Quantum information processing with nuclear spins mediated by a weak-mechanically controlled electron spin

At a Glance

Metadata	Details
Publication Date	2022-02-21
Journal	Communications in Theoretical Physics
Authors	Wan-Jun Su, Guang-Zheng Ye, Yadong Wu, Zhen‐Biao Yang, Barry C. Sanders
Institutions	University of Calgary, University of Hong Kong
Analysis	Full AI Review Included

Executive Summary

This research proposes a robust scheme for achieving quantum information processing (QIP) using nuclear spins in diamond, mediated by a mechanically controlled Nitrogen-Vacancy (NV) center electron spin.

Core Value Proposition: Achieves high-fidelity two-qubit entangling gates and Quantum State Transfer (QST) between distant nuclear spins (e.g., ¹³C) using a weak mechanical drive, overcoming challenges related to small coupling coefficients and positional disorder.
Mediation Mechanism: The NV center electron spin acts as a mediator, coupling two nuclear spins via magnetic dipole-dipole interactions.
Control Method: A gigahertz-frequency mechanical (stress) wave is used to drive the magnetically forbidden spin transition (|m_s = -1> ↔ |m_s = +1>) of the NV center.
Robustness via Zeno Dynamics: The scheme operates in the Quantum Zeno regime, where the driving Rabi frequency (Ω) is much smaller than the dipole-coupling strength (g). This confines the system evolution to a quantum dark subspace (Z₀), making the gates robust against decoherence and positional uncertainties (fluctuating distances, r).
Performance Metrics: The required gate operation time is fast (T ≈ 2.5 µs), which is significantly shorter than the typical T₁ and T₂ coherence times of the nuclear spins, leading to high fidelity (F > 0.96).

Technical Specifications

Parameter	Value	Unit	Context
NV Center Zero-Field Splitting (D)	2.87	GHz	Energy gap between
Dipole-Coupling Strength (g)	~2π x 2	MHz	Interaction between ¹⁴NV electron spin and ¹³C nuclear spin.
Driving Rabi Frequency (Ω)	~2π x 210	kHz	Mechanical (stress) wave driving the
Optimized Driving Ratio (Ω/g)	0.1	N/A	Ratio chosen to balance high fidelity and short operating time.
Gate Operation Time (T)	~2.5	µs	Required time for entangling gate or QST (T = π/Ω).
NV Spontaneous Decay Rate (Γ_NV)	~1	KHz	Used in numerical simulations.
Nuclear Spin Dephasing Rate (γ_N)	~1/3	KHz	Used in numerical simulations.
Required NV T₂ (Room Temp)	> 600	µs	Coherence time required for high-fidelity operation.
QST Fidelity (Robustness)	≥ 0.98	N/A	Achieved despite 10% fluctuations in coupling strength (δg/g) and time (δt/t).
Average Gate Fidelity (Detuning)	0.995	N/A	Achieved with scaled off-resonant coupling Δ/Ω = 0.1.

Key Methodologies

The protocol relies on precise initialization and control of the NV center spin using mechanical waves while leveraging the strong dipole coupling to enforce Zeno dynamics.

System Setup: An NV center electron spin is positioned to mediate magnetic dipole-dipole interaction between two nearby nuclear spins (e.g., ¹³C) in a diamond lattice.
NV Spin Initialization: The NV center is initialized into the |m_s = 0> state via linearly polarized optical excitation. This state is then robustly transferred to the required initial state, |m_s = +1> (|f>_NV), using a magnetic adiabatic passage technique.
Mechanical Driving Application: A gigahertz-frequency mechanical (stress) wave is applied, tuned to the resonance frequency (ω_HBAR), to drive the magnetically forbidden spin transition |m_s = +1> ↔ |m_s = -1> of the NV center.
Quantum Zeno Regime Enforcement: The driving field Rabi frequency (Ω) is intentionally kept weak relative to the dipole-coupling strength (g), satisfying the condition Ω << g. This ensures a large energy splitting (ΔE >> Ω) that confines the system evolution to the zero-energy dark subspace (Z₀).
Gate Execution: The entangling gate or QST is executed by maintaining the weak mechanical drive for a precise duration T = π/Ω. The system coherently evolves within the dark subspace, achieving the desired nuclear-nuclear interaction indirectly.

Commercial Applications

Industry/Application	Relevance to Technology
Solid-State Quantum Computing	Nuclear spins offer superior coherence times compared to electron spins, making them ideal for long-term quantum memory (qubit storage) in diamond-based quantum processors.
Scalable Quantum Architecture	Provides a robust method for generating multi-nuclear-spin gates and multi-party communication, essential for scaling up quantum systems beyond two qubits.
Quantum State Transfer (QST)	Enables reliable, high-fidelity transfer of quantum information between distant nuclear qubits, a fundamental requirement for building distributed quantum networks.
Nanoscale Quantum Sensing	The NV center acts as a sensitive dipole “antenna,” allowing detection and characterization of nuclear spins at different spatial locations, applicable in detecting charge recombination rates in radical pair reactions.
Chemical and Biological Probes	The robust coupling mechanism can be used to study structural information of nuclear spins in single molecules, offering high-resolution sensing for chemical and biological processes.
Advanced Diamond Materials	Requires high-purity diamond substrates (e.g., those produced by specialized CVD techniques) with precise control over NV center placement and the concentration of ¹³C nuclear spins.

View Original Abstract

Abstract We propose a scheme to achieve nuclear-nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy (NV) center in a diamond. Here we demonstrate two-qubit entangling gates and quantum-state transfer between two carbon nuclei. When the dipole-dipole interaction strength is much larger than the driving field strength, the scheme is robust against decoherence caused by coupling between the NV center (nuclear spins) and the environment. Conveniently, precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center. Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication.

Tech Support

Original Source

DOI: https://doi.org/10.1088/1572-9494/ac56d1