Qldpc Full Extractor Construction

---
name: qldpc-full-extractor-construction
description: "Full extractor construction for logical processing in Hypergraph Product (HGP) codes — surgery systems for measuring arbitrary logical Pauli operators on QLDPC code blocks. Enables Pauli-based computation without compilation overhead. Use when: QLDPC code processing, logical operator measurement, hypergraph product codes, fault-tolerant quantum memory, quantum error correction, Pauli-based computation."
metadata:
  arxiv_id: "2606.03507"
  published: "2026-06-03"
  tags: [quantum, qldpc, error-correction, fault-tolerance, hypergraph-product, logical-processing]
---

# Full Extractors for Logical Processing in QLDPC Codes

## Core Innovation

QLDPC codes promise low-overhead quantum memories but lack practical logical processing methods. This work constructs full extractors — surgery systems capable of measuring arbitrary logical Pauli operators on a code block — for hypergraph product (HGP) codes, enabling Pauli-based computation (PBC) without compilation overhead.

## Methodology

### Extractor Construction
1. **Partial extractors**: Build smaller extractors for individual logical operators
2. **Assembly**: Combine partial extractors into a single full extractor
3. **Verification**: Each partial extractor has verifiable fault-tolerance properties
4. **Size efficiency**: Extractors are 50-80% the size of base HGP codes

### Fixed Connectivity Support
- Extractor-augmented codes support fixed connectivity hardware
- Maximum qubit degree of 10 — compatible with near-term architectures
- No compilation overhead compared to surface code PBC

### Fault Tolerance
- Circuit-level noise simulations at distance 10
- Logical measurement error rate ~10⁻⁶ at physical error rate 0.1%
- Verifiable fault-tolerance guarantees for each partial extractor

## Key Results

| Metric | Value |
|--------|-------|
| Extractor size | 50-80% of base HGP code |
| Max qubit degree | 10 |
| Logical error rate | ~10⁻⁶ @ 0.1% physical error |
| Code distance | 10 (simulated) |
| Compilation overhead | None vs surface code PBC |

## When to Use

- Building fault-tolerant quantum memories with QLDPC codes
- Needing logical processing without compilation overhead
- Fixed connectivity hardware constraints
- Comparing QLDPC vs surface code architectures

## Pitfalls

- Partial extractor assembly must preserve fault-tolerance properties
- Distance 10 is simulated — higher distances need more validation
- Fixed connectivity (degree 10) may limit some code families
- PBC compilation overhead comparison is against surface code — other codes may differ

## Activation

qldpc full extractors, hypergraph product codes, logical pauli measurement, pauli-based computation, quantum error correction processing, fault-tolerant qldpc, quantum memory logical operations

## Related Skills

- quantum-error-correction-methods
- distributed-quantum-error-correction
- quantum-fault-tolerance-verification