 nm) or develop alternative low-loss, high-performance metal layers directly onto diamond substrates.
- Precision Dimensions: We provide custom plates and wafers:
- SCD: Thicknesses from 0.1 ”m up to 500 ”m.
- Substrates: Up to 10 mm thick for robust thermal management in cryogenic systems.
- Ultra-Smooth Polishing: Achieving high-fidelity gates requires extremely smooth surfaces. 6CCVD guarantees surface roughness (Ra) < 1 nm for SCD and < 5 nm for inch-size PCD, ensuring optimal lithography and gate performance.
- Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) for time-sensitive research projects.
Engineering Support
Section titled âEngineering SupportâThe successful generation of the GHZ state relied on careful mitigation of low-frequency noise and precise material selection (Si/SiGe). 6CCVDâs in-house PhD team specializes in the material science of solid-state quantum platforms and can assist researchers transitioning to or optimizing diamond-based systems.
We offer consultation on:
- Material Selection: Choosing the optimal diamond grade (e.g., high-purity SCD vs. BDD) for specific multiqubit quantum algorithm projects.
- Defect Engineering: Controlling NV center density and location for scalable quantum register development.
- Interface Optimization: Designing metalization and surface treatments to minimize charge noise and maximize gate performance on diamond.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.