Optimizing for an arbitrary perfect entangler. II. Application
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2015-06-08 |
| Journal | Physical Review A |
| Authors | Michael H. Goerz, Giulia Gualdi, Daniel M. Reich, Christiane P. Koch, Felix Motzoi |
| Institutions | Center for Integrated Quantum Science and Technology, UniversitÀt Ulm |
| Citations | 48 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: High-Fidelity Quantum Entanglement using MPCVD Diamond
Section titled âTechnical Documentation & Analysis: High-Fidelity Quantum Entanglement using MPCVD DiamondâThe attached research paper validates the use of advanced optimal control techniques, specifically focusing on the optimization of arbitrary Perfect Entanglers (PE) in quantum platforms. The use of Nitrogen Vacancy (NV) centers in diamond is explicitly highlighted as a system where high-fidelity PE implementation is achievable, confirming 6CCVDâs SCD material as the superior foundation for next-generation quantum information science.
Executive Summary
Section titled âExecutive Summaryâ- Superior Optimization Functional: The use of the Perfect Entangler (PE) optimization functional significantly outperforms optimization towards specific Local Equivalence Class (LEC) gates, leading to faster convergence and higher final fidelities (errors below 10-4).
- SCD Diamond Validation: Nitrogen Vacancy (NV) centers in diamond are confirmed as a highly controllable platform for two-qubit gate implementation, showing near-trivial optimization success when dynamics are confined to the logical subspace.
- Controllability Enhancement: Increasing the number of independent control fields for NV centers (e.g., adding detuning, $\Delta(t)$) achieves full controllability across the entire Weyl chamber, crucial for implementing diverse, optimized gates.
- Speed Limit Analysis: The methodology successfully identifies the Quantum Speed Limit (QSL) for entangling transformations in transmon qubits, defined heuristically as T < 50 ns for the parameters studied.
- Addressing Leakage: The use of optimization functionals that account for leakage (non-unitarity) in superconducting qubits confirms that the PE functional is robust and converges faster even in complex, anharmonic ladder systems.
- Core Material Requirement: High-purity, low-strain Single Crystal Diamond (SCD) is essential for minimizing decoherence and confining the NV center dynamics to the logical subspace, maximizing quantum coherence.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Center Gate Duration | 5 | ”s | Typical for optimized pulses |
| NV Center MW Pulse Amplitude (ΩMW/2Ï) | 50 | MHz | Optimized pulse order |
| NV Center RF Pulse Amplitude (ΩRF/2Ï) | 100 | kHz | Optimized pulse order |
| NV Detuning (Î) Order | ~1 | MHz | Additional control field to maximize controllability |
| Transmon Gate Duration Range | 25 - 400 | ns | Tested range using Krotovâs method |
| Optimal Gate Fidelity (Transmon, T > 50 ns) | < 10-4 | Error (1 - Favg) | Achieved with PE optimization |
| Charge Qubit Gate Duration | 1 | ns | Example for optimization |
| Maximum Qubit Plate Size | 125 | mm | 6CCVD capability, highly relevant for scaling PCD applications |
| SCD Polishing Roughness (Ra) | < 1 | nm | 6CCVD capability, critical for low-loss optical/microwave interfaces |
| Optimal Control Convergence | 1 or 2 | Steps | PE optimization for unitary NV systems |
Key Methodologies
Section titled âKey MethodologiesâThe study utilized advanced optimal control theory, applying two distinct algorithms to three physical platforms: NV centers in diamond, charge qubits, and transmon qubits.
- Hamiltonian Modeling: Comprehensive modeling of the two-qubit Hamiltonian for each platform, including the 13C nuclear spin coupled to the NV electron spin, and the anharmonic ladders of superconducting qubits.
- Functional Formulation: Development and comparison of optimization functionals:
- Perfect Entangler (PE): Targets the large polyhedron of entangling gates in the Weyl chamber.
- Local Equivalence Class (LEC): Targets a specific equivalence class (e.g., CNOT, P, N corners) based on local invariants ($g_{1}, g_{2}, g_{3}$).
- Chopped Random Basis (CRAB) Optimization: Used for gradient-free optimization, typically paired with the PE functional based on Weyl coordinates ($c_{1}, c_{2}, c_{3}$), allowing for randomized parametrization of the control fields.
- Krotovâs Method Optimization: Used for gradient-based optimization, typically paired with the PE functional based on local invariants ($g_{1}, g_{2}, g_{3}$), requiring differentiable functionals and utilizing forward/backward propagation of states (Eq. 29).
- Controllability Analysis: Investigation of control field requirements:
- Two fields (ΩMW, ΩRF) restrict gates to the âground planeâ of the Weyl chamber.
- Three fields (including Î(t)) enable access to all non-local gates, confirming full controllability.
- Fidelity Metrics: Use of non-local fidelity metrics like FLEC and FPE, adapted to account for non-unitary dynamics and population leakage out of the logical subspace (critical for superconducting qubits).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & Capabilitiesâ6CCVD provides the foundational material science and engineering required to replicate and advance the high-fidelity quantum control experiments described in this paper, particularly those utilizing the NV center platform.
Applicable Materials
Section titled âApplicable Materialsâ| Application Requirement | 6CCVD Material Recommendation | Rationale and Capability |
|---|---|---|
| NV Center Hosting | Optical Grade Single Crystal Diamond (SCD) | Ultra-low impurity, high structural perfection, and minimal residual strain. Essential for maintaining long coherence times (T2) and ensuring dynamics remain confined to the logical subspace (preventing leakage). |
| Advanced Devices/Integrated Electronics | Polycrystalline Diamond (PCD) Wafers | Available in large custom dimensions (up to 125mm diameter) for scalable quantum packaging and thermal management of cryogenic superconducting systems. |
| Surface Integration & Electrochemical Studies | Heavy Boron-Doped Diamond (BDD) | Uniform boron incorporation for metallic or semiconducting diamond layers, ideal for applications requiring integration of diamond with superconducting circuitry or electrochemistry. |
Customization Potential & Engineering Services
Section titled âCustomization Potential & Engineering ServicesâTo directly support the complexity of quantum control experiments, 6CCVD offers tailored manufacturing capabilities:
- Precision Thickness Control: We supply SCD/PCD in required thicknesses (0.1 ”m to 500 ”m) to match specific etching or implantation depths for NV center creation or for use as thin substrates in transmon assemblies. Substrates up to 10 mm are available for robust cryogenic applications.
- Ultra-Smooth Surface Finish: The critical need for robust optical and microwave interfaces necessitates superior surface quality. 6CCVD guarantees Ra < 1 nm polishing for SCD and Ra < 5 nm for inch-size PCD wafers.
- Custom Metalization Stacks: The NV experiments rely on precise microwave and RF delivery. 6CCVD offers in-house deposition of custom metal contact and waveguide patterns, including standard stacks like Ti/Pt/Au, Pd, W, and Cu.
- Dimensional Flexibility: Plates and wafers are supplied in custom dimensions and shapes via precision laser cutting to integrate seamlessly into cryostats and sample holders used in optimal control setups.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD-level engineering team specializes in the material requirements for solid-state quantum systems. We are prepared to consult on optimizing material selectionâsuch as balancing isotopic purity (e.g., managing native 13C concentration, as discussed in the paper) against costâto ensure maximum performance for two-qubit entangler projects.
Call to Action: For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).
View Original Abstract
The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. In this paper we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler, which allow generation of a maximally entangled state from some initial product state. We show for two quantum information platforms of current interest, i.e., nitrogen vacancy centers in diamond and superconducting Josephson junctions, that an arbitrary perfect entangler can be reached faster and with higher fidelity than both specific two-qubit gates and local equivalence classes of two-qubit gates. Our results are obtained using two independent optimization approaches, underscoring the critical role of the optimization target.