Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2024-03-28 |
| Journal | Quantum |
| Authors | Evangelia Takou, Edwin Barnes, Sophia E. Economou |
| Institutions | Virginia Tech |
| Citations | 6 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Scalable Entanglement Generation: Developed optimized Dynamical Decoupling (DD) protocols (sequential and multi-spin) for generating high-fidelity Greenberger-Horne-Zeilinger (GHZ)-like states in solid-state defect systems (NV centers coupled to 13C nuclear spins).
- High Qubit Count: Demonstrated the theoretical capability to prepare GHZ-like states involving up to M = 10 qubits (electron + 9 nuclei) within the nuclear spin coherence time constraints (T2).
- M-Tangling Power Metric: Introduced a novel, scalable metricâthe M-tangling powerâderived from Makhlin invariants, which quantifies genuine all-way entanglement capability of a gate, simplifying optimization and verification compared to traditional fidelity calculations.
- Speed and Efficiency: The multi-spin (single-shot) entanglement protocol significantly reduces gate duration, achieving GHZ3 states at least two times faster than the sequential scheme, crucial for scalability.
- Robustness to Errors: Showed that combining the proposed protocols with XY decoupling sequences (e.g., XY2) provides superior robustness against systematic and random pulse control errors compared to standard CPMG sequences.
- High Fidelity Achieved: Protocols yield GHZ-like states with maximal all-way correlations exceeding 95% and composite gate errors due to cross-talk remaining below 0.05%.
Technical Specifications
Section titled âTechnical SpecificationsâThe following specifications are derived from simulations using experimentally reported hyperfine parameters for a 27-nuclear spin register coupled to an NV center electron spin.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Entanglement Size | 10 | Qubits | Electron + 9 13C nuclear spins (GHZ10) |
| Nuclear Register Size | 27 | Spins | 13C nuclear spin bath (NV center in diamond) |
| Target M-Tangling Power | > 0.95 | Dimensionless | Metric for genuine all-way correlation saturation |
| Maximum Gate Time (GHZ10, Sequential) | 4000 | ”s | Total sequence duration, constrained by T2 |
| Gate Error (GHZ3, Sequential) | < 0.05 | Dimensionless | Infidelity due to residual entanglement cross-talk |
| Nuclear Coherence Time (T2) | 3 to 17 | ms | Typical range for 13C nuclei |
| Pulse Error Robustness (XY2) | Up to 8 | % | Tolerance for systematic over-rotation error |
| HF Parameter Uncertainty Impact | 10-3 | Relative Error | Deviation in M-tangling power for 0.01 kHz shift |
| Dephasing Robustness (Multi-spin) | Superior | N/A | Multi-spin scheme is more robust to electronic dephasing errors (Edeph) |
Key Methodologies
Section titled âKey MethodologiesâThe entanglement generation relies on Dynamical Decoupling (DD) sequences (CPMG or XY2) applied to the electron spin, which selectively induce conditional rotations on target nuclear spins based on their hyperfine parameters.
- System Initialization: The electron spin is initialized into a superposition state (e.g., |+>), and target nuclear spins are polarized (e.g., |0>).
- DD Sequence Design: DD sequences (trains of Ï-pulses interleaved by free evolution periods, t) are optimized by tuning the unit time (t) and number of iterations (N) to meet resonance conditions for specific nuclear spins.
- Optimization via M-Tangling Power (Ep,M(U)): The DD sequence parameters (t, N) are systematically searched to maximize the unitary M-tangling power, ensuring the resulting gate maximizes all-way correlations.
- Cross-Talk Minimization: Optimization simultaneously minimizes the nuclear one-tangles (a measure of entanglement) for all unwanted nuclei, thereby suppressing cross-talk from the nuclear spin bath.
- Sequential Protocol: M-1 consecutive DD sequences are composed, where each sequence selectively entangles one target nucleus with the electron.
- Multi-Spin Protocol (Single-Shot): A single DD sequence is optimized to simultaneously entangle the electron with M-1 target nuclei, achieving faster gate times.
- Mixed State Analysis (Non-Unitary M-Tangling Power): A non-unitary M-tangling power (Ep,M(E)) is derived using Kraus operators to quantify the entanglement of the target subspace when unwanted nuclei are traced out, capturing the effect of residual entanglement links.
- Error Mitigation: The performance is evaluated under systematic and random pulse errors. XY decoupling sequences are identified as the preferred choice due to their inherent robustness against control imperfections, leading to high-fidelity GHZ state preparation.
Commercial Applications
Section titled âCommercial ApplicationsâThe ability to generate high-fidelity, scalable, and robust multipartite entanglement in solid-state defect systems is critical for advancing quantum technologies.
| Industry/Application | Relevance to Defect-Nuclear Entanglement |
|---|---|
| Fault-Tolerant Quantum Computing | GHZ states are essential building blocks for encoding logical qubits and implementing quantum error correction (QEC) schemes, enabling reliable computation in noisy environments. |
| Quantum Networking and Communication | NV centers serve as robust quantum network nodes. Nuclear spins act as long-lived quantum memories, requiring high-fidelity entanglement generation for quantum teleportation and entanglement distribution between distant nodes. |
| Quantum Sensing and Metrology | Entangled GHZ states enhance the sensitivity and precision of measurements (e.g., magnetic field sensing) beyond classical limits, crucial for advanced metrology applications. |
| Quantum Cryptography | High-quality multipartite entanglement is a necessary resource for secure communication protocols, including Quantum Key Distribution (QKD) and Quantum Secret Sharing. |
| Solid-State Qubit Manufacturing | Provides validated, systematic protocols for designing and calibrating control sequences (DD sequences) in hybrid spin registers, accelerating the development and scaling of solid-state quantum processors. |
View Original Abstract
Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ<mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:msub><mml:mi/><mml:mi>M</mml:mi></mml:msub></mml:math>-like states with minimal cross-talk. We introduce the <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:mi>M</mml:mi></mml:math>-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ<mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:msub><mml:mi/><mml:mi>M</mml:mi></mml:msub></mml:math>-like states of up to <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:math> qubits within time constraints that saturate bounds on <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:mi>M</mml:mi></mml:math>-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:mi>M</mml:mi></mml:math>-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:mi>M</mml:mi></mml:math>-tangling power which incorporates the impact of electronic dephasing errors on the <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ><mml:mi>M</mml:mi></mml:math>-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.