Deterministic preparation of W states via spin-photon interactions

At a Glance

Metadata	Details
Publication Date	2021-05-18
Journal	Physical review. A/Physical review, A
Authors	Fatih Özaydin, Can Yesilyurt, Sinan Bugu, Masato Koashi
Institutions	The University of Tokyo, Tokyo International University
Citations	29
Analysis	Full AI Review Included

Technical Documentation & Analysis: Deterministic W State Preparation using NV Centers in MPCVD Diamond

This document analyzes the research paper “Deterministic preparation of W States via spin-photon interactions” (arXiv:2105.10191v1) and outlines how 6CCVD’s advanced MPCVD diamond materials and customization capabilities are essential for replicating and scaling this deterministic quantum computing architecture.

Executive Summary

The research presents a highly efficient, deterministic method for creating and expanding arbitrary-size W states, a critical resource for quantum networks, utilizing solid-state spin systems.

Deterministic Operation: Proposes a three-qubit operation (O) that serves as a fundamental building block for W state creation, eliminating the need for probabilistic post-measurement or post-processing common in fusion schemes.
Solid-State Platform: Focuses on Nitrogen Vacancy (NV) centers embedded in diamond coupled to high-quality optical microcavities (e.g., photonic crystals or microtoroids).
High Fidelity: Theoretical analysis confirms high operational fidelity (greater than 0.97) even when accounting for combined imperfections in Controlled-Z (CZ), Hadamard (H), and T’ gates at $\Theta = \pi/60$.
Spin-Photon Interaction: The scheme relies exclusively on spin-photon interactions, avoiding direct interaction between logical qubits, which simplifies scalability for spatially separated systems.
Scalability: The operation allows for deterministic doubling of an existing W state size (W_n to W_2n) or creation from separable qubits.
Material Requirement: Requires ultra-high quality, low-strain Single Crystal Diamond (SCD) substrates to host NV centers with long coherence times, especially for room-temperature applications.

Technical Specifications

The following hard data points and system requirements are extracted from the analysis of the proposed quantum circuit and physical model:

Parameter	Value	Unit	Context
Target Quantum State	W State	N/A	Deterministic preparation and expansion (W_n to W_2n)
Required Gate Fidelity	> 0.97	N/A	Combined imperfection tolerance at $\Theta = \pi/60$
Core Qubit System	NV Centers	N/A	Exemplary solid-state spin system in diamond
Gate Decomposition	4 CZ, 6 H, 2 T’	N/A	Components of the three-qubit operation (O)
Cavity Q-Factor (Reference)	Up to 10⁷	N/A	Required for efficient spin-photon coupling (Photonic Crystal Cavities)
Spin Coherence Requirement	High	N/A	Essential for room temperature operation and multi-step expansion
Ancillary Qubit Role	Catalyzer	N/A	Left in ideal initial state after operation; reusable
CZ Gate Mechanism	Spin-dependent phase shift	N/A	Realized via optical Faraday rotation

Key Methodologies

The deterministic W state preparation relies on precise material engineering and controlled quantum gate implementation:

System Integration: NV centers are coupled to high-Q optical microcavities (e.g., microtoroids or photonic crystals) to enhance the interaction between the NV electronic spin and incident photons.
Spin-Selective Reflectivity: The physical model leverages the spin-dependent optical transition rules of the NV center, where the reflection coefficient of an incident photon depends on the spin state of the NV center.
Controlled-Z (CZ) Gate Realization: A controlled-Z gate between the NV electronic spin and the incident photon is realized by applying a phase shift to the reflected photon path, contingent on the NV spin state.
Single-Qubit Gate Implementation:
- Photonic qubits: Hadamard (H) and T’ gates are realized using Half Wave Plates (HWP).
- NV Spin qubits: H and T’ gates are realized using Holonomic Quantum Control via nanosecond Electro-Magnetic (EM) pulses.
Three-Qubit Operation (O): The core operation is constructed from a sequence of CZ, H, and T’ gates, enabling interaction between two logical qubits via a single ancillary qubit (spin or photon) without direct logical qubit interaction.
Deterministic Expansion: The operation (O) is applied sequentially to expand an n-qubit W state to a 2n-qubit W state, requiring no post-selection or measurement that would destroy the target state.

6CCVD Solutions & Capabilities

The deterministic preparation of W states using NV centers demands diamond materials with exceptional purity, precise geometry, and atomic-scale surface quality—all core competencies of 6CCVD’s MPCVD manufacturing.

Applicable Materials

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

Optical Grade Single Crystal Diamond (SCD): Essential for hosting NV centers. Our SCD offers ultra-low strain and defect densities (e.g., nitrogen concentration [N] < 1 ppb), maximizing the NV center’s spin coherence time, which is critical for multi-step deterministic gate sequences and achieving the required high fidelity (> 0.97).
Custom Nitrogen Doping: 6CCVD provides controlled nitrogen incorporation during growth or post-growth implantation services to achieve optimal NV density and spatial separation for scalable quantum networks.

Customization Potential

The integration of NV centers with high-Q microcavities (photonic crystals, microtoroids) necessitates stringent material specifications that 6CCVD is uniquely positioned to meet:

Research Requirement	6CCVD Capability	Specification Range
Substrate Dimensions	Custom Plates/Wafers	Up to 125 mm (PCD), Custom SCD sizes
Thin Film Thickness	Precise SCD Layer Control	0.1 µm to 500 µm
Surface Quality	Ultra-Low Roughness Polishing	Ra < 1 nm (SCD)
Gate Implementation	Custom Metalization Services	Au, Pt, Pd, Ti, W, Cu deposition
Context	Required for fabricating high-Q photonic crystal cavities directly onto the diamond surface.
Context	Essential for minimizing optical losses and maximizing spin-photon coupling efficiency.
Context	Enables integration of electrodes for EM pulse control of NV spins (Holonomic Quantum Control).

Engineering Support

6CCVD’s in-house PhD team specializes in optimizing MPCVD diamond growth parameters specifically for solid-state quantum applications. We offer comprehensive engineering support for similar NV Center Quantum Network projects, including:

Material Selection: Guidance on choosing the optimal SCD grade and thickness for specific microcavity designs (e.g., single-sided vs. double-sided cavities).
Defect Engineering: Consultation on controlled nitrogen doping and post-processing techniques to ensure high-yield, high-coherence NV center creation.
Interface Optimization: Assistance in preparing diamond surfaces for subsequent nanofabrication steps (e.g., etching for photonic crystals) to maintain the required Ra < 1 nm finish.

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

View Original Abstract

Spin systems such as silicon or nitrogen vacancy centers in diamond, quantum\ndots and quantum dot molecules coupled to optical cavities appear as key\nelements for creating quantum networks as not only constituting the nodes of\nthe network, but also assisting the creation of photonic networks. Here we\nstudy deterministic preparation of arbitrary size $W$ states with spin systems.\nWe present an efficient operation on three qubits, two being the logical qubits\nand one being the ancillary qubit, where no interaction between the logical\nqubits are required. The proposed operation can create a $W$-type\nEinstein-Podolsky-Rosen (EPR) pair from two separable qubits, and expand that\nEPR pair or an arbitrary size $W$ state by one, creating a $W$-like state.\nTaking this operation as the fundamental building block, we show how to create\na large scale $W$ state out of separable qubits, or double the size of a $W$\nstate. Based on this operation and focusing on nitrogen vacancy (NV) centers in\ndiamond as an exemplary spin system, we propose a setup for preparing $W$\nstates of circularly polarized photons, assisted by a single spin qubit, where\nno photon-photon interactions are required. Next, we propose a setup for\npreparing $W$ states of spin qubits of spatially separated systems, assisted by\na single photon. We also analyze the effects of possible imperfections in\nimplementing the gates on the fidelity of the generated $W$ states. In our\nsetups, neither post-measurement, nor post-processing on the states of spin or\nphotonic qubit is required. Our setups can be implemented with current\ntechnology, and we anticipate that they contribute to quantum science and\ntechnologies.\n