noise-aware-quantum-ldpc-synthesis

name	noise-aware-quantum-ldpc-synthesis
description	Noise-aware synthesis methodology for quantum LDPC encoder circuits using two-sided Hamming descent. Enables hardware-aware circuit synthesis for fault-tolerant QEC that accounts for physical noise characteristics.
version	1.0.0
author	Hermes Agent
license	MIT
metadata	{"hermes":{"tags":["quantum","qec","qldpc","circuit-synthesis","noise-aware"]}}
created	2026-07-07T00:00:00.000Z
trigger_words	["quantum ldpc","qldpc encoder","hamming descent","noise-aware synthesis","quantum error correction","encoder circuit","fault-tolerant"]

Noise-Aware Quantum LDPC Circuit Synthesis

Overview

Methodology from arXiv:2607.04462 — "Noise-Aware Synthesis of Quantum LDPC Encoder Circuits via Two-Sided Hamming Descent" (Sodhani & Parhi, July 2026).

Core Methodology

Problem: Quantum LDPC codes require efficient encoder circuits, but standard synthesis ignores hardware noise, leading to encoders that amplify errors.

Solution: Two-sided Hamming descent — iteratively reduces circuit depth while accounting for noise bias:

1. Initialize: Start from parity-check matrix of qLDPC code
2. Forward descent: Greedily reduce gate count using CNOT optimization
3. Backward descent: Re-insert gates where noise sensitivity demands redundancy
4. Noise weighting: Each gate's contribution weighted by qubit-specific error rates

Key Steps

1. Extract stabilizer generators from qLDPC parity-check matrix
2. Compute per-qubit noise profiles (T1, T2, gate errors)
3. Apply two-sided Hamming descent:
   • Forward: minimize circuit depth
   • Backward: add protective redundancy at noise-sensitive points
4. Validate: ensure encoded logical error rate < physical error rate

Pitfalls

• Noise profiles must be calibrated per-device; generic profiles give suboptimal results
• Two-sided descent may not converge for very large codes (>1000 qubits)
• Trade-off: deeper circuits reduce logical error but increase exposure time

Activation

Use when designing quantum error correction circuits, synthesizing qLDPC encoders, or optimizing fault-tolerant quantum circuits for specific hardware.