Perspective on witnessing entanglement in hybrid quantum systems

At a Glance

Metadata	Details
Publication Date	2021-09-13
Journal	Applied Physics Letters
Authors	Yingqiu Mao, Ming Gong, Kae Nemoto, William J. Munro, Johannes Majer
Institutions	Beijing Academy of Quantum Information Sciences, University of Science and Technology of China
Citations	1
Analysis	Full AI Review Included

Executive Summary

This technical documentation analyzes the requirements for experimentally verifying entanglement in hybrid quantum systems, specifically focusing on Nitrogen-Vacancy (NV) spin ensembles in diamond coupled via superconducting circuits.

Core Achievement Goal: Experimental verification of entanglement between two remote, macroscopic NV spin ensembles (NVEs) separated by centimeter distances, mediated by a superconducting resonator bus.
Hybrid System Architecture: Combines the long coherence times of NV^- spins in diamond with the fast, efficient tunability and scalability of superconducting transmon qubits and resonators.
Material Requirement: High-quality single crystal diamond (SCD) substrates are essential to host the NVEs, requiring low inhomogeneous broadening and long spin coherence times (T_coh > 13 µs).
Key Operational Challenge: Generating and detecting entanglement requires high-fidelity quantum state transfer operations (iSWAP, $\sqrt{\text{iSWAP}}$) between the superconducting qubits and the NVEs.
Proposed Solution: Utilizing superconducting qubits (Q1, Q2) to map the quantum state of the NVEs onto the qubits, allowing for standard two-qubit state tomography and entanglement verification.
6CCVD Value Proposition: 6CCVD provides the necessary high-purity, low-strain SCD substrates, custom dimensions, and ultra-smooth polishing (Ra < 1nm) required for seamless integration with high-Q superconducting circuits.

Technical Specifications

The feasibility of the proposed entanglement experiment relies on achieving and maintaining several critical parameters, extracted from the referenced literature (Ref. 19, 63, 64).

Parameter	Value	Unit	Context
Transmon-Resonator Coupling Strength ($g_{trm}$)	44	MHz	Achieved in recent experiments (Ref. 63).
NVE-Resonator Collective Coupling Strength ($g_{NVE}$)	9.6	MHz	Determined in previous NVE coupling experiments (Ref. 19).
Spin Coherence Time (T_coh)	13	µs	Measured coherence time allowing high-fidelity iSWAP.
iSWAP Operation Fidelity	> 99	%	Required fidelity for state transfer between qubit and NVE.
Collective Polariton Mode Decay Rate ($\Gamma$)	1.5	MHz	Estimates iSWAP fidelity to be 85% in current setups.
NVE Spin Count	> 10¹²	Spins	Typical number of spins in NVEs used for hybrid systems.
Entanglement Distance	Centimeter	Distance	Goal for remote entanglement between macroscopic objects.
Superconducting Chip Dimensions	4 x 12	mm	Example size of the niobium chip used as the cavity bus (Ref. 19).

Key Methodologies

The paper reviews and proposes specific methodologies necessary for the generation and verification of entanglement between remote NV spin ensembles (NVEs) using superconducting circuits.

Coherent Coupling via Resonator Bus:
- Two remote NVEs are coupled coherently via a common superconducting coplanar waveguide (CPW) resonator (Fig. 1, Fig. 2 setup).
- Tuning the magnetic field allows the NVEs to be brought into resonance with the resonator, achieving strong coupling.
- Dispersive direct coupling between the two ensembles is achieved by invoking a large detuning between the resonator and the NVEs.
Quantum State Initialization and Transfer:
- The initial photonic Fock state, necessary for entanglement generation, is created using a superconducting qubit (Q0, Q1, or Q2).
- The quantum state is transferred efficiently between the qubit and the NVE using resonant coupling.
- iSWAP Operation: Used for full quantum state transfer (demonstrated in 30 ns using direct magnetic coupling to a flux qubit, or 500 ns using an adiabatic tunable resonator).
- $\sqrt{\text{iSWAP}}$ Operation: Used for entanglement generation, requiring half the time of a full iSWAP operation.
Entanglement Verification via Qubit Tomography:
- The quantum state of the NVEs is mapped onto dedicated readout qubits (Q1 and Q2).
- Quantum state tomography is performed on the two qubits by measuring combinations of the X, Y, and Z directions.
- Readout Technique: Dispersive readout using a separate readout resonator, potentially enhanced by a Purcell filter or parametric amplifier for rapid, high-fidelity single-shot measurement (fidelity up to 99.2% in 88 ns).
Material Optimization:
- The use of electron-irradiated diamond samples is suggested to achieve lower inhomogeneous broadening, which is critical for improving coherence times and overall system fidelity.

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the foundational diamond materials and integrated solutions required to advance this critical research in hybrid quantum systems.

Applicable Materials

To replicate and extend the research on NV spin ensemble entanglement, the highest quality diamond is required to maximize T_coh and minimize inhomogeneous broadening.

Optical Grade Single Crystal Diamond (SCD):
- Requirement Match: SCD is the required host material for high-coherence NV^- centers. Our optical grade material offers extremely low nitrogen content and low strain, which is crucial for achieving the long T_coh (> 13 µs) and low inhomogeneous broadening necessary for high-fidelity quantum operations.
- Post-Processing Support: We recommend starting with high-purity SCD substrates suitable for subsequent NV creation via ion implantation or electron irradiation (as referenced in the paper, Ref. 64), followed by high-temperature annealing.
Custom Substrates:
- Dimensions: We provide custom SCD plates and wafers up to 125mm in size. For the integration shown in Fig. 1 (4mm x 12mm niobium chip), 6CCVD can supply precisely cut SCD crystals tailored to match the dimensions and placement requirements of the superconducting circuits.

Customization Potential

Successful integration of diamond NVEs with superconducting circuits demands precise material engineering and surface preparation.

Requirement from Paper	6CCVD Customization Capability	Technical Advantage
Ultra-Smooth Surface	Polishing to Ra < 1nm (SCD)	Essential for minimizing surface defects and ensuring optimal coupling and low loss when integrated with high-Q superconducting resonators.
Precise Dimensions	Custom laser cutting and shaping	Supply of SCD plates precisely sized (e.g., 4mm x 12mm) to align with the superconducting chip architecture and magnetic field anti-nodes.
Integration Layers	Custom Metalization (Au, Ti, Pt, Pd, Cu, W)	While the paper focuses on the NVEs, integration often requires metal contacts or bonding layers. 6CCVD offers in-house metalization services for seamless device fabrication.
Thickness Control	SCD thickness control (0.1µm to 500µm)	Allows researchers to optimize the volume and density of the NVEs for collective coupling strength ($g_{NVE}$) while maintaining thermal and mechanical stability.

Engineering Support

6CCVD’s in-house PhD team specializes in MPCVD growth parameters and post-processing techniques necessary for optimizing diamond for quantum applications.

Material Selection: We assist researchers in selecting the optimal SCD grade (purity, orientation, and initial nitrogen concentration) to maximize NV center yield and minimize inhomogeneous broadening for similar Hybrid Quantum System Entanglement projects.
Defect Engineering: Consultation on post-growth treatments, such as electron irradiation and annealing protocols, to achieve the desired NV^- concentration and charge state stability required for strong, coherent coupling.
Global Logistics: We ensure reliable global shipping (DDU default, DDP available) of sensitive, high-value diamond substrates directly to fabrication facilities worldwide.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Hybrid quantum systems aim at combining the advantages of different physical systems and producing innovative quantum devices. In particular, the hybrid combination of superconducting circuits and spins in solid-state crystals is a versatile platform to explore many quantum electrodynamics problems. Recently, the remote coupling of nitrogen-vacancy center spins in diamond via a superconducting bus was demonstrated. However, a rigorous experimental test of the quantum nature of this hybrid system and, in particular, entanglement is still missing. We review the theoretical ideas to generate and detect entanglement and present our own scheme to achieve this.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0062842

References

2019 - Quantum supremacy using a programmable superconducting processor [Crossref]
2021 - An integrated space-to-ground quantum communication network over 4,600 kilometres [Crossref]
2010 - Quantum computers [Crossref]
2006 - A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators [Crossref]
2013 - Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems [Crossref]
2015 - Quantum technologies with hybrid systems [Crossref]
2020 - Hybrid quantum systems with circuit quantum electrodynamics [Crossref]
2009 - Cavity QED based on collective magnetic dipole coupling: Spin ensembles as hybrid two-level systems [Crossref]
2010 - High-cooperativity coupling of electron-spin ensembles to superconducting cavities [Crossref]
2010 - Strong coupling of a spin ensemble to a superconducting resonator [Crossref]