gem-quantum-error-mitigation

name

gem-quantum-error-mitigation

description

Generalized Error Mitigation (GEM) framework for quantum computing - zero-noise extrapolation-free error mitigation using measurement statistics. Reduces effective circuit depth by learning noise-free output distribution from noisy measurements. Use when: quantum error mitigation, zero-noise extrapolation, near-term quantum computing, NISQ device noise reduction, quantum noise characterization, scalable quantum algorithms, GEM framework, randomized compiling.

Generalized Error Mitigation (GEM) Framework

GEM enables scalable quantum computation on NISQ devices by learning noise-free output distributions from noisy measurements — without Zero-Noise Extrapolation (ZNE) or Probabilistic Error Cancellation (PEC).

Key Principle

GEM learns the noise channel by comparing randomized compiled circuit outputs against ideal distributions, then inverts the noise to recover quasi-probabilities for error-mitigated results.

Core Algorithm

The GEM framework operates in four stages:

1. Target Distribution: Collect measurement statistics from the target circuit on noisy hardware
2. Randomized Compiling: Generate Pauli-twirled variants to convert coherent noise into stochastic Pauli noise
3. Noise Channel Learning: Compare rich (diverse) vs poor (concentrated) output distributions to learn the noise transformation matrix
4. Error Mitigation: Invert the learned noise channel to recover quasi-probabilities

Detailed Implementation

Step 1: Define Target Distribution

def target_distribution(circuit, backend, n_samples=1000):
    """Run circuit and get raw noisy distribution."""
    job = backend.run(circuit, shots=n_samples)
    counts = job.result().get_counts()
     {k: v/n_samples  k, v  counts.items()}