| name | modular-quantum-shor-compilation |
| description | Distributed compilation of Shor's algorithm on modular atomic quantum processors. Methodology for large-scale integer factorization across multiple quantum modules with optimized inter-module communication and intra-module clock rates. Use when: compiling Shor's algorithm for distributed quantum hardware, designing modular quantum architectures, optimizing quantum communication between modules, analyzing resource requirements for large-scale factoring, or planning fault-tolerant quantum cryptography attacks. Trigger words: Shor's algorithm, quantum factoring, modular quantum processor, distributed quantum compilation, RSA factoring, quantum cryptography, inter-module communication, Bell pairs, atomic processor.
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Modular Quantum Shor Compilation
Overview
Methodology for compiling and optimizing Shor's algorithm across modular atomic quantum processors.
Addresses the challenge of distributing ~10^6 physical qubits across multiple interconnected modules
while minimizing the overhead from inter-module communication.
Based on: "Factoring 2048-bit RSA integers with a half-million-qubit modular atomic processor" (arXiv: 2605.03951, 2026-05-08)
Architecture
CPU-Inspired Modular Design
The processor architecture organizes quantum modules analogous to CPU cores:
- Modules: Each contains a subset of physical qubits with local operations
- Inter-module links: Bell pair distribution channels for remote operations
- Measurement units: Local measurement with specified latency (e.g., 1 ms)
Key Parameters
| Parameter | Value (2048-bit RSA) | Impact |
|---|
| Total qubits | ~500,000 | Hardware scale |
| Bell pair rate | 10^5 /sec | Communication bandwidth |
| Measurement time | 1 ms | Gate latency |
| Time overhead vs single-module | 16% | Communication efficiency |
Compilation Strategy
Step 1: Problem Decomposition
Decompose the factoring problem into module-local and cross-module operations:
- Modular exponentiation: Core of Shor's algorithm, requires most gates
- Quantum Fourier Transform (QFT): Requires cross-module entanglement
- Measurement and classical post-processing: Determines factors from output
Step 2: Qubit Mapping
Map logical qubits to physical locations across modules:
- Data qubits: Distributed to minimize cross-module operations
- Ancilla qubits: Placed near frequently accessed data qubits
- Communication qubits: Dedicated qubits for Bell pair distribution
Step 3: Communication Optimization
Optimize the interplay between inter-module communication and intra-module clock rate:
- Pipelining: Overlap communication with local computation
- Batching: Group remote operations to amortize Bell pair setup cost
- Scheduling: Order operations to minimize idle time waiting for remote results
Step 4: Gate Compilation
Compile logical gates into module-local and cross-module primitives:
- Local gates: Direct execution within a module
- Remote CNOT: Teleportation-based using pre-distributed Bell pairs
- Measurement-based: Use measurement outcomes to control subsequent operations
Performance Analysis
Resource Scaling
For N-bit RSA integer factorization:
- Physical qubits: O(N^2) with surface code error correction
- Logical gates: O(N^3) for modular exponentiation
- Communication cost: Scales with the fraction of cross-module operations
Time Complexity
The distributed compilation achieves:
- 16% time overhead vs ideal single-module for 2048-bit RSA
- Linear scaling of overhead with communication latency
- Sub-linear scaling with number of modules (due to pipelining)
Practical Considerations
Error Correction
- Surface code or similar QEC required for fault tolerance
- Logical error rate must be below algorithm threshold
- Error correction overhead dominates physical qubit count
Communication Bottlenecks
- Bell pair distribution rate limits remote gate throughput
- Measurement latency affects feedback-dependent operations
- Network topology affects worst-case communication distance
Verification
- Classical verification of factoring result is O(N^2)
- Quantum volume benchmarks validate module performance
- Cross-module entanglement fidelity must exceed threshold
Pitfalls
- Underestimating communication overhead can negate parallelism benefits
- Module size must balance local computation vs communication frequency
- Error correction resource estimates vary significantly by code choice
- Classical preprocessing (selecting smoothness bounds) affects quantum resource needs
