quantum-fault-tolerance-benchmark

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