quantum-fault-tolerance-benchmark - SKILL.md Agent Skill

name: quantum-fault-tolerance-benchmark description: > Evaluate quantum error-correcting codes under hardware-motivated and biased noise models. Benchmark fault-tolerant quantum computing primitives via noisy stabilizer simulation. Use when: (1) evaluating QEC code performance, (2) designing fault-tolerant quantum circuits, (3) simulating quantum error correction under realistic noise, (4) comparing logical error rates across hardware platforms, (5) FTPrimitiveBench methodology.

Quantum Fault Tolerance Benchmark

Evaluate fault-tolerant quantum computing primitives under realistic noise models. Based on FTPrimitiveBench methodology (arXiv:2605.04049).

Core Components

1. Noise Models

Biased noise: Depolarizing, dephasing, amplitude damping with bias ratios
Hardware-motivated: Derived from physical qubit characteristics (T1, T2, gate fidelities)
Correlated errors: Spatial and temporal correlations matching hardware behavior

2. Error-Correcting Codes

Surface codes: Planar, rotated, XZZX variants
Color codes: 2D and 3D topological codes
LDPC codes: Quantum low-density parity-check codes
Concatenated codes: Recursive encoding schemes

3. Fault-Tolerant Primitives

Logical gates: Transversal, lattice surgery, magic state distillation
State preparation: Logical |0>, |+, magic states
Measurement: Logical Pauli measurements
Memory: Idle logical qubit preservation

Workflow

Step 1: Define Noise Model

noise_model = {
    "gate_error_rate": 1e-3,
    "measurement_error_rate": 1e-3,
    "idle_error_rate": 1e-4,
    "bias_ratio": 100,  # Z errors >> X errors
    "correlation_length": 5  # Spatial correlation
}

Step 2: Select QEC Code and Distance

Choose code type and code distance d. Logical error rate typically scales as: p_L ≈ A * (p/p_th)^((d+1)/2)

Step 3: Run Noisy Stabilizer Simulation

Simulate circuit with noise injection at each operation
Track syndrome measurements and apply decoder
Count logical errors over many trials

Step 4: Extract Metrics

Logical error rate: Fraction of runs with uncorrectable errors
Threshold: Physical error rate below which increasing d improves p_L
Overhead: Physical qubits per logical qubit
Circuit depth: Time to execute FT primitive

Key References

FTPrimitiveBench: arXiv:2605.04049
Related: quantum-error-correction, quantum-systems-engineering

Limitations

Stabilizer simulation limited to Clifford circuits + magic states
Computational cost scales with number of qubits and circuit depth
Real hardware may have noise features not captured by models