Arbitrary nuclear-spin gates in diamond mediated by a nitrogen-vacancy-center electron spin

At a Glance

Metadata	Details
Publication Date	2017-09-11
Journal	Physical review. A/Physical review, A
Authors	J. Casanova, Z.-Y. Wang, Martin B. Plenio
Institutions	Universität Ulm
Citations	28
Analysis	Full AI Review Included

Technical Documentation and Analysis: Arbitrary Nuclear Spin Gates in Diamond

This documentation analyzes the key findings of “Arbitrary Nuclear Spin Gates in Diamond Mediated by a NV-center Electron Spin” and aligns the material requirements with 6CCVD’s specialized capabilities in custom MPCVD diamond manufacturing.

Executive Summary

This research establishes a foundational protocol for scalable solid-state quantum computation using diamond NV centers and coupled nuclear spins ($^{13}\text{C}$). The findings directly necessitate ultra-high-purity Single Crystal Diamond (SCD) material platforms.

Qubit Robustness: Demonstrates the use of nuclear spins ($^{13}\text{C}$) as highly coherent, robust quantum registers in diamond for quantum information processing.
Gate Efficiency: Achieves arbitrary single and N-qubit interactions among nuclear spins by leveraging the electron spin of the NV center as a fast, dynamically controlled mediator.
High Fidelity: Numerical simulation resulted in 98.8% fidelity for generating entangled three-qubit GHZ-like nuclear states, proving the viability of the AXY-8 dynamical decoupling sequence.
Scalability Advancement: The protocol eliminates the necessity of slow, external radio frequency (RF) control on the nuclear spins, relying solely on fast microwave (MW) control of the electron spin, simplifying integration.
Material Demand: Requires ultra-high-purity, low-nitrogen concentration Single Crystal Diamond (SCD) wafers to maximize NV electron spin coherence times ($T_2$).
Versatility: The methodology is transferable to other solid-state defects acting as mediators, such as those found in silicon carbide (SiC) or germanium vacancy centers.

Technical Specifications

The following parameters were critical for achieving high-fidelity gate operations and long coherence times:

Parameter	Value	Unit	Context
Material Type	IIa (High Purity)	-	Required for long NV T₂, low intrinsic nitrogen noise
Operating Temperature (T)	4.2	K	Required for NV electron T₂ > 25 ms coherence
Static Magnetic Field (B_z)	0.65	T	Aligned precisely with the NV axis (z-axis)
MW $\pi$-Pulse Duration	12.5	ns	Time resolution for fast electron spin control
Minimum AXY-8 Block Duration	$\approx$ 6.9 - 9.8	µs	Time required to execute individual dynamical decoupling units
Total Gate Time (3-Qubit GHZ)	$\approx$ 0.7	ms	Total evolution time using 3202 imperfect MW pulses
Achieved GHZ State Fidelity	98.8	%	Fidelity achieved for $\exp(i\phi \sigma_{x}^{1} \sigma_{x}^{2} I_{x}^{3})$ propagator
NV Electron T₂ Coherence	> 25	ms	Measured in high purity diamond at 4.2 K
Nuclear Qubit Species	¹³C (4.7% natural abundance)	-	Target nuclear spin register species

Key Methodologies

The robust creation of arbitrary N-body nuclear interactions relied upon precise synthesis and control protocols:

High-Purity Material Platform: Utilization of high-purity, low-nitrogen concentration Single Crystal Diamond (SCD) to minimize electronic noise (e.g., P₁ centers) and maximize NV electron spin coherence ($T_2$).
Defect Engineering: The NV center serves as the active electronic mediator, selectively coupled to nearby nuclear spins (e.g., $^{13}\text{C}$) via electron-nuclear hyperfine interaction ($A_{j}$).
Microwave-Only Control: The entire gate sequence is executed using high-frequency microwave $\pi$-pulses (12.5 ns duration) applied solely to the NV electron spin; no weak radio frequency (RF) control is needed for the nuclear spins.
Dynamical Decoupling (DD) Sequences: Robustness and selective coupling are ensured via advanced DD sequences, specifically the AXY-8 block structure (a sequence of composite $\pi$-pulses $X/Y$) which prolongs electron spin coherence and decouples the electron from noise sources.
Gate Sequence Concatenation: Complex N-body nuclear interactions ($U_{\phi}$) are synthesized by concatenating elementary, highly selective electron-nuclear entangling gates ($Q(\phi)$) interspersed with single-qubit electron rotations ($X_{\phi+\pi}$ or $Y_{\phi+\pi}$).
Quantum State Readout: Nuclear spin states are transferred back to the NV electron spin via a selective SWAP gate, enabling high-fidelity optical readout (demonstrated fidelities > 95% at low temperatures).

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the requisite MPCVD diamond materials and customization services necessary to replicate, optimize, and scale this high-coherence quantum research.

Applicable Materials

To achieve the exceptional coherence times ($T_2$ > 25 ms at 4.2 K) and low noise environment required by the AXY-8 DD sequence, the following 6CCVD material is essential:

Optical Grade Single Crystal Diamond (SCD): This material features ultra-low residual nitrogen concentration (< 1 ppb), guaranteeing the intrinsic purity required for maximizing NV $T_2$ and minimizing decoherence from P₁ centers and background $^{14}\text{N}$ noise.
Isotopically Purified SCD (Recommended Extension): To maximize the target nuclear qubit density and reduce non-qubit coupling noise, we recommend isotopically pure $^{12}\text{C}$ SCD wafers (reducing the natural 1.1% $^{13}\text{C}$ background) combined with precise implantation of the necessary $^{13}\text{C}$ nuclear spins.

Customization Potential

The success of this protocol requires tailored materials optimized for NV creation and integrated microwave control elements.

Research Requirement	6CCVD Custom Capability	Benefit to Project
Custom Wafer Size	Plates and wafers up to 125mm (PCD) / SCD wafers standard sizes.	Enables seamless scaling from proof-of-concept experiments to integrated, inch-size quantum devices.
NV Creation/Defect Density	Post-growth processing services including electron irradiation and high-temperature annealing.	Allows precise control over NV density necessary for addressing specific nuclear spins in proximity to the NV center.
Surface Quality	SCD Polishing to Ra < 1nm.	Ensures high-quality surface integrity crucial for lithography, deposition of MW antennae, and minimization of surface noise effects.
Microwave Circuit Integration	Custom metalization (Au, Pt, Pd, Ti, W, Cu) patterning.	Essential for integrating high-speed microwave transmission lines (e.g., co-planar waveguides or strip lines) necessary for applying the 12.5 ns control pulses described in the paper.
Substrate Thickness	SCD wafers available from 0.1 µm up to 500 µm, or custom Substrates up to 10 mm.	Offers flexibility for maximizing coupling efficiency or optimizing heat sinking in cryo-setups.

Engineering Support

Replicating and extending this research involves navigating complex material science challenges, including optimizing NV creation yields, managing isotopic purity, and designing integrated microwave structures.

6CCVD’s in-house PhD team provides comprehensive engineering support focused on:

Material Selection: Assisting researchers in selecting the optimal SCD or BDD material purity and thickness for highly sensitive NV-based Quantum Sensing and Computation projects.
Defect Control: Consulting on best practices for post-growth irradiation and annealing recipes to achieve target NV-center densities and maximize yield.
Integration Support: Providing technical guidance on metalization schemes and surface preparation necessary for reliable device integration (e.g., high-quality ohmic contacts for MW control).

Call to Action: For custom specifications or material consultation concerning high-purity SCD platforms for quantum technology, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

View Original Abstract

We propose a protocol that achieves arbitrary N-qubit interactions between\nnuclear spins and that can measure directly nuclear many-body correlators by\nappropriately making the nuclear spins interact with a nitrogen vacancy (NV)\ncenter electron spin. The method takes advantage of recently introduced\ndynamical decoupling techniques and demonstrates that action on the electron\nspin is sufficient to fully exploit nuclear spins as robust quantum registers.\nOur protocol is general, being applicable to other nuclear spin based platforms\nwith electronic spin defects acting as mediators as the case of silicon\ncarbide.\n