Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2015-04-23 |
| Journal | ACS Nano |
| Authors | Ya Wang, Florian Dolde, Jacob Biamonte, Ryan Babbush, Ville Bergholm |
| Institutions | Google (United States), University of Stuttgart |
| Citations | 146 |
| Analysis | Full AI Review Included |
6CCVD Technical Documentation: Quantum Simulation using Diamond NV Centers
Section titled â6CCVD Technical Documentation: Quantum Simulation using Diamond NV CentersâReference Paper: Quantum Simulation of Helium Hydride in a Solid-State Spin Register (arXiv:1405.2696v1)
Executive Summary
Section titled âExecutive SummaryâThe reported research establishes a crucial benchmark for solid-state quantum computing, demonstrating the first quantum chemistry simulation using a Nitrogen-Vacancy (NV) center in MPCVD diamond. 6CCVD, as a leading supplier of high-purity CVD diamond substrates, provides the foundational material necessary for this high-precision work.
- Pioneering Solid-State Simulation: Achieved the first quantum simulation of a molecular system ($\text{HeH}^+$ cation) utilizing a solid-state NV electron spin and a coupled ${}^{14}\text{N}$ nuclear spin register in diamond.
- Unprecedented Precision: Extracted molecular energy eigenvalues with an uncertainty of $\pm 1.4 \times 10^{-14}$ Hartree, exceeding standard chemical precision by ten orders of magnitude.
- High-Fidelity Control: Validated the use of optimal control theory (GRAPE algorithm) to implement quantum gates with fidelities greater than 0.99, a necessary step for scaling up quantum simulators.
- Material Foundation: The experiment relied upon high-purity diamond substrates grown via Microwave Plasma CVD (MPCVD), specifically enriched to $99.9% \text{ }^{12}\text{C}$ with nitrogen content below 1 ppb to ensure extended spin coherence.
- Scalability Blueprint: The work provides critical insight into the requirements for developing robust, scalable quantum simulators based on highly controllable solid-state spin systems.
- Key Results: Successfully determined the equilibrium bond length of $\text{HeH}^+$ to be $91.3$ pm and the corresponding minimal energy surface.
Technical Specifications
Section titled âTechnical SpecificationsâThe core experimental achievement relies on stringent material specifications and precise control parameters, summarized below:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Quantum Register | Electron Spin-1 / $\text{ }^{14}\text{N}$ Nuclear Spin-1 | Register | Simulation & Probe Qubit System (Qutrit Pair) |
| Energy Measurement Uncertainty | $\pm 1.4 \times 10^{-14}$ | Hartree | Achieved after 13 IPEA repetitions (10 orders better than chemical precision). |
| Ground State Energy (R=90 pm) | $-1.020170538763387$ | Hartree | Compared to theoretical value of $-1.020170538763381$ Hartree. |
| Optimal Equilibrium Bond Length | $91.3$ | pm | Corresponds to minimal energy of $-2.86269$ Hartree. |
| Electron Spin Coherence Time ($T_2$) | $\approx 600$ | ”s | Measured at room temperature in highly enriched diamond. |
| Electron Spin Lifetime ($T_1$) | $\approx 1.9$ | ”s | Nuclear spin under laser illumination. |
| Zero-Field Splitting ($\Delta$) | $\approx 2.87$ | GHz | NV electronic spin (S=1). |
| Hyperfine Coupling ($A_{\text{hf}}$) | $\approx 2.16$ | MHz | Between electron and $\text{ }^{14}\text{N}$ spins. |
| Isotopic Purity ($\text{ }^{12}\text{C}$) | $99.9$ | % | Enriched content in the CVD diamond substrate. |
| Intrinsic Nitrogen Content | < 1 | ppb | Ultra-low concentration in the high-purity CVD diamond. |
| Applied Magnetic Field ($B_0$) | $11$ | Gauss | Used to align spin systems along the NV axis. |
| Controlled Gate Fidelity ($U^*$) | > 0.99 | - | Optimized via the GRAPE control algorithm. |
Key Methodologies
Section titled âKey MethodologiesâThe following is an ordered summary of the specialized material science and quantum control methodologies employed in the research:
- CVD Material Synthesis: Utilization of high-purity diamond grown by Microwave-Assisted Chemical Vapor Deposition (MPCVD) with strict isotopic control ($99.9% \text{ }^{12}\text{C}$) and ultra-low intrinsic nitrogen (< 1 ppb).
- NV Qubit Registration: The NV center provides a solid-state spin register, where the electron spin ($S=1$) maps the molecular basis, and the nearby $\text{ }^{14}\text{N}$ nuclear spin ($I=1$) acts as the probe qubit for energy readout.
- Spin Initialization: The $\text{ }^{14}\text{N}$ nuclear spin is polarized from a thermal state into the $|m_I = 0\rangle$ state using optical pumping of the electron spin followed by precise polarization transfer and control (requiring $\pi$ pulses).
- Quantum Gate Implementation (Optimal Control): The controlled time evolution operator $U(t) = \text{exp}(-iH_{\text{sim}}t)$ is realized not by simple decomposition, but by customized, high-fidelity microwave pulse sequences optimized using the GRAPE (Gradient Ascent Pulse Engineering) algorithm.
- Energy Eigenvalue Extraction: The Iterative Phase Estimation Algorithm (IPEA) is applied, utilizing Fourier analysis on signals measured at varying time intervals ($t_s, 2t_s, \dots, Lt_s$) to iteratively resolve decimal digits of the energy eigenvalue.
- Potential Energy Surface Mapping: The experimental procedure is repeated across multiple internuclear distances ($R$) to construct the electronic potential energy surfaces, validating molecular properties like equilibrium geometry.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis quantum simulation research highlights the critical reliance on superior material qualityâspecifically, high-purity, isotopically enriched CVD Single Crystal Diamond (SCD)âwhich is a core offering of 6CCVD. To replicate or extend this work, researchers require diamond substrates engineered for maximum spin coherence and precise optical access.
Applicable Materials
Section titled âApplicable MaterialsâThe foundation of achieving microsecond coherence times ($T_2 \approx 600$ ”s) in this experiment is the ultra-pure, isotopically controlled MPCVD diamond. 6CCVD delivers:
- Optical Grade SCD (Single Crystal Diamond): Directly applicable, matching the specifications required: intrinsic nitrogen content guaranteed < 1 ppb.
- Isotopically Enriched Substrates: Supply of $\text{ }^{12}\text{C}$ enriched diamond up to $99.99%$ purity, surpassing the $99.9%$ used in this study, enabling researchers to push spin coherence times even further for larger, more complex quantum registers.
- Substrate Selection Support: Our in-house PhD engineering team assists clients in controlling specific impurities (e.g., intentionally introducing NV precursors or managing $P1$ centers) critical for specific solid-state quantum applications.
Customization Potential
Section titled âCustomization PotentialâThe utilization of optimal control sequences often requires specific chip designs, microwave antennae, and integrated readout mechanisms. 6CCVD supports these advanced engineering requirements:
| Custom Capability | Technical Offering | Value Proposition |
|---|---|---|
| Precision Substrates | SCD plates/wafers with thickness from $0.1$ ”m up to $500$ ”m, and substrates up to $10$ mm thick. | Provides the required volume and stability for integrated solid-state quantum devices operating at room temperature. |
| Ultra-Smooth Polishing | Surface roughness Ra < 1 nm (for SCD). | Essential for high-fidelity optical initialization and readout protocols (like those used in the IPEA sequence), minimizing signal loss and optical noise. |
| Custom Metalization | In-house deposition of Au, Pt, Pd, Ti, W, and Cu structures. | Enables direct integration of critical microwave control circuitry, required for realizing the high-fidelity optimal control (GRAPE) pulses necessary for scalable quantum simulation. |
| Custom Dimensions | Plates/wafers up to 125 mm (PCD) and custom laser cutting/machining. | Facilitates unique experimental mounting and complex microwave geometry fabrication needed for advanced quantum computing architectures. |
Engineering Support
Section titled âEngineering Supportâ6CCVDâs commitment extends beyond material supply. The complexity demonstrated in this studyâcombining Iterative Phase Estimation with Optimal Control theory on a solid-state platformârequires deep technical understanding.
Our in-house PhD team can assist with material selection for similar solid-state quantum computation and molecular simulation projects, ensuring the NV precursor control, isotopic purity, and surface preparation meet the exact demands of achieving ultra-high fidelity quantum operations. We offer global shipping (DDU default, DDP available) for seamless worldwide project deployment.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Ab initio computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH(+). Moreover, we report an energy uncertainty (given our model basis) of the order of 10(-14) hartree, which is 10 orders of magnitude below the desired chemical precision. As NV centers in diamond provide a robust and straightforward platform for quantum information processing, our work provides an important step toward a fully scalable solid-state implementation of a quantum chemistry simulator.