Trispectrum reconstruction of non-Gaussian noise
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2019-10-09 |
| Journal | Physical review. B./Physical review. B |
| Authors | Guy Ramon |
| Institutions | Santa Clara University |
| Citations | 21 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Non-Gaussian Noise Polyspectra Reconstruction in Qubit Systems
Section titled âTechnical Documentation & Analysis: Non-Gaussian Noise Polyspectra Reconstruction in Qubit Systemsâ6CCVD Reference: Diamond Platform Noise Spectroscopy (DDNS)
Executive Summary
Section titled âExecutive SummaryâThis study details robust theoretical protocols for Dynamic Decoupling Noise Spectroscopy (DDNS) tailored to characterize highly correlated, non-Gaussian noise environments (specifically Random Telegraph Noise, RTN) in solid-state qubits.
- Critical Achievement: Simultaneous reconstruction of the Power Spectral Density ($S_{1}$) and the Trispectrum ($S_{3}$) across a wide range of qubit-fluctuator coupling strengths ($v/\gamma = 0.1$ to $3$).
- Decoherence Mitigation: The technique provides complete characterization of charge noise environments (e.g., Two-Level Fluctuators, TLFs) responsible for non-Gaussian $1/f$ noise, crucial for effective decoherence mitigation strategies.
- Methodology: Utilizes optimized pulse sequences, specifically Mixed-order Concatenated DD (MCDD), to form multidimensional frequency combs necessary for polyspectra reconstruction, overcoming inherent numerical instabilities.
- Robustness: Demonstrated successful reconstruction even when faced with significant measurement errors and sequence repetition variation ($M=1$ to $100$), confirming protocol viability in realistic experimental settings.
- Direct Application in Diamond: The developed protocols are explicitly cited as âreadily testableâ in key solid-state platforms, most notably NV Centers in Diamond, confirming the direct relevance to 6CCVDâs core single-crystal material offerings.
- 6CCVD Value Proposition: Faithful reconstruction relies on ultra-high purity, highly controlled diamond substrates capable of hosting long-coherence qubits. 6CCVD provides the necessary Single Crystal Diamond (SCD) materials and custom engineering services (polishing, metalization) to implement these advanced DDNS protocols.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target Noise Source | Random Telegraph Noise (RTN) | N/A | Modeled classical noise from Two-Level Fluctuators (TLFs) |
| Reconstructed Spectra | PSD ($S_{1}$), Trispectrum ($S_{3}$) | N/A | Cumulants $C_{2}(T)$ and $C_{4}(T)$, respectively |
| Protocol Type | Dynamic Decoupling Noise Spectroscopy (DDNS) | N/A | Utilizes Mixed-order Concatenated DD (MCDD) sequences |
| Base Sequence Time ($T$) | $256\delta$ | N/A | Total length of base sequence |
| Time Resolution ($\delta$) | $1 / (16\gamma)$ | N/A | Related to inverse RTN switching rate ($\gamma$) |
| Standard Repetitions ($M$) | 30 | N/A | Used to increase accuracy via delta approximation |
| Min Interpulse Separation ($\tau$) | $4\delta$ | N/A | Required for MCDD sequence pool generation |
| Coupling Strength Range ($v/\gamma$) | 0.1 to 3 | N/A | Successfully reconstructed from weak (0.1) to strong (3) coupling |
| PSD Frequency Cutoff | $\pi / (4\delta)$ | N/A | Truncated at $n_{max}^{PSD} = 32$ harmonics |
| Trispectrum Frequency Cutoff | $\pi / (16\delta)$ | N/A | Truncated at $n_{max}^{TRI} = 8$ harmonics |
| Reconstruction Quality ($Q$) | $1.8 \times 10^{-3}$ to $0.02$ | N/A | Achieved using optimized, corrected protocols |
Key Methodologies
Section titled âKey MethodologiesâThe experiment relies on a multi-layered algorithm for generating and selecting an optimized pool of control sequences to solve a set of linear equations linking the polyspectra to the measured qubit signals (attenuation factor, $\chi(T)$).
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Sequence Pool Generation:
- Base sequences were Mixed-order Concatenated DD (MCDD) or Fixed Induction Decay (FID) segments.
- All sequences have a fixed time $T = 256\delta$.
- Criterion (i): Pulse times must be integer multiples of $\delta$ ($T_{i}/\delta \pmod{2l_{i}} = 0$).
- Criterion (ii): Minimum interpulse separation was enforced at $\tau = 4\delta$, limiting the effective maximum CDD order to 5.
- Criterion (iii): Total number of pulses was required to be even to avoid non-zero odd multiples of $\pi/T$.
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Cumulant Calculation:
- Delta-approximated second ($C_{2}(T)$) and fourth ($C_{4}(T)$) cumulants were calculated for a nominal RTN source ($\gamma = 1$) using truncated summation formulas (Eqs. 8 & 9).
- Exact cumulant calculations for repeated sequences ($M$ repetitions) were performed in the time domain using recursive formulae.
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Sequence Selection Optimization:
- Initial Filtering (Absolute/Relative Error Test): Sequences were screened to pass stringent absolute and relative error thresholds ($\epsilon_{2}, \epsilon_{4}, \epsilon_{set}$) on the calculated cumulants, ensuring sufficient filtering accuracy.
- Final Optimization (Condition Number Minimization): The remaining subset was optimized to minimize the condition number of the reconstruction matrix $\mathbf{A}$, ensuring numerical stability and accurate matrix inversion.
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Error Correction:
- A correction term was applied to the attenuation factors to account for errors introduced by truncating the cumulant series higher than $C_{4}(T)$, achieving excellent agreement with theoretical spectra even at strong coupling.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research validates the urgent need for high-quality, ultra-low-noise Single Crystal Diamond (SCD) material for advancing quantum control and noise spectroscopy. 6CCVD is uniquely positioned to supply the foundational materials required for immediate experimental replication and extension of these protocols in NV center diamond systems.
| Material Requirement (Paper) | 6CCVD Solution (Technical Specification) | Value Proposition for Quantum Engineering |
|---|---|---|
| Qubit Platform (NV Centers) | Single Crystal Diamond (SCD): Optical Grade, CVD-grown. | Ensures high purity and low native nitrogen concentration, essential for maximizing NV coherence time ($T_{2}$) critical for DDNS accuracy. |
| Material Thickness | Custom SCD Thickness: From $0.1$ ”m up to $500$ ”m. | Provides flexibility for engineers, accommodating requirements for high-density NV shallow implants or bulk applications. |
| High Control / Planarity | Precision Polishing: Surface roughness ($R_{a}$) < $1$ nm (SCD). | Minimizes surface charge noise (TLFs) and crystal defects, directly mitigating the non-Gaussian noise sources being probed. |
| Microwave Control Structure | Custom Metalization & Geometry: In-house deposition of Au, Pt, Pd, Ti, W, Cu. Custom laser cutting up to $125$ mm wafers. | Enables high-fidelity implementation of the necessary MCDD pulse sequences via high-frequency coplanar waveguide structures. |
| Substrate Dimensions | Large-Area Wafers: SCD/PCD wafers up to $125$ mm. | Supports scaling from research prototypes to industrial quantum device fabrication. |
Customization Potential & Engineering Support
Section titled âCustomization Potential & Engineering SupportâThe robust reconstruction of the trispectrum depends directly on the quality of the host diamond and the precision of the control pulses.
- Custom Dimensions: Successful DDNS implementation requires specific sample geometries and potentially through-wafer structures for pulse delivery. 6CCVD offers high-precision laser cutting and deep reactive ion etching (DRIE) services to meet the exact dimensions needed for microwave circuit integration.
- Surface Preparation: For optimal control of NV centers near the surface (where environmental noise is highest), the surface termination (e.g., oxygen, hydrogen) is critical. 6CCVD provides detailed analysis and specification of custom surface finishing protocols to stabilize the charge environment.
- Engineering Consultation: 6CCVDâs in-house PhD team specializes in material science for quantum systems. We offer comprehensive engineering consultation to assist researchers in selecting the optimal MPCVD diamond specifications (e.g., high-purity vs. controlled boron-doping (BDD)) required to replicate or extend this advanced Non-Gaussian Noise Spectroscopy research.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. Global shipping (DDU default, DDP available) ensures rapid delivery of mission-critical materials worldwide.
View Original Abstract
Using a qubit to probe non-Gaussian noise environments is theoretically\nstudied in the context of classical random telegraph processes. Protocols for\ncontrol pulses are developed to effectively scan higher noise correlations,\noffering valuable information on the charge environment of the qubit.\nSpecifically, the noise power spectrum and trispectrum are reconstructed\nsimultaneously for a wide range of qubit-fluctuator coupling strengths,\ndemonstrating the methodâs robustness. These protocols are readily testable in\nvarious qubit systems with well-developed quantum control, including quantum\ndot spins, superconducting qubits and NV centers in diamond.\n