pauli-propagation-error-mitigation

name

pauli-propagation-error-mitigation

description

Hybrid quantum-classical error mitigation framework embedding Pauli propagation with noise-canceling inverse channels. Use when mitigating errors in observable estimation on NISQ processors, combining classical simulation (Pauli propagation) with quantum hardware measurements, or extending observable estimation beyond classical/quantum limits alone. Activation: Pauli propagation, noise-canceling observable, hybrid error mitigation, quantum-centric supercomputing, observable estimation, inverse channel noise cancellation, truncated Pauli paths, quantum-classical co-simulation, 56-qubit benchmark, noise-aware Pauli truncation

Pauli Propagation Error Mitigation

Methodology from arXiv:2606.20441 for hybrid error mitigation combining classical Pauli propagation with quantum noise cancellation.

Core Insight

Classical Pauli propagation and quantum hardware have complementary limitations:

• Pauli propagation: accuracy limited by exponential growth of operator paths; requires truncation
• Quantum hardware: accuracy limited by error rates and sampling overhead

By embedding Pauli propagation within a noise-canceling framework, both limitations are mitigated simultaneously.

Framework Architecture

Step 1: Define target observable O to be estimated Step 2: Classically propagate O backwards through noise-canceling inverse channels

• This produces a modified observable O' = N^{-1}(O)
• The inverse channel N^{-1} counteracts hardware noise Step 3: Truncate the expanded Pauli paths at a chosen order Step 4: Measure O' directly on the quantum processor Step 5: The measurement outcome approximates <psi|O|psi> with reduced error

Two Truncation Strategies

Strategy 1: Path-count truncation

Keep only the K largest-magnitude Pauli paths after propagation. Best for observables with few dominant terms.

Strategy 2: Weight-threshold truncation

Keep all paths above magnitude epsilon. Best for distributed-weight observables.

Key Results

• Benchmarked on 56 superconducting qubits (IBM hardware)
• Lower truncation errors with fewer classical resources vs. traditional Pauli propagation
• Reduced quantum sampling overhead vs. pure hardware approach
• Trade-offs between the two truncation strategies characterized numerically

Usage Pattern

Pattern 1: Shallow Circuit Observable Estimation

For circuits with depth < 20: propagate observable through 2-3 layers of inverse channels. Truncation at order 3-4 typically sufficient.

Pattern 2: Deep Circuit with Local Observables

For circuits with depth > 20: focus propagation on local observable support. Use weight-threshold truncation to capture dominant error channels.

Pattern 3: Global Observables

For global observables (e.g., magnetization): use path-count truncation with K ~ O(n log n) paths to balance accuracy vs. classical cost.

Implementation Steps

1. Specify circuit and noise model (depolarizing, amplitude damping, etc.)
2. Choose target observable (local operator, Hamiltonian term, etc.)
3. Compute inverse channel N^{-1} from noise model
4. Back-propagate observable: O' = N^{-1} compose U_dagger compose O compose U
5. Truncate Pauli expansion of O' at chosen threshold
6. Execute measurement of O' on quantum hardware
7. Post-process: combine measurement outcomes to estimate

Error Handling

• Truncation error too large: increase truncation order or use path-count truncation with higher K
• Sampling overhead too large: reduce number of retained Pauli terms or use importance sampling
• Inverse channel unstable: regularize N^{-1} with small identity term (Tikhonov regularization)

References

• arXiv:2606.20441 - Computing noise-canceling observables via Pauli propagation