QUSIM - NV Center Quantum Simulator

QUSIM is a hyperrealistic quantum simulator for nitrogen-vacancy (NV) centers in diamond. It provides a complete framework for simulating NV center physics, including spin dynamics, optical transitions, and realistic hardware interfaces.

Note

This documentation includes the complete mathematical framework used in the simulator, with all equations derived from first principles.

Key Features

• 18-dimensional Hilbert space: Full \(|g/e\rangle \otimes |m_s\rangle \otimes |m_I\rangle\) basis

• Realistic Hamiltonians: ZFS, Zeeman, Hyperfine (N14/C13), MW drive, Optical, Stark, Strain

• Open quantum systems: Lindblad master equation with T₁, T₂*, optical decay

• Pulse sequences: Ramsey, Spin Echo, CPMG, XY4, XY8

• Hardware interfaces: AWG, Laser, Photon Counter with realistic noise models

Quick Start

from sim import HamiltonianBuilder, LindbladSolver
from sim.hamiltonian.terms import ZFS, Zeeman, HyperfineN14
from sim.states import ground_state, projector_ms

# Build NV Hamiltonian
H = HamiltonianBuilder()
H.add(ZFS(D=2.87))           # 2.87 GHz zero-field splitting
H.add(Zeeman(B=10))          # 10 mT magnetic field
H.add(HyperfineN14())        # N14 hyperfine structure

# Setup dissipation
solver = LindbladSolver(H)
solver.add_t1_relaxation(gamma=1e3)   # T1 = 1 ms
solver.add_t2_dephasing(gamma=1e6)    # T2* = 1 μs

# Evolve from ground state
rho0 = ground_state()
result = solver.evolve(rho0, t_span=(0, 1e-6), n_steps=100)

# Measure ms=0 population
pop = result.population(projector_ms(0))

Physical Background

The NV center consists of a substitutional nitrogen atom adjacent to a vacancy in the diamond lattice. The negatively charged NV⁻ center has a spin-1 ground state with remarkable properties:

\[\hat{H}_{\text{NV}} = \hat{H}_{\text{ZFS}} + \hat{H}_{\text{Zeeman}} + \hat{H}_{\text{HF}} + \hat{H}_{\text{MW}} + \cdots\]

The electronic structure features:

• Ground state \({}^3A_2\): Spin triplet with \(S=1\)

• Excited state \({}^3E\): Optically accessible at 637 nm (ZPL)

• Singlet states \({}^1A_1, {}^1E\): Enable spin polarization

Contents

Theory & Physics

• The Nitrogen-Vacancy Center
  • Physical Structure
  • Electronic Structure
  • Hilbert Space
  • Spin-1 Operators
  • Physical Constants
  • Optical Transitions
• Hamiltonian Terms
  • Zero-Field Splitting (ZFS)
  • Zeeman Effect
  • N14 Hyperfine Coupling
  • C13 Hyperfine Coupling
  • Microwave Drive
  • Optical Coupling
  • Stark Effect
  • Strain
  • Jahn-Teller Effect
• Open Quantum System Dynamics
  • Lindblad Master Equation
  • T₁ Relaxation (Spin-Lattice)
  • T₂* Dephasing (Inhomogeneous)
  • T₂ (Homogeneous / Echo)
  • Optical Decay
  • Intersystem Crossing (ISC)
  • Nuclear Spin Relaxation
  • Numerical Integration
  • Steady State
• Measurement and Readout
  • Projective Measurements
  • Expectation Values
  • Optical Readout
  • Photon Detection
  • ODMR Spectroscopy

User Guide

• Installation
  • Requirements
  • Installation
  • Verification
  • Optional Dependencies
• Quickstart
  • Basic Simulation
  • Rabi Oscillations
  • Eigenvalue Analysis
  • Saving Results
• ODMR Simulation
  • CW-ODMR
  • Hyperfine Structure
  • Pulsed ODMR
  • Magnetic Field Sensing
• Pulsed Experiments
  • Rabi Oscillations
  • Ramsey Interferometry
  • Spin Echo (Hahn Echo)
  • CPMG Dynamical Decoupling
  • XY8 Sequence for AC Sensing

API Reference

• Core Module
  • Physical Constants
  • Spin Operators
  • Nuclear Operators
• Hamiltonian Module
  • Hamiltonian Builder
  • Hamiltonian Terms
  • Creating Custom Terms
• Dynamics Module
  • Lindblad Solver
  • Dissipation Operators
  • Solver Options
  • Time-Dependent Hamiltonians
• States Module
  • Initial States
  • Density Matrix
  • Projectors
  • State Tomography
  • Visualization
• Pulses Module
  • Basic Pulses
  • Pulse Shapes
  • Pulse Sequences
  • Custom Sequences
  • AWG Integration
• Interfaces Module
  • AWG Interface
  • Laser Interface
  • Photon Counter
  • Complete Measurement

Indices and tables

• Index

• Module Index

• Search Page

Citation

If you use QUSIM in your research, please cite:

@software{qusim2024,
  author = {Kaiser, Leon},
  title = {QUSIM: Hyperrealistic NV Center Quantum Simulator},
  year = {2024},
  institution = {MSQC, Goethe University Frankfurt},
  url = {https://github.com/xleonplayz/QUSIM}
}

References

[Doherty2013]

Doherty, M. W. et al. “The nitrogen-vacancy colour centre in diamond.” Physics Reports 528, 1-45 (2013).

[Maze2011]

Maze, J. R. et al. “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach.” New J. Phys. 13, 025025 (2011).

[Childress2013]

Childress, L. & Hanson, R. “Diamond NV centers for quantum computing and quantum networks.” MRS Bulletin 38, 134 (2013).