quantum-stabilizer-code-surgery

name

quantum-stabilizer-code-surgery

description

Compiler techniques for synthesizing resource-efficient code surgery protocols on arbitrary quantum stabilizer codes. Covers structure-aware graph optimization, ancilla qubit reduction, dynamic expansion-congestion balancing, and code degree constraints for fault-tolerant logical operations. Use when: designing fault-tolerant quantum operations, synthesizing code surgery for stabilizer codes, optimizing ancilla overhead in QLDPC codes, implementing cross-code logical communication, or reducing resource requirements for code deformation (arXiv: 2605.21746 GeneCS).

Quantum Stabilizer Code Surgery Compilation

Methodology for synthesizing resource-efficient code surgery protocols for arbitrary quantum stabilizer codes.

Problem Statement

Code surgery provides a general framework with provable guarantees for logical operations via joint logical measurements, but existing constructions are largely theoretical and incur substantial ancilla overhead in practice.

GeneCS: Resource-Efficient Code Surgery Compiler

From arXiv:2605.21746 (Zhou, Javadi-Abhari, Li).

Key Optimizations

1. Structure-Aware Graph Construction

   • Eliminate redundancy in measurement graph construction
   • Identify and remove unnecessary ancilla qubits and checks
   • Exploit code structure to minimize overhead

2. Dynamic Expansion-Congestion Balancing

   • Balance graph expansion (adding necessary ancillas) with congestion (avoiding bottlenecks)
   • Prevent resource explosion while maintaining fault-tolerance guarantees

3. Code Degree Constraints

   • Incorporate physical qubit connectivity constraints
   • Enforce maximum degree limits on measurement graphs
   • Map logical operations to physical hardware topology

Results

• 10x average reduction in ancillary qubits and checks
• Scales to codes with 1000+ qubits at ~1 second per instance
• Preserves logical error rates

Workflow

Step 1: Parse Stabilizer Code

Input: Stabilizer code description (check matrix, logical operators)
Output: Code graph representation

Step 2: Build Measurement Graph

For each logical operation:
    1. Identify required joint measurements
    2. Build initial measurement graph with full ancilla overhead
    3. Mark degree constraints based on hardware topology

Step 3: Apply Structure-Aware Optimization

While redundant nodes exist:
    1. Identify structurally redundant ancilla qubits
    2. Remove redundant checks while preserving fault-tolerance
    3. Verify logical error rate preservation

Step 4: Balance Expansion vs Congestion

Iteratively:
    1. Expand graph where necessary for connectivity
    2. Check congestion at high-degree nodes
    3. Rebalance by redistributing measurements
    4. Stop when constraints satisfied

Step 5: Generate Executable Protocol

Output: Compiled code surgery protocol
    - Measurement sequence
    - Ancilla qubit schedule
    - Cross-code communication plan (if applicable)

Pitfalls

• Theoretical overhead: Naive code surgery constructions use excessive ancillas; always apply structure-aware optimization first
• Degree violations: Physical hardware has connectivity limits; enforce code degree constraints during synthesis
• Cross-code communication: Different stabilizer codes require careful interface handling; use GeneCS cross-code synthesis
• Scalability: For codes >1000 qubits, amortized compilation time should remain ~1s per instance; optimize graph representation if needed

Activation Keywords

GeneCS, quantum stabilizer code surgery, QLDPC compiler, ancilla optimization, code deformation, logical operations, fault-tolerant quantum computing, cross-code communication