| name | fault-tolerant-ancilla-preparation-bch |
| description | Efficient fault-tolerant ancilla preparation for quantum BCH codes via cyclic symmetry. Two-stage approach using non-fault-tolerant preparation + entanglement distillation with cyclic symmetry exploitation. arXiv: 2605.19471. |
Fault-Tolerant Ancilla Preparation for Quantum BCH Codes
arXiv: 2605.19471 (May 2026)
Authors: Kohei Yamamoto, Keisuke Fujii
Category: quant-ph
Overview
Framework for efficient fault-tolerant ancilla preparation for quantum BCH codes, leveraging cyclic symmetry to reduce overhead in fault-tolerant quantum computing (FTQC).
Problem
- FTQCs require large numbers of physical qubits
- High-rate quantum error correcting codes (QECCs) efficiently embed logical qubits into physical qubits
- Quantum BCH codes offer high rates and large code distances
- No fault-tolerant ancilla preparation method specialized for quantum BCH codes existed
Two-Stage Approach
Stage 1: Non-Fault-Tolerant Preparation
- Prepare ancilla states using standard (non-FT) circuits
- Lower overhead but susceptible to errors
Stage 2: Entanglement Distillation
- Purify the prepared states to fault-tolerant quality
- Key innovation: Leverage cyclic symmetry of quantum BCH codes
- Determines which non-FT circuits can successfully produce FT states
- Lower spatial overhead than conventional distillation circuits
Key Results
- Demonstrated on quantum BCH codes up to 127 qubits
- Lower spatial overhead than conventional distillation
- Lower logical error rates under circuit-level noise model
- Particularly suitable for highly connected platforms (neutral atom systems)
Design Principles
Cyclic Symmetry Exploitation
- Identify cyclic symmetry group of the quantum BCH code
- Use symmetry to constrain valid distillation circuits
- Reduce search space for effective distillation protocols
- Achieve lower overhead through symmetry-guided circuit design
Performance Benchmarking
- Evaluate under circuit-level noise model (realistic settings)
- Compare spatial overhead vs conventional methods
- Measure logical error rates across code distances
Activation
quantum BCH code, fault-tolerant ancilla, entanglement distillation, cyclic symmetry, quantum error correction, FTQC, high-rate code
Pitfalls
- Method requires codes with cyclic symmetry structure
- Two-stage approach adds circuit depth vs single-stage methods
- Best suited for highly connected quantum hardware (neutral atoms)
- Distillation circuit design must respect code's cyclic structure
Reusable Patterns
Pattern 1: Symmetry-Guided Circuit Design
Use algebraic symmetries of error-correcting codes to constrain and optimize quantum circuit construction. This reduces the search space for valid circuits and enables lower-overhead implementations.
Pattern 2: Two-Stage Fault Tolerance
Separate state preparation (cheap, error-prone) from error purification (expensive, error-free). This decoupling allows optimization of each stage independently.
Pattern 3: Code-Specific Distillation
Design distillation protocols tailored to specific code families rather than using generic approaches. Code structure (cyclic symmetry, stabilizer properties) guides protocol selection.
