Optimisation of diamond quantum processors
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-09-01 |
| Journal | New Journal of Physics |
| Authors | YunHeng Chen, Sophie Stearn, Scott Vella, Andrew. Horsley, Marcus W. Doherty |
| Institutions | Australian National University |
| Citations | 16 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Optimisation of Diamond Quantum Processors
Section titled âTechnical Documentation & Analysis: Optimisation of Diamond Quantum ProcessorsâExecutive Summary
Section titled âExecutive SummaryâThis research demonstrates a critical advancement in diamond quantum computing by achieving ultra-high gate fidelities through optimized control pulse design, positioning MPCVD diamond as the leading platform for room-temperature quantum information processing.
- Ultra-High Fidelity: Theoretically achieved single-qubit gate infidelities approaching $10^{-5}$ and two-qubit CZ gate infidelities of $10^{-6}$ by minimizing control errors (amplitude, phase, frequency noise).
- Speed Optimization: The primary strategy for overcoming intrinsic decoherence (electron spin relaxation $T_{1,e} \approx 1.8 \text{ ms}$) was maximizing gate speed. Optimal gate times achieved are $1 \mu\text{s}$ for both single-qubit and two-qubit CZ operations.
- Material System: The processor relies on Nitrogen-Vacancy (NV) centers coupled to surrounding nuclear spins (intrinsic N and isotopic 13C impurities) operating at room temperature.
- Methodology: A novel three-step semi-analytical optimal control method was developed, utilizing frequency-shifted sinc functions (Fourier transforms) to generate robust, high-speed radiofrequency (RF) and microwave (MW) control pulses.
- Decoherence Benchmark: Control errors were successfully reduced below the unavoidable decoherence errors (which are on the order of $10^{-3}$ to $10^{-4}$), establishing a clear path toward fault-tolerant quantum computation.
- Application Proof: Simulations of 3-qubit and 5-qubit Quantum Fourier Transforms (QFT) demonstrated high output fidelities (up to 0.964), confirming the viability of the optimized gates for complex quantum algorithms.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target Infidelity (Single-Qubit X/Hadamard) | $\approx 10^{-5}$ | Dimensionless | Theoretical minimum achieved by optimal control |
| Target Infidelity (Two-Qubit CZ) | $10^{-6}$ | Dimensionless | Achieved with $\tau = 1 \mu\text{s}$ and 6 basis functions |
| Fastest Single-Qubit Gate Time ($\tau$) | $1$ | $\mu\text{s}$ | Conservative estimate for $10^{-6}$ infidelity |
| Fastest Two-Qubit CZ Gate Time ($\tau$) | $1$ | $\mu\text{s}$ | Optimal duration for $10^{-6}$ infidelity |
| Electron Spin Relaxation Time ($T_{1,e}$) | $1.8$ | $\text{ms}$ | Used for Lindblad equation decoherence simulation |
| Room Temperature Coherence Time ($T_2$) | $\approx 2.4$ | $\text{ms}$ | Longest reported for solid-state spin at room T |
| Static Magnetic Field ($B_0$) | $0.62$ | $\text{T}$ | Applied along the NV axis for simulation |
| 15N Hyperfine Interaction ($A_N$) | $\approx 3$ | $\text{MHz}$ | Used in two-qubit system example |
| 13C Hyperfine Interaction ($A_C$) | $\approx 0.413$ | $\text{MHz}$ | Used in two-qubit system example (S family lattice site) |
| Max Pulse Amplitude (Single-Qubit RF/MW) | $25$ | $\text{Mrad/s}$ | Experimental hardware constraint |
| Max Pulse Amplitude (Two-Qubit CZ MW) | $80$ | $\text{Mrad/s}$ | Experimental hardware constraint |
| Simulated QFT3 Fidelity | $0.964$ | Dimensionless | 3-qubit QFT performance under decoherence |
| Simulated QFT5 Fidelity | $0.855$ | Dimensionless | 5-qubit QFT performance under decoherence |
Key Methodologies
Section titled âKey MethodologiesâThe core of the research is the development and simulation of a three-step semi-analytical optimal control method for generating robust RF/MW pulses.
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Qubit Architecture:
- The quantum processor utilizes the electron spin of the Nitrogen-Vacancy (NV) center as a quantum bus, coupled to nearby nuclear spins (intrinsic N and 13C lattice impurities) which serve as physical qubits.
- The system operates primarily in the $m_s = -1$ computational subspace, utilizing the $m_s = 0$ state as an auxiliary subspace for two-qubit Conditional-Z (CZ) gates.
-
Pulse Basis Generation (Step 1): Minimizing Cross-Talk:
- Control pulses $B_1(t)$ were parameterized in the frequency domain using frequency-shifted sinc functions as a complete basis set.
- The initial coefficients ($f^{(n)}, g^{(n)}$) were optimized to minimize intrinsic infidelity (Equation 2.33) in the absence of control errors, ensuring frequency selectivity and minimizing spurious cross-talk between individually addressed nuclear spin qubits.
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Linear Minimization (Step 2): Minimizing Control Errors:
- The control field was modeled to include Gaussian distributed random errors: fractional amplitude error ($\epsilon$), phase noise ($\phi$), and frequency noise ($\delta$).
- Linear combinations of the basis functions were solved to minimize the average gate infidelity $\langle I \rangle$ (Equation 2.38), achieving infidelities down to $10^{-6}$ for single-qubit gates.
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Time-Ordering Optimization (Step 3):
- The final optimization step incorporated the effects of time-ordering in the quantum evolution (neglected in the initial steps for computational efficiency) using numerical methods (finite-difference method, grid search).
- This step confirmed that infidelities of $10^{-5}$ or lower can be achieved, placing control errors below the intrinsic decoherence limit.
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Decoherence Modeling:
- The effects of decoherence were modeled using the Lindblad master equation, driven by the electron spin relaxation time ($T_{1,e} \approx 1.8 \text{ ms}$).
- The simulation confirmed that decoherence errors ($\approx 10^{-3}$) dominate control errors, necessitating the use of ultra-fast gates ($1 \mu\text{s}$) to maintain high fidelity.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful implementation of this optimal control strategy relies fundamentally on high-quality, precisely engineered diamond substrates. 6CCVD is uniquely positioned to supply the materials required to replicate and advance this research.
Applicable Materials for Quantum Processors
Section titled âApplicable Materials for Quantum ProcessorsâTo achieve the long electron spin relaxation times ($T_{1,e}$) and controlled nuclear spin environments necessary for high-fidelity, room-temperature quantum computing, researchers require specialized MPCVD diamond.
| Material Requirement (Paper) | 6CCVD Solution | Technical Justification & Sales Advantage |
|---|---|---|
| High $T_{1,e}$ and $T_2$ | High-Purity Single Crystal Diamond (SCD) | SCD offers the lowest background nitrogen concentration, maximizing $T_{1,e}$ and $T_2$ coherence times essential for minimizing decoherence errors ($\approx 10^{-3}$). |
| Controlled Nuclear Qubits | Isotopically Engineered Diamond | We offer diamond with controlled 13C concentration (natural abundance, enriched, or depleted). Precise isotopic control is crucial for selecting nuclear spin qubits with well-aligned hyperfine fields, as required by the optimization model. |
| Substrate Size & Uniformity | Large-Area Polycrystalline Diamond (PCD) | We provide PCD plates/wafers up to 125mm in diameter, necessary for scaling up the array of NV-processor nodes shown in Figure 1(a). Our PCD maintains high uniformity for consistent device fabrication. |
| Boron Doping (BDD) | Boron-Doped Diamond (BDD) | While not the primary qubit, BDD is often used in device architectures (e.g., for conductive layers or electrodes). We offer BDD films (0.1”m - 500”m) for integrated control systems. |
Customization Potential & Fabrication Support
Section titled âCustomization Potential & Fabrication SupportâThe research relies on integrating microwave control systems (surface structures) with the diamond chip. 6CCVD provides the necessary customization capabilities to facilitate device fabrication.
- Custom Dimensions and Thickness: We supply SCD and PCD plates/wafers in custom dimensions, ensuring compatibility with specific lithography and control system designs (e.g., surface microwave structures). We offer precise thickness control for SCD (0.1”m to 500”m) and substrates up to 10mm.
- Integrated Metalization: The implementation of RF/MW pulses requires high-quality metal electrodes. 6CCVD offers in-house metalization services, including deposition of Au, Pt, Pd, Ti, W, and Cu, directly onto the diamond surface, streamlining the fabrication of the control systems described in the paper.
- Surface Quality: Achieving reliable NV center performance and high-fidelity gate operations requires minimal surface defects. We guarantee ultra-smooth polishing: Ra < 1nm for SCD and Ra < 5nm for inch-size PCD, optimizing the interface for subsequent device processing.
Engineering Support
Section titled âEngineering SupportâThe complexity of optimizing diamond quantum processors, particularly concerning Hamiltonian modeling, hyperfine field misalignment mitigation, and pulse design, necessitates expert material consultation.
- PhD-Level Consultation: 6CCVDâs in-house team of PhD material scientists specializes in MPCVD growth and defect engineering. We provide authoritative support for researchers aiming to:
- Optimize diamond growth parameters to maximize $T_{1,e}$ and $T_2$ for room-temperature operation.
- Select the optimal isotopic composition (e.g., 13C concentration) to match the specific qubit register requirements of the optimal control model.
- Design substrates compatible with advanced numerical optimization techniques and feedback control systems for NV-based Quantum Computing and Quantum Sensing projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract Diamond quantum processors consisting of a nitrogen-vacancy centre and surrounding nuclear spins have been the key to significant advancements in room-temperature quantum computing, quantum sensing and microscopy. The optimisation of these processors is crucial for the development of large-scale diamond quantum computers and the next generation of enhanced quantum sensors and microscopes. Here, we present a full model of multi-qubit diamond quantum processors and develop a semi-analytical method for designing gate pulses. This method optimises gate speed and fidelity in the presence of random control errors and is readily compatible with feedback optimisation routines. We theoretically demonstrate infidelities approaching âŒ10 â5 for single-qubit gates and established evidence that this can also be achieved for a two-qubit CZ gate. Consequently, our method reduces the effects of control errors below the errors introduced by hyperfine field misalignment and the unavoidable decoherence that is intrinsic to the processors. Having developed this optimal control, we simulated the performance of a diamond quantum processor by computing quantum Fourier transforms. We find that the simulated diamond quantum processor is able to achieve fast operations with low error probability.