Quantum MetaTT: Complete Implementation Tutorial

Core Classes

1. BellInequality (Base Class)

• Abstract base class for Bell inequality implementations
• Methods: classical_bound(), quantum_bound(), compute_from_density_matrix()

2. CHSH (BellInequality)

• CHSH inequality for qubits (d=2)
• Classical bound: 2.0, Quantum bound: 2√2 ≈ 2.828
• Key methods:
  • predict_chsh(visibility): Analytical prediction
  • compute_from_density_matrix(rho): Compute from density matrix
  • compute_from_density_matrix_specific_qubits(rho, qubits): For specific qubit pairs

3. CGLMP_Analytical (BellInequality)

• CGLMP inequality for qudits (generalizes CHSH to d>2)
• Supports d=2, d=4, d=8 dimensions
• Quantum bound: 2.0 + (d-1)/d × √2
• Key methods:
  • predict_cglmp(visibility): Analytical prediction
  • compute_from_density_matrix(rho): Direct computation from density matrix
  • _expectation_value(rho, setting_a, setting_b): Compute correlation functions

4. NoiseAnalysis

• Comprehensive noise and latency analysis
• Methods:
  • compare_bell_inequalities(visibility_range): Compare CHSH vs CGLMP
  • noise_threshold_analysis(): Find minimum visibility for violations
  • latency_budget(hardware_spec, n_tomo_measurements): Complete latency breakdown
  • optimization_strategies(current_latency_us, target_us): Suggest optimizations

5. AaronsonAnalysis

• Quantum information supremacy analysis (arXiv:2509.07255)
• Maps Bell violations → visibility → FXEB → classical bits required
• Key methods:
  • bell_to_visibility(bell_value, bell_type): Convert Bell value to visibility
  • visibility_to_fxeb(visibility): Convert to FXEB parameter ε
  • classical_bits_required(epsilon, n_qubits, measurement_type): Compute classical bits
  • comprehensive_fiber_channel_analysis(max_distance_km): Distributed entanglement analysis

6. MinimalTomography

• Minimal Pauli tomography for 6-qubit system (Schwemmer et al., arXiv:1310.8465)
• Methods:
  • generate_minimal_pauli_set(): Generate ~45 Pauli measurements
  • run_tomography(qc): Execute tomography
  • reconstruct_density_matrix(expectations): Three reconstruction methods (LIN, ML, Physical)

7. QuantumMetaTT_Hybrid (PyTorch Model)

• Hybrid classical-quantum neural network
• Components:
  • HybridQubitQuditMPSLayer: Quantum MPS layer with 12 qubits, bond dimension d=8
  • Classical input/output layers
  • 8-class financial prediction output

8. HardwareSpec

• Real hardware specifications for superconducting, trapped ion, Quantinuum
• Methods:
  • get_spec(platform): Get hardware specs
  • build_noise_model(platform): Build realistic noise model

Step 1: Load LOBSTER Data

• Loads limit order book data from LOBSTER dataset
• Preprocesses: 40 features → 8-class labels (price movement + volume regime)
• Function: load_lob_data(data_dir, use_test)

Step 2: Train Quantum MetaTT

• Trains hybrid quantum-classical model on financial data
• 15 epochs, batch size 512, Adam optimizer
• Output: Trained model with test accuracy

Step 3: Prepare Bell State Circuit

• Creates d=8 qudit Bell state using 6 qubits
• Function: create_bell_state_d8()
• Structure: 3 Bell pairs (qubits 0-3, 1-4, 2-5)

Step 4: Run Minimal Tomography

• 49 Pauli string measurements (vs 4,096 for full tomography)
• 5,000 shots per measurement
• Output: Dictionary of Pauli expectation values

Step 5: Reconstruct Density Matrix

• Three methods: Linear Inversion (LIN), Maximum Likelihood (ML), Physical Projection
• Compares with ideal state and direct noisy simulation
• Output: Density matrices and fidelities

Step 6: Compute CGLMP & CHSH

• Computes Bell inequality values from reconstructed density matrix
• Compares measured vs predicted values
• Analyzes noise sensitivity

Step 7: ISM Trading Certification

• Complete latency breakdown
• Checks if total latency < 10 μs target
• Provides optimization strategies if exceeding budget

Step 8: Aaronson Framework Analysis

• Maps Bell violations → visibility → FXEB → classical bits
• Compares CHSH vs CGLMP at same visibility
• Error impact analysis
• Comparison to Kretschmer et al. paper results

Step 9: Comprehensive Fiber Channel Analysis

• Analyzes CGLMP vs CHSH over fiber optic channels (0-300 km)
• Three hardware scenarios: Superconducting, Trapped Ion, Quantinuum
• Corrected physics model: Signal-to-noise visibility (not just photon loss)
• Output: Maximum violation ranges, distance advantages

Prerequisites

• Python 3.8+
• Required packages: numpy, pandas, torch, qiskit, qiskit-aer
• LOBSTER dataset (or synthetic data will be used if unavailable)

Running the Script

# Clone the repository first
git clone https://github.com/teraq-platform/teraq-finance.git
cd teraq-finance
pip install -r requirements.txt

# Basic execution
python3 quantum_metatt_final_corrected.py

# The script will:
# 1. Prompt for hardware platform selection (1-3)
# 2. Load/train on LOBSTER data
# 3. Execute full pipeline
# 4. Output comprehensive analysis

Configuration

• DATA_DIR: Path to LOBSTER dataset
• USE_TEST_FILES_FOR_TRAINING: Use test files for training (faster)
• FAST_MODE_SHOTS: Number of shots per measurement (default: 5000)

Google's Approach: N-Player GHZ Parity Game

• State: N-qubit GHZ state |GHZ⟩ = (|0...0⟩ + |1...1⟩)/√2
• Game: N players receive classical bits xⱼ ∈ {0,1} with promise Σⱼ xⱼ is even
• Win Condition: Players output yⱼ such that Σⱼ yⱼ = Σⱼ xⱼ/2 (mod 2)
• Classical Success: 1/2 + 1/2⌊N/2⌋ (random guessing)
• Quantum Success: Perfect (100%) with GHZ state
• Contextuality: Demonstrates measurement contextuality in many-body systems

Google's Key Results

• Implemented magic square game and Kochen-Specker-Bell inequality violation
• Demonstrated N-player GHZ game exceeding classical success rate
• Solved 2D hidden linear function problem with quantum advantage
• Proposed contextuality-based benchmarking for quantum processors
• Emphasis: Contextuality (not just entanglement) as computational resource

Distributed GHZ State Coding: Optimal Performance

Key Insight from Google Paper: GHZ states enable perfect coordination in distributed scenarios through measurement contextuality, not just entanglement.

MetaTT's Distributed GHZ-Like Architecture:

• Current Implementation: 3 Bell pairs (qubits 0-3, 1-4, 2-5) creating distributed entanglement
• GHZ Extension: Can be extended to full GHZ state: |GHZ₆⟩ = (|000000⟩ + |111111⟩)/√2
• Advantage: GHZ states provide:
  • Perfect correlation across all qubits (not just pairs)
  • Measurement contextuality enabling classically impossible coordination
  • Optimal performance for distributed quantum computing tasks

Performance Comparison: