High-fidelity entangling gates for electron and nuclear spin qubits in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2025-06-03 |
| Journal | Physical review. B./Physical review. B |
| Authors | Regina Finsterhoelzl, Wolf-RĂŒdiger Hannes, Guido Burkard |
| Institutions | University of Konstanz |
| Citations | 1 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research proposes and validates a synchronization protocol for achieving fast, high-fidelity entangling gates (CNOTe and CCNOTe) using the electron and nuclear spins of Nitrogen-Vacancy (NV) centers in diamond.
- Error Suppression: The core innovation is exploiting synchronization effects between resonant and off-resonant transitions, allowing for the complete suppression of spin-flip errors caused by strong microwave driving.
- High Fidelity Achieved: The protocol predicts maximum average gate fidelity (Fav) of 1.0 for two-qubit systems (NV-15N and NV-14N) under specific, analytically determined driving strengths (Bsync).
- Fast Operation Speed: Gate times are significantly reduced compared to the weak-driving regime, achieving CNOTe operations in the range of 0.4 ”s for the NV-15N system.
- Multiqubit Scalability: The scheme is extended to multiqubit registers including surrounding 13C nuclear spins, predicting fidelities >0.99 for conditional logic (Toffoli-equivalent CCNOTe gates).
- Simplified Control: This method avoids the need for complex, digitally designed pulse sequences based on optimal control algorithms, simplifying the implementation of high-fidelity quantum operations.
- Native CZ Correction: The scheme incorporates a free-evolution waiting time (tw) to compensate for the native CZ phase accumulated due to the always-on hyperfine interaction, ensuring the final operation is a pure CNOTe.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Electron Spin State | Triplet (S=1) | - | Ground state of the negatively charged NV center. |
| Zero-Field Splitting (D/2Ï) | 2.88 | GHz | Separation between ms=0 and ms=±1 electronic spin levels. |
| Reduced Electron Gyromagnetic Ratio (Îłe/2Ï) | 14.00 | GHz/T | Used for calculating Zeeman splitting (He). |
| 15N Nuclear Spin (I15N) | 1/2 | - | Qubit-qubit system; no quadrupole splitting (Q=0). |
| 14N Nuclear Spin (I14N) | 1 | - | Qubit-qutrit system; includes quadrupole splitting (Q14N). |
| 15N Parallel Hyperfine (A||15N/2Ï) | 3.03 | MHz | Coupling constant for the 15N NV center. |
| Fastest Synchronized Gate Time (tg) | ~0.4 | ”s | Predicted for Fav=1.0 in 15N NV system (B1 â 2.47 MHz). |
| High-Fidelity Multiqubit Gate Time (tg) | ~10 | ”s | Predicted for Fav=0.998 in NV-14N-13C system. |
| Electron Spin Decoherence Time (T2*) | 2 to 6 | ”s | Typical range for natural 1.1% 13C abundance diamond. |
| Electron Spin Decoherence Time (T2*) | Up to 90 | ”s | Achieved in isotopically purified diamond material. |
| Predicted Average Gate Fidelity (Fav) | 1.0 | - | Achieved for two-qubit CNOTe using synchronization. |
| Predicted Average Gate Fidelity (Fav) | >0.99 | - | Achieved for multiqubit CCNOTe (Toffoli-equivalent). |
| 13C Natural Abundance | 1.1 | % | Concentration of nuclear spins in the host lattice. |
Key Methodologies
Section titled âKey MethodologiesâThe high-fidelity entangling gate protocol relies on precise control of the microwave driving field (B1) and the total gate duration (tg + tw) to exploit synchronization effects.
- Hamiltonian Definition: The system is modeled using the Hamiltonian H = He + ÎŁHjn + ÎŁHjint, including the electronic spin (S=1), nuclear spins (Ij), Zeeman splitting (Bz), quadrupole splitting (Q), and hyperfine interaction (Aj).
- Conditional Driving Field: A constant microwave driving field HD = B1 cos(Ï0t)Sx is applied. The frequency Ï0 is tuned to be resonant with the desired electron spin flip transition, conditioned on a specific nuclear spin state (e.g., |1>n|0>e â |1>n|1>e).
- Synchronization Condition (Bsync): The driving strength B1 is chosen such that the Rabi frequency (Ω) of the unwanted, off-resonant transition results in a 2Ï rotation (or an integer multiple thereof) during the gate time tg. This ensures the off-resonant state returns to its initial state, canceling the error.
- For the NV-15N system, the synchronization condition is analytically derived as Bsync(n, m) = A||15N * (2n + 1)2 / [4m2 - (2n + 1)2]1/2.
- Gate Time Selection (tg): The gate time tg is determined by the resonant Rabi frequency (tg = Ï/B1) to achieve the desired Ï-rotation (electron spin flip) in the target nuclear subspace.
- Native CZ Phase Compensation: Since the hyperfine interaction is always on, the driven operation (Uact) accumulates a native CZ phase (Ξ = -A||tg). A subsequent free evolution waiting time (tw) is introduced, where tw = 2Ï/A|| - tg, to compensate for this phase and ensure the final operation Uact,CNOT is locally equivalent to a pure CNOTe gate.
- Fidelity Calculation: Average gate fidelity (Fav) is calculated using Fav = [d + |Tr(UCNOTâ Uact,CNOT)|2] / [d(d + 1)], where d is the Hilbert space dimension (d=4 for two-qubit, d=12 for multiqubit).
- Noise Modeling: The impact of the 13C nuclear spin bath (Overhauser field) is included by averaging the gate fidelity over a Gaussian distribution of magnetic field fluctuations, characterized by the electron spin decoherence time T2*.
Commercial Applications
Section titled âCommercial ApplicationsâThe development of fast, high-fidelity entangling gates in diamond NV centers is critical for advancing solid-state quantum technology across several sectors.
- Quantum Computing Hardware:
- Fault-Tolerant Qubits: Enables the creation of logical qubits with error rates <1%, a requirement for implementing fault-tolerant quantum computation (FTQC) using codes like the surface code.
- Scalable Registers: Provides a robust method for conditional control over multi-qubit registers (electron spin coupled to multiple 14N/15N and 13C nuclear spins), forming the core memory and processing unit.
- Quantum Networks and Communication:
- Entanglement Generation: Supports fast, high-fidelity local entanglement operations, which are necessary building blocks for generating and distributing entanglement across long-range quantum networks (e.g., via cavity-mediated electron-photon coupling).
- Advanced Quantum Sensing:
- High-Precision Magnetometry: The ability to perform conditional logic on nuclear spins allows for enhanced sensing protocols, leveraging the long coherence times of nuclear spins to achieve higher sensitivity and stability in diamond-based magnetometers.
- Solid-State Material Engineering:
- Isotope Selection Criteria: The synchronization scheme provides a new criterion for selecting optimal 13C nuclear spin qubits based on the ratio of hyperfine couplings (A||13C/A||15N) that allow for high-fidelity synchronization.
- Microwave Control Systems:
- Pulse Sequence Simplification: Reduces the reliance on complex, high-power arbitrary waveform generators (AWGs) typically needed for optimal control sequences, potentially simplifying the microwave control electronics required for quantum processors.
View Original Abstract
Motivated by the recent experimental progress in exploring the use of a nitrogen-vacancy (NV) center in diamond as a quantum computing platform, we propose schemes for fast and high-fidelity entangling gates on this platform. Using both analytical and numerical calculations, we demonstrate that synchronization effects between resonant and off-resonant transitions may be exploited such that spin-flip errors due to strong driving may be eliminated by adjusting the gate time or the driving field. This allows for fast, high-fidelity entangling operations between the electron spin and one or several nuclear spins. We investigate a two-qubit system where the NV center comprises a <a:math xmlns:a=âhttp://www.w3.org/1998/Math/MathMLâ><a:mmultiscripts><a:mi mathvariant=ânormalâ>N</a:mi><a:mprescripts/><a:none/><a:mn>15</a:mn></a:mmultiscripts></a:math> atom and a qubit-qutrit system for the case of a <c:math xmlns:c=âhttp://www.w3.org/1998/Math/MathMLâ><c:mmultiscripts><c:mi mathvariant=ânormalâ>N</c:mi><c:mprescripts/><c:none/><c:mn>14</c:mn></c:mmultiscripts></c:math> atom. In both cases, we predict a complete suppression of off-resonant driving errors for two-qubit gates when addressing the NV electron spin conditioned on states of nuclear spins of the nitrogen atom of the defect. Additionally, we predict fidelities <e:math xmlns:e=âhttp://www.w3.org/1998/Math/MathMLâ><e:mrow><e:mo>&gt;</e:mo><e:mn>0.99</e:mn></e:mrow></e:math> for multiqubit gates when including the surrounding <f:math xmlns:f=âhttp://www.w3.org/1998/Math/MathMLâ><f:mmultiscripts><f:mi mathvariant=ânormalâ>C</f:mi><f:mprescripts/><f:none/><f:mn>13</f:mn></f:mmultiscripts></f:math> atoms in the diamond lattice in the conditioned logic.