Generation of multipartite entanglement between spin-1 particles with bifurcation-based quantum annealing

At a Glance

Metadata	Details
Publication Date	2022-09-02
Journal	Scientific Reports
Authors	Yuichiro Matsuzaki, Takashi Imoto, Yuki Susa
Institutions	National Institute of Advanced Industrial Science and Technology
Citations	5
Analysis	Full AI Review Included

Technical Documentation: Bifurcation-Based Quantum Annealing using NV Centers in Diamond

Source Paper: Generation of multipartite entanglement between spin-1 particles with bifurcation-based quantum annealing (Scientific Reports, 2022)

Executive Summary

This research proposes a novel scheme for generating highly entangled Greenberger-Horne-Zeilinger (GHZ) states using bifurcation-based Quantum Annealing (QA) implemented via Nitrogen Vacancy (NV) centers in diamond.

Core Achievement: Demonstration of a protocol to generate multipartite GHZ entanglement (up to L=4 spins) using spin-1 particles (NV centers).
Methodology: Utilizes bifurcation-based QA, where the system evolves adiabatically under a time-dependent Hamiltonian, transitioning from a trivial ground state to the target GHZ state.
Physical System: The scheme is designed for implementation using NV centers arranged in a one-dimensional chain within a diamond lattice, leveraging intrinsic dipole-dipole interactions.
Performance: Numerical simulations show high fidelity (F > 0.999) for L=2 systems under ideal conditions, and robust fidelity (F ≈ 0.89) even for L=4 systems under realistic strain and decoherence rates (γ = 0.5 kHz).
Material Requirement: Successful implementation relies critically on high-purity, low-strain Single Crystal Diamond (SCD) substrates to ensure long spin coherence times (T₂*) necessary for adiabatic evolution over the required time T = 0.1 ms.
6CCVD Value Proposition: 6CCVD provides the necessary high-quality MPCVD SCD substrates, custom metalization, and engineering support required to realize scalable quantum computing architectures based on NV centers.

Technical Specifications

The following parameters were extracted from the numerical simulations used to validate the GHZ state generation scheme, primarily focusing on the L=2 and L=4 qubit systems.

Parameter	Value (Simulation)	Unit	Context / Real-World Requirement
Annealing Time (T)	0.1	ms	Required duration for adiabatic evolution.
Magnetic Field (σ)	0.2	T	Applied external field.
Decoherence Rate (γ)	0.5	kHz	Used in noisy environment simulations (Fig. 2b, 3b).
Zero-Field Splitting (D₀/2π)	400 / 200	kHz	Simulation values (L=2 / L=4). Real NV D₀/2π is ~2.88 GHz.
Microwave Frequency (ω/2π)	40	MHz	Used in simulations for computational efficiency.
Microwave Amplitude (B/2π)	100 / 340	kHz	Used in L=2 / L=4 simulations.
Strain (E_x/2π)	0 to 16	kHz	Tested range. Higher strain reduces fidelity (F).
Flip-Flop Coupling (J₁₂/2π)	30	kHz	Dipole-dipole interaction strength.
Ising Interaction (I₁₂/2π)	60	kHz	Dipole-dipole interaction strength.
Maximum Fidelity (L=2, No Strain)	> 0.999	N/A	Achieved under unitary dynamics.
Fidelity (L=4, γ=0.5 kHz, E_x/2π=3 kHz)	0.89	N/A	Achieved under realistic noisy conditions.

Key Methodologies

The proposed scheme leverages the unique properties of spin-1 NV centers in diamond and the principles of adiabatic quantum computation.

Physical System Setup: Spin-1 particles (NV centers) are arranged in a one-dimensional chain, utilizing the intrinsic dipole-dipole interactions for coupling (J_jk and I_jk).
Initial State Preparation: Each spin-1 particle is initialized in the trivial ground state, $|0\rangle$.
Hamiltonian Evolution: The system evolves under a total Hamiltonian $H = H_{D} + H_{P}$, where $H_{D}$ is the driving Hamiltonian (inducing quantum fluctuation) and $H_{P}$ is the problem Hamiltonian (encoding the GHZ state).
Spin-Lock QA Implementation: To overcome the large positive zero-field splitting (D₀/2π ≈ 2.88 GHz) of real NV centers, the experiment is proposed in a rotating frame (spin-lock QA). This allows the detuning (D’) to act as the longitudinal field, which can be dynamically controlled.
Adiabatic Protocol: The detuning (D’) is gradually decreased while the amplitude of the external microwave driving fields is adiabatically changed over the annealing time (T = 0.1 ms).
Symmetry Protection: The total Hamiltonian is shown to commute with a parity operator, which suppresses non-adiabatic transitions between the target ground state ($|GHZ^{+}\rangle$) and the first excited state ($|GHZ^{-}\rangle$), maintaining high fidelity.
Microwave Control: The protocol requires only global application of time-dependent microwave fields, avoiding the need for complex, individual addressing of NV centers, which is crucial for scaling.

6CCVD Solutions & Capabilities

The successful implementation and scaling of this bifurcation-based quantum annealing scheme using NV centers demand diamond materials with exceptional purity, low strain, and precise engineering. 6CCVD is uniquely positioned to supply the required MPCVD diamond solutions.

Applicable Materials

To replicate and extend this research, the following 6CCVD materials are essential:

Optical Grade Single Crystal Diamond (SCD): Required for hosting high-quality NV centers. Our SCD features extremely low nitrogen concentration (< 1 ppb) and low strain, which is critical for achieving the long coherence times (T₂*) necessary to satisfy the adiabatic condition over the required T = 0.1 ms annealing time.
Isotopically Pure ¹²C Diamond: While not explicitly detailed in the paper, achieving the long coherence times cited (few milliseconds) often requires isotopically purified ¹²C diamond to minimize decoherence from nuclear spin baths. 6CCVD offers custom isotopic purity control during MPCVD growth.

Customization Potential

The proposed scheme requires precise control over the NV environment and the application of external fields. 6CCVD offers comprehensive customization services to meet these engineering demands:

Research Requirement	6CCVD Customization Capability	Technical Advantage
Scalability (L > 4)	Plates/wafers up to 125mm (PCD) and large-area SCD substrates.	Enables the fabrication of larger quantum registers and complex 1D/2D arrays of NV centers.
Microwave Delivery	Custom Metalization (Au, Pt, Ti, Cu, W) services.	Allows researchers to deposit high-conductivity microwave strip lines and coplanar waveguides directly onto the diamond surface for efficient B-field delivery.
Precise NV Depth	SCD Thickness Control (0.1µm - 500µm).	Essential for controlling the depth of implanted NV centers relative to surface metalization and minimizing surface-related decoherence.
Low Surface Roughness	Polishing (Ra < 1nm for SCD).	Ultra-smooth surfaces are necessary for high-fidelity lithography and subsequent metalization steps required for microwave circuitry.
Substrate Handling	Substrates up to 10mm thickness.	Provides robust mechanical support for complex experimental setups involving high magnetic fields (σ = 0.2 T) and cryogenic environments.

Engineering Support

6CCVD’s in-house team of PhD material scientists and quantum engineers can assist researchers in optimizing material selection for similar Bifurcation-Based Quantum Annealing projects. We provide consultation on:

Strain Management: Selecting growth parameters to minimize internal strain (E_x), directly improving the achievable GHZ state fidelity (as shown in Fig. 2a).
NV Center Integration: Advising on optimal diamond thickness and surface preparation for subsequent ion implantation or delta-doping techniques used to create the NV centers.
Metalization Stack Design: Designing multi-layer metal stacks (e.g., Ti/Pt/Au) for robust ohmic contacts and high-frequency microwave transmission lines.

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

View Original Abstract

Abstract Quantum annealing is a way to solve a combinational optimization problem where quantum fluctuation is induced by transverse fields. Recently, a bifurcation-based quantum annealing with spin-1 particles was suggested as another mechanism to implement the quantum annealing. In the bifurcation-based quantum annealing, each spin is initially prepared in $$|0\rangle$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mo>|</mml:mo> <mml:mn>0</mml:mn> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> , let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by $$|\pm 1\rangle$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> at the end of the evolution. Here, we propose a scheme to generate multipartite entanglement, namely GHZ states, between spin-1 particles by using the bifurcation-based quantum annealing. We gradually decrease the detuning of the spin-1 particles while we adiabatically change the amplitude of the external driving fields. Due to the dipole-dipole interactions between the spin-1 particles, we can prepare the GHZ state after performing this protocol. We discuss possible implementations of our scheme by using nitrogen vacancy centers in diamond.

Tech Support

Original Source

DOI: https://doi.org/10.1038/s41598-022-17621-1