Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm

At a Glance

Metadata	Details
Publication Date	2016-01-28
Journal	New Journal of Physics
Authors	XUE KE SONG, Hao Zhang, Qing Ai, Jing Qiu, Fu-Guo Deng
Institutions	Beijing Normal University
Citations	129
Analysis	Full AI Review Included

Technical Documentation & Analysis: Accelerated Holonomic Quantum Computation using NV Diamond

Project Reference: Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm (arXiv:1509.00097v2)

Executive Summary

This research demonstrates a robust and efficient scheme for universal Holonomic Quantum Computation (HQC) by leveraging the Transitionless Quantum Driving Algorithm (TQDA) within a Decoherence-Free Subspace (DFS). The physical implementation relies critically on high-quality diamond Nitrogen-Vacancy (NV) centers.

Accelerated Quantum Gates: TQDA is successfully applied to speed up adiabatic HQC, significantly reducing the long runtime errors associated with traditional adiabatic protocols.
Universal Gate Set Achieved: The scheme realizes shortcuts for two noncommuting single-qubit holonomic gates and an accelerated two-qubit controlled-phase (CP) gate, providing the necessary elements for universal quantum computation.
Robustness via DFS: Operation within the DFS ensures the protocol is inherently robust against collective noise and local fluctuations, a key advantage for scalable quantum systems.
Simplified Implementation: The protocol requires only two-body interactions (via a virtual photon process) rather than complex four-body interactions, greatly simplifying experimental realization.
High Fidelity Demonstrated: Numerical simulations using current experimental parameters confirm high gate fidelities: up to 99.91% for single-qubit bit-phase gates and 99.76% for the two-qubit CP gate.
Material Requirement: The feasibility hinges on the long electron-spin coherence time provided by high-purity diamond NV centers coupled dispersively to high-Q microsphere cavities.

Technical Specifications

The following hard data points were extracted from the numerical simulations and experimental context used to validate the proposed scheme.

Parameter	Value	Unit	Context
Cavity Quality Factor (Q)	10⁸ - 10¹⁰	Dimensionless	Fused-silica microsphere
NV Center Spontaneous Decay Rate ($\Gamma_0$)	$2\pi \times 83$	MHz	Excited state $
Cavity Frequency ($\omega_c$)	$2\pi \times 74.8$	THz	WGM mode frequency
Cavity Decay Rate ($\kappa$)	$2\pi \times 0.0748$	MHz	Used in Lindblad master equation simulation
NV Center Zero Field Splitting ($\omega_{10}$)	2.87	GHz	Ground state transition frequency
NV Center Zero-Phonon Line ($\omega_{e0}$)	471	THz	Corresponds to 637 nm transition wavelength
NV-Cavity Coupling Strength (G)	$\approx 2\pi \times 1$	GHz	Characteristic interaction volume
Effective Rabi Frequency ($g$)	$2\pi \times 50$	MHz	Used for gate simulation
Single-Qubit Bit-Phase Gate Fidelity	99.91	%	Achieved with optimized detuning ($\delta_1 = 2\pi \times 7$ GHz)
Two-Qubit CP Gate Fidelity	99.76	%	Achieved with optimized detuning ($\delta_1 = 2\pi \times 4$ GHz)

Key Methodologies

The experimental feasibility of this quantum computation scheme relies on precise material engineering and external control fields.

System Configuration: The setup consists of multiple identical NV centers, each in a separate diamond nanocrystal, dispersively coupled to a quantized Whispering-Gallery Mode (WGM) of a fused-silica microsphere cavity.
Qubit Definition: The qubit states $|0\rangle$ and $|1\rangle$ are encoded in the ground state manifold of the NV center ($|^3A, m_s=0\rangle$ and $|^3A, m_s=-1\rangle$).
Adiabatic Elimination: The excited state $|e\rangle$ ($|^3E, m_s=0\rangle$) is eliminated by ensuring the detuning ($\Delta$) between the NV transition and the cavity/laser fields is significantly larger than the coupling strengths ($G$ and $\Omega_L$).
Transitionless Quantum Driving (TQDA): TQDA is employed as a reverse engineering approach to construct an auxiliary Hamiltonian $H_1(t)$ that drives the system along the instantaneous eigenstates of the fundamental Hamiltonian $H_0(t)$, thereby accelerating the adiabatic process.
Gate Control: Quantum gates are realized by precisely tuning the frequencies of external classical laser pulses. This tuning controls the effective Rabi frequencies ($\lambda’_{jk}$) between the NV centers, which dictates the gate operation.
Interaction Mechanism: The effective interaction between NV centers is mediated by a virtual photon process, enabling the required two-body interactions while suppressing cavity decay.

6CCVD Solutions & Capabilities

The successful physical implementation of this accelerated HQC scheme requires diamond materials with exceptional purity, precise geometry, and surface quality—core competencies of 6CCVD.

Applicable Materials

To replicate or extend this research, the highest quality Single Crystal Diamond (SCD) is essential for maximizing NV center coherence time and minimizing optical loss.

Optical Grade Single Crystal Diamond (SCD): Required for hosting high-coherence NV centers. 6CCVD provides SCD plates with ultra-low nitrogen content, ideal for quantum applications demanding long spin coherence times (up to 0.6 s at 77 K, as cited in the paper).
Custom Thickness: We offer SCD wafers in the critical thickness range of 0.1 µm to 500 µm, allowing researchers to optimize the diamond volume for NV creation and integration into microcavity systems.

Customization Potential

The integration of NV centers with WGM microspheres demands precise material dimensions and surface preparation. 6CCVD specializes in meeting these stringent requirements.

Research Requirement	6CCVD Capability	Technical Advantage
High-Purity Substrates	MPCVD Single Crystal Diamond (SCD)	Ensures minimal defects and impurities, maximizing NV spin coherence and optical properties.
Precise Geometry	Custom Dimensions & Laser Cutting	We provide plates/wafers up to 125 mm (PCD), and offer precision laser cutting for creating the small diamond nanocrystals or thin membranes necessary for optimal coupling to the WGM cavity.
Surface Quality	Ultra-High Polishing (SCD)	Our SCD polishing achieves surface roughness Ra < 1 nm. This is critical for minimizing scattering losses and maintaining the ultrahigh Q factor of the coupled microsphere system.
Integration & Readout	Custom Metalization Services	We offer in-house deposition of metals (Au, Pt, Pd, Ti, W, Cu). This capability is vital for future extensions requiring electrical control, microwave delivery, or robust bonding pads for complex chip integration.

Engineering Support

6CCVD’s in-house team of PhD material scientists and quantum engineers are experts in optimizing diamond growth parameters for specific quantum defects.

Material Selection for Quantum Projects: Our team can assist researchers in selecting the optimal SCD grade and thickness required for similar NV-based Quantum Computation projects, ensuring the material properties support the high fidelity and robustness demonstrated by the TQDA-HQC protocol.
Defect Engineering Consultation: We provide consultation on post-processing techniques (e.g., nitrogen implantation, annealing) to achieve the desired density and location of NV centers for efficient coupling to photonic structures.

Call to Action

The realization of accelerated, high-fidelity holonomic quantum gates depends fundamentally on the quality of the diamond substrate. Partner with 6CCVD to secure the highest purity MPCVD diamond materials tailored precisely to your quantum architecture.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We offer reliable, DDU global shipping (DDP available upon request) to ensure your research stays on schedule.

View Original Abstract

By using transitionless quantum driving algorithm (TQDA), we present an\nefficient scheme for the shortcuts to the holonomic quantum computation (HQC).\nIt works in decoherence-free subspace (DFS) and the adiabatic process can be\nspeeded up in the shortest possible time. More interestingly, we give a\nphysical implementation for our shortcuts to HQC with nitrogen-vacancy centers\nin diamonds dispersively coupled to a whispering-gallery mode microsphere\ncavity. It can be efficiently realized by controlling appropriately the\nfrequencies of the external laser pulses. Also, our scheme has good scalability\nwith more qubits. Different from previous works, we first use TQDA to realize a\nuniversal HQC in DFS, including not only two noncommuting accelerated\nsingle-qubit holonomic gates but also a accelerated two-qubit holonomic\ncontrolled-phase gate, which provides the necessary shortcuts for the complete\nset of gates required for universal quantum computation. Moreover, our\nexperimentally realizable shortcuts require only two-body interactions, not\nfour-body ones, and they work in the dispersive regime, which relax greatly the\ndifficulty of their physical implementation in experiment. Our numerical\ncalculations show that the present scheme is robust against decoherence with\ncurrent experimental parameters.\n

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Original Source

DOI: https://doi.org/10.1088/1367-2630/18/2/023001