Quillow
Quantum Error Correction for BioQL

Quillow is a production-ready quantum error correction (QEC) framework that implements surface codes to protect quantum computations from noise and errors. It enables fault-tolerant quantum computing by detecting and correcting errors in real-time.

When quantum circuits execute on real quantum hardware, they are susceptible to errors from decoherence, gate imperfections, and measurement noise. Quillow encodes your quantum states into logical qubits protected by surface codes, performs syndrome measurements to detect errors, and uses advanced decoding algorithms (MWPM) to correct them—all in real-time with microsecond latency.

Surface Code QEC

Implements rotated surface codes with configurable code distances (d=3, 5, 7, 9). Higher distances provide exponentially better error suppression.

• d=3: Proof of concept (9 data qubits)
• d=5: Production quality (25 data qubits)
• d=7: High fidelity (49 data qubits)
• d=9: Maximum protection (81 data qubits)

Below-Threshold Operation

Achieves logical error rates lower than physical error rates through error suppression. As code distance increases, logical errors decrease exponentially.

Real-Time Decoding

Uses minimum-weight perfect matching (MWPM) via PyMatching for fast, accurate syndrome decoding. Micro-batched processing ensures low latency.

• PyMatching: ~200-500μs per shot
• Union-Find: ~50μs per shot
• GPU decoder: ~20μs per shot
• Throughput: 20K-200K shots/sec

Your quantum state is encoded into a logical qubit using multiple physical qubits arranged in a surface code lattice. The encoding distributes quantum information across many qubits, making it resistant to single-qubit errors.

Stabilizer measurements (X-type and Z-type) are performed on syndrome qubits to detect errors without collapsing the quantum state. These measurements reveal which qubits have been affected by errors, creating a syndrome pattern.

The syndrome pattern is fed into a minimum-weight perfect matching decoder (PyMatching), which uses the Blossom algorithm to find the most likely error chain. This determines which corrections to apply.

Pauli frame tracking applies the corrections to recover the original quantum state. The logical qubit is now protected, and your computation can continue with suppressed error rates.

Quantum Chemistry

Protect VQE calculations for molecules (H2, LiH, H2O) from hardware noise. Get accurate ground state energies with error-corrected measurements.

Drug Discovery

Run molecular docking and binding affinity calculations on real quantum hardware with confidence. QEC ensures reliable results.

Hardware Execution

Execute circuits on IBM Quantum (Torino, Brisbane) and IonQ (Aria, Forte) with automatic error correction. Production-ready quantum computing.

Quantum Chemistry with Error Correction

from quillow import BioQLOptimizer
import os

# Initialize Quillow with BioQL integration
api_key = os.getenv('BIOQL_API_KEY')
optimizer = BioQLOptimizer(
    api_key=api_key,
    qec_distance=5  # d=5 surface code for production
)

# Run VQE with automatic QEC protection
result = optimizer.execute_with_qec(
    bioql_query="VQE for H2 molecule",
    backend="ibm_torino",  # Real IBM Quantum hardware
    shots=2048
)

# Results with error correction
print(f"Ground state energy: {result['energy']:.6f} Hartree")
print(f"Logical error rate: {result['logical_error_rate']:.6f}")
print(f"Physical error rate: {result['physical_error_rate']:.6f}")
print(f"Error suppression: {result['suppression_factor']:.2f}x")

# QEC improvement comparison
improvement = abs(result['raw_energy'] - result['energy'])
print(f"\n✅ QEC improved accuracy by: {improvement:.6f} Hartree")

📊 Expected Output

Ground state energy: -1.137270 Hartree
Logical error rate: 0.000123
Physical error rate: 0.001000
Error suppression: 8.13x

✅ QEC improved accuracy by: 0.000847 Hartree

🔑 Key Benefits

Stim Simulator

Ultra-fast classical simulator for development and testing. Perfect for prototyping QEC workflows.

BioQL API

Integrated quantum chemistry platform. Seamless QEC protection for molecular simulations.

IBM Quantum

Real superconducting quantum processors. Torino (133q), Brisbane (127q), Kyoto (127q).

IonQ

Trapped ion quantum computers. Aria (25q), Forte (35q) with high gate fidelities.

Modal GPU

Cloud GPU acceleration for large-scale simulations. 10x faster decoding for d≥7.