Preserving entanglement in a solid-spin system using quantum autoencoders
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-09-26 |
| Journal | Applied Physics Letters |
| Authors | Feifei Zhou, Yu Tian, Yumeng Song, Chu-Dan Qiu, Xiangyu Wang |
| Institutions | Hefei University of Technology, Zhejiang Lab |
| Citations | 8 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research demonstrates a novel method for preserving fragile quantum entanglement in a solid-state system using a trained Quantum Autoencoder (QAE).
- Core Value Proposition: The QAE, optimized via a Hybrid Quantum-Classical Approach (HQCA), compresses high-dimensional entangled states into a low-dimensional subspace inherently robust to decoherence.
- System and Achievement: Experiments conducted on Nitrogen-Vacancy (NV) centers in bulk diamond successfully encoded electron-nuclear Bell states into the long-coherence 14N nuclear spin subspace.
- Lifetime Extension: The entanglement lifetime was dramatically extended from 2.22 ”s (unencoded) to 3.03 ms (encoded), achieving a three orders of magnitude improvement.
- Methodology Advantage: The HQCA training method proved highly effective in complex solid-spin systems, automatically compensating for unknown experimental errors and control imperfections.
- Performance Comparison: The QAE encoding outperformed traditional CNOT gate decoupling by 19.8% in extending entanglement lifetime, demonstrating the superiority of the HQCA optimization approach.
- Universality: The QAE scheme is general, paving the way for utilizing long-lifetime nuclear spins as robust, immediate-access quantum memories in various quantum information tasks.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Entanglement Lifetime (Unencoded) | 2.22 ± 0.43 | ”s | Bell state free evolution without protection. |
| Entanglement Lifetime (QAE Encoded) | 3.03 ± 0.56 | ms | Achieved by encoding into the nuclear spin subspace. |
| Entanglement Lifetime (CNOT Decoupling) | 2.53 ± 0.76 | ms | Using traditional CNOT gates for comparison. |
| Lifetime Improvement Factor | ~1360 | N/A | QAE encoded vs. unencoded state. |
| Static Magnetic Field (Bz) | ~52 | mT | Applied along the NV axis to enable optical polarization via excited state level anti-crossing (esLAC). |
| Laser Wavelength | 532 | nm | Green laser used for optical polarization and detection. |
| Fluorescence Detection Range | 650 to 800 | nm | Detected via avalanche photodiode (APD). |
| Zero-Field Splitting (D) | ~2.87 | GHz | Intrinsic splitting of the NV electron spin ground state. |
| Microwave Pulse Duration (t) | 800 | ns | Fixed duration for MW1 and MW2 pulses in the encoder PQC. |
| Final Encoder Voltage (B1) | 0.164 | V | Optimized peak-peak voltage for MW1 (AWG output). |
| Final Encoder Voltage (B2) | 0 | V | Optimized peak-peak voltage for MW2 (AWG output). |
| Optimization Fidelity (P|0>) | >0.93 | N/A | Final probability of the electron spin occupying |
| QAE Performance Gain | 19.8 | % | Improvement over CNOT decoupling method. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment relies on a hybrid quantum-classical optimization loop to train the quantum autoencoder (QAE) unitary transformation (UE).
- System Setup: Experiments utilized an NV center in bulk diamond within a home-built Optically Detected Magnetic Resonance (ODMR) system. A static magnetic field (Bz â 52 mT) was applied along the NV axis.
- Initialization: The electron and 14N nuclear spins were simultaneously polarized to the |01> state using a 532 nm green laser pulse, exploiting the esLAC mechanism.
- Encoder Design (PQC): The encoder UE was implemented as a Parameterized Quantum Circuit (PQC) consisting of two microwave (MW) pulses (MW1 and MW2) applied exclusively to the electron spin, ensuring fast operation.
- HQCA Optimization: The parameters (amplitudes B1, B2, and phases Ï1, Ï2) of the PQC were optimized using the Hybrid Quantum-Classical Approach (HQCA) and gradient descent.
- Cost Function Definition: The cost function f(UE) was defined as the average probability (P) that the electron spin occupies the |0> state after encoding the input states (|00> and |11>). Maximizing P ensures successful compression into the nuclear spin subspace.
- Gradient Measurement: The cost function and its gradient were measured directly on the NV quantum processor, allowing the optimization to inherently account for and correct experimental imperfections and noise specific to the solid-spin system.
- Encoding and Preservation: Once optimized, the QAE encoded the fragile electron-nuclear Bell state into the robust 14N nuclear spin (the latent space). The state was allowed to freely evolve for extended periods (up to milliseconds) before a decoder (UD = UEâ ) was applied to recover the original entangled state for fidelity measurement.
Commercial Applications
Section titled âCommercial ApplicationsâThe demonstrated technology addresses fundamental challenges in building stable quantum hardware, particularly in solid-state platforms.
- Solid-State Quantum Computing: Provides a robust, hardware-efficient method for error mitigation and entanglement protection, essential for scaling up NV-based quantum processors.
- Quantum Memory Devices: Enables the creation of high-fidelity, long-duration quantum memories by leveraging the extremely long coherence times of nuclear spins (T2 > 3 ms) while maintaining fast access via the electron spin.
- Quantum Sensing and Metrology: Stabilizes entangled sensor states (e.g., electron-nuclear spin pairs) against environmental noise, leading to enhanced sensitivity and longer integration times in magnetic field or temperature sensing applications.
- Quantum Data Compression: The QAE serves as a general-purpose quantum data compressor, reducing the dimensionality of complex quantum states, which is critical for efficient resource management in future quantum networks.
- Hybrid Quantum Systems: Validates the HQCA as a powerful training paradigm for optimizing complex unitary gates in noisy, hard-to-characterize solid-state systems, applicable to superconducting qubits or trapped ions.
View Original Abstract
Entanglement, as a key resource for modern quantum technologies, is extremely fragile due to the decoherence. Here, we show that a quantum autoencoder, which is trained to compress a particular set of quantum entangled states into a subspace that is robust to decoherence, can be employed to preserve entanglement. The training process is based on a hybrid quantum-classical approach to improve the efficiency in building the autoencoder and reduce the experimental errors during the optimization. Using nitrogen-vacancy centers in diamond, we demonstrate that the entangled states between the electron and nuclear spins can be encoded into the nucleus subspace, which has much longer coherence time. As a result, lifetime of the Bell states in this solid-spin system is extended from 2.22 ± 0.43 Όs to 3.03 ± 0.56 ms, yielding a three orders of magnitude improvement. The quantum autoencoder approach is universal, paving the way of utilizing long lifetime nuclear spins as immediate-access quantum memories in quantum information tasks.