syndrome-adaptive-gain-control - SKILL.md Agent Skill

name: syndrome-adaptive-gain-control description: Syndrome Adaptive Gain Control methodology for quantum LDPC error correction decoding. Adapts message gain during iterative decoding based on syndrome patterns. category: quantum

Syndrome Adaptive Gain Control

Description

Syndrome Adaptive Gain Min-Sum (SAGMS) decoding methodology for quantum LDPC codes. Dynamically adjusts message scaling during iterative belief-propagation-style decoding based on the fraction of unsatisfied stabilizers, eliminating the need for per-code or per-noise-level offline optimization.

Activation Keywords

syndrome adaptive gain
SAGMS decoding
QLDPC decoding
quantum LDPC error correction
adaptive min-sum decoder
quantum error correction adaptive control
自适应量子纠错解码

Core Concepts

The Problem

Min-Sum (MS) decoding is a low-complexity alternative to belief propagation (BP) for QLDPC codes
MS systematically overestimates message magnitudes
Scaled Min-Sum (SMS) uses a fixed scaling factor, but optimal factor varies with check-node degree and noise level
Fixed scaling incurs growing penalty as code parameters vary

The Solution: SAGMS

Adapts message gain online during decoding
Gain is a function of the fraction of unsatisfied stabilizers (syndrome weight)
No per-code or per-noise-level optimization needed
Matches or outperforms offline-optimized SMS decoder
Approaches BP performance while retaining MS-level complexity

Mathematical Framework

Syndrome-Based Gain Adaptation

gain = f(syndrome_weight / total_stabilizers)

Where:

syndrome_weight = number of unsatisfied stabilizer checks
As syndrome weight decreases → gain converges toward 1.0 (no scaling)
As syndrome weight increases → gain reduces to prevent overestimation

Key Insight

The scaling factor required for SMS to match BP decreases with check-node degree
Any fixed scaling optimized for one degree incurs penalty as CN degree varies
SAGMS avoids this by adapting dynamically

Instructions for Agents

Step 1: Identify the QLDPC Code

Determine code parameters: n qubits, m stabilizers, check-node degrees
Identify the noise model (depolarizing, biased, etc.)

Step 2: Initialize MS Decoder

Set up Min-Sum message passing on the Tanner graph
Initialize messages (typically uniform or channel-based)

Step 3: Implement Adaptive Gain

At each iteration, compute syndrome weight (unsatisfied checks)
Calculate adaptive gain: gain = g(syndrome_weight / m)
Apply gain to outgoing check-to-variable messages
Common gain functions: linear, sigmoid, or piecewise

Step 4: Iterate and Converge

Run message passing with adaptive gain
Monitor syndrome convergence
Stop when syndrome = 0 (success) or max iterations reached

Usage Patterns

Pattern 1: Fixed SMS Baseline Comparison

# Compare SAGMS vs optimized SMS
fer_sms = benchmark_sms_decoder(code, noise_level, fixed_gain=optimal_gain)
fer_sagms = benchmark_sagms_decoder(code, noise_level)
# SAGMS should match or exceed SMS performance

Pattern 2: BP Performance Target

# SAGMS should approach BP performance
fer_bp = benchmark_bp_decoder(code, noise_level)
fer_sagms = benchmark_sagms_decoder(code, noise_level)
# SAGMS approaches BP while being much faster

Error Handling

Decoder Failure (non-zero syndrome at max iterations)

Increase max iterations
Check if noise level exceeds code capacity
Consider combining with other error mitigation techniques

Gain Function Tuning

Default: linear gain function works for most cases
For specific codes: optimize gain function shape via grid search
The gain function should be monotonically decreasing with syndrome weight

Performance Characteristics

Complexity: Same as MS decoding (O(edges × iterations))
FER Performance: Matches/exceeds offline-optimized SMS
BP Gap: Approaches BP performance
Adaptivity: No offline tuning needed

Limitations

Performance depends on gain function design
May not achieve optimal performance for all code families
Primarily validated on generalized bicycle QLDPC codes

Resources

arXiv:2605.10433 - "Syndrome Adaptive Gain Control for Min-Sum Decoding of Quantum LDPC Codes"
Authors: Hernan Cordova, Alexios Balatsoukas-Stimming, Yunus Can Gültekin, Gabriele Liga, Alex Alvarado

Related Skills

quantum-error-correction-methods
syndrome-adaptive-gain-qldpc