Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2016-05-17 |
| Journal | New Journal of Physics |
| Authors | Kai Zhang, Naufer Nusran, Bradley R. Slezak, Meenakshi Dutt |
| Institutions | University of Pittsburgh |
| Citations | 9 |
| Analysis | Full AI Review Included |
Technical Documentation: Geometric Phase Gates in NV Diamond
Section titled âTechnical Documentation: Geometric Phase Gates in NV DiamondâAnalysis of Experimental Limits on Adiabatic Geometric Phase Gates in Solid-State Spin Qubits
Section titled âAnalysis of Experimental Limits on Adiabatic Geometric Phase Gates in Solid-State Spin QubitsâThis document analyzes the requirements and findings of the research paper âExperimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubitâ (Zhang et al., 2016). It highlights how 6CCVDâs advanced MPCVD diamond materials and customization capabilities are essential for replicating and advancing this critical quantum information research.
Executive Summary
Section titled âExecutive Summaryâ- Core Achievement: The study successfully measured the Berry phase and implemented an adiabatic geometric phase gate using a single Nitrogen-Vacancy (NV) center in a Type-IIa diamond substrate.
- Fidelity Measurement: A high gate fidelity ($F_G = 0.978 \pm 0.026$) was achieved for a single $\pi/2$ phase shift gate operation.
- Limiting Factor Identified: The decay in gate fidelity is primarily attributed to fast control field noise (fluctuations in the dynamic phase) occurring at frequencies higher than the spin echo clock frequency.
- Material Requirement: The experiment relied on ultra-high purity, low-strain Single Crystal Diamond (SCD) to achieve a long environmental coherence time ($T_2 \sim 300$ ”s).
- Methodology: Geometric manipulation was achieved via precise microwave control using an IQ modulator and Arbitrary Waveform Generator (AWG), coupled via a 20 ”m copper wire on the diamond surface.
- 6CCVD Value Proposition: 6CCVD provides the necessary Optical Grade SCD substrates and custom metalization services required to minimize material-intrinsic noise and optimize microwave delivery for high-fidelity quantum control.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental results:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Material | Type-IIa SCD | N/A | Bulk single crystal sample used for NV center |
| Crystal Orientation | [1 1 1] | N/A | Used for NV axis alignment |
| NV Ground State Splitting ($D$) | 2.87 | GHz | Zero magnetic field splitting |
| Static Bias Magnetic Field ($B_0$) | $\approx 450$ | Gauss | Applied along the NV z-axis |
| Spin Echo Coherence Time ($T_2$) | $\sim 300$ | ”s | Environmental limit without external control fields |
| Rabi Frequency ($\Omega$) | 12.5 | MHz | Used in amplitude scan experiments |
| Detuning ($\Delta$) | 10 | MHz | Used in Berry phase amplitude scan |
| $\pi/2$ Rotation Time | $\sim 20$ | ns | Achieved via microwave pulses |
| Gate Fidelity ($F_G$) | $0.978 \pm 0.026$ | N/A | Measured fidelity for a single $\pi/2$ phase shift gate |
| Microwave Coupling | 20 | ”m | Diameter of copper wire placed on diamond surface |
| Decay Time Scale ($T_f$) | 2.2 | ”s | Fitted decay time for long-time Rabi oscillation |
Key Methodologies
Section titled âKey MethodologiesâThe experiment utilized advanced quantum control techniques on a solid-state spin qubit:
- Qubit System Definition: A single NV center in a Type-IIa SCD sample was biased with a 450 Gauss DC magnetic field to create a pseudo-spin-1/2 qubit system ($|m_s = 0\rangle \leftrightarrow |m_s = -1\rangle$).
- Optical Control: Qubit initialization was performed via 532 nm laser excitation (optical pumping), and readout was achieved by measuring spin-dependent fluorescence (650-750 nm).
- Microwave Hamiltonian Control: Microwave radiation was delivered via a 20 ”m copper wire coupled to the diamond surface. The drive field was precisely modulated using an IQ modulator and an Arbitrary Waveform Generator (AWG).
- Adiabatic Circuit Generation: Fast amplitude and phase modulation were applied to the microwave drive field to create an effective rotating magnetic field, tracing a closed contour in parameter space to accumulate the geometric Berry phase.
- Noise Mitigation Technique: A resonant spin echo interferometry sequence was implemented to cancel the average dynamic phase and filter out slow environmental noise (extending $T_2$).
- Fidelity Analysis: Numerical simulations were performed, incorporating measured control field imperfections (e.g., single channel nonlinearity and amplitude imbalance in the IQ modulator), confirming that fast dynamic phase fluctuations limit gate fidelity.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & Capabilitiesâ6CCVD is uniquely positioned to supply the foundational materials and custom engineering required to replicate and extend this high-fidelity quantum control research. The paperâs findings underscore the necessity of minimizing both material-intrinsic noise and control-field imperfectionsâareas where 6CCVD excels.
Applicable Materials
Section titled âApplicable MaterialsâTo achieve the long coherence times ($T_2$) and high fidelity demonstrated, researchers require the highest quality diamond available.
| Research Requirement | 6CCVD Material Recommendation | Technical Specification |
|---|---|---|
| Ultra-Low Defect Density (Type-IIa equivalent) | Optical Grade Single Crystal Diamond (SCD) | Nitrogen concentration < 1 ppb; extremely low strain and low substitutional defects, maximizing $T_2$. |
| High-Efficiency Qubit Readout | Optical Grade SCD | High transparency across the 532 nm excitation and 650-750 nm fluorescence windows. |
| Future Sensing/High-Power Applications | Boron-Doped Diamond (BDD) (If conductivity is required) | Available for electrochemical or high-power microwave applications where grounding or charge dissipation is critical. |
Customization Potential
Section titled âCustomization PotentialâThe experiment utilized a 20 ”m copper wire for microwave delivery, highlighting the need for precise integration of control electronics onto the diamond surface. 6CCVD offers comprehensive in-house engineering solutions:
- Custom Metalization: We offer internal deposition and patterning of thin films, including Ti/Pt/Au (standard for quantum devices), Cu (as used in this study), Pd, and W. This capability allows researchers to integrate microstrip lines or coplanar waveguides directly onto the SCD substrate with high precision.
- Precision Polishing: The paper noted systematic deviations due to imperfect driving waveforms (IQ modulator nonlinearity). Our Ra < 1 nm polishing for SCD ensures an atomically flat surface, minimizing surface defects that can interfere with metalization adhesion and microwave propagation uniformity.
- Custom Dimensions: We provide SCD plates up to 500 ”m thick and PCD wafers up to 125 mm in diameter, cut to custom dimensions via laser processing, ensuring perfect fit for specialized quantum setups (e.g., confocal microscopy or cryogenic systems).
Engineering Support
Section titled âEngineering SupportâThe research identified control field noise and imperfect driving waveforms (IQ modulator nonlinearity) as the primary limitations to gate fidelity.
- Material Optimization for Noise Reduction: 6CCVDâs in-house PhD team specializes in material science for quantum applications. We assist clients in selecting the optimal SCD grade and thickness to mitigate environmental noise sources (e.g., surface spins, strain fields) that affect $T_2$ and $T_2$*.
- Integration Consultation: We provide technical consultation on optimizing the interface between the diamond substrate and external control electronics (e.g., microwave antennas, electrodes) to minimize signal distortion and improve the fidelity of geometric quantum logic gates.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (~10) operations. This occurs in spite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. In conclusion, we have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.