Technology Stack

Core Technologies Used in the Project

Technical Overview

This project explores cutting-edge research combining quantum computing and graph theory. We implemented innovative approaches to overcome classical GNN limitations through quantum circuits.

Quantum Computing Technologies

QGNN

Quantum Graph Neural Network

Quantum graph neural network constructing rich representation spaces through superposition and entanglement

Key Architectures

  • QRecGNN: Recurrent quantum GNN
  • QConvGNN: Convolutional quantum GNN
  • EQGC: Equivariant Quantum Graph Circuit
  • EDU-QGC: Diagonal unitary-based structure

QAOA

Quantum Approximate Optimization Algorithm

Variational quantum algorithm for solving combinatorial optimization problems

Implementation Details

  • Max-Cut problem optimization
  • p=1, p=2 layer structure implementation
  • Gradient-based parameter optimization
  • Expected cut value measurement and analysis

VQE

Variational Quantum Eigensolver

Laplacian approximation using variational quantum eigensolver

Application Methods

  • Surrogate loss function design
  • Rayleigh quotient structure utilization
  • Z-expectation vector-based optimization
  • Shallow-depth ansatz implementation

Graph Theory Technologies

1-WL Test

Weisfeiler-Lehman Test

Classical algorithm for graph isomorphism testing

Characteristics

  • Node color multiset-based updates
  • Message passing mechanism
  • Expressiveness upper bound limitations
  • Cannot distinguish SRGs

Laplacian λ₂

Algebraic Connectivity

Indicator representing graph's algebraic connectivity

Implementation Methods

  • Classical: Power Method
  • Quantum: VQE-style surrogate
  • L = D - A matrix construction
  • Second eigenvalue approximation

SRG

Strongly Regular Graph

Special graph structures with uniform local patterns

Test Subjects

  • SRG(16,6,2,2) structure
  • Rook Graph
  • Shrikhande Graph
  • For 1-WL limitation verification

Implementation Technologies

Quantum Circuit Design

Circuit Architecture

Encoding Methods

  • RY rotation gate encoding
  • Amplitude encoding
  • Angle encoding

Entanglement Structure

  • CNOT-RZ-RX-CNOT blocks
  • Edge-based entanglement generation
  • Permutation equivariance guarantee

Optimization Techniques

Optimization Methods

Gradient Calculation

  • Parameter-shift rule
  • Finite difference method
  • Automatic differentiation

Optimizers

  • Gradient Descent
  • Adam optimizer
  • Learning rate scheduling

Noise Modeling

Noise Simulation

Noise Types

  • Depolarizing noise
  • Amplitude damping
  • Shot noise

Mitigation Techniques

  • Error mitigation
  • Shallow-depth circuit design
  • Hybrid-QGNN architecture

Development Environment

Frameworks

  • Python 3.x
  • Qiskit / PennyLane
  • NetworkX (graph processing)
  • NumPy / SciPy
  • Matplotlib (visualization)

Simulators

  • Statevector simulator
  • Sampling simulator
  • Noise simulator
  • NISQ environment emulation

Analysis Tools

  • Jupyter Notebook
  • TensorBoard (learning monitoring)
  • Git (version control)
  • LaTeX (report writing)

Technical Challenges & Solutions

🎯 Barren Plateau Problem

Gradient vanishing in deep circuits → Resolved with shallow-depth design

📊 Noise Sensitivity

NISQ device noise impact → Applied error mitigation techniques

⚡ Scale Limitations

Qubit number constraints → Hybrid classical-quantum approach

🔄 Convergence Instability

Unstable optimization process → Multiple initial value sampling