Parallel Spooky Pebbling Makes Regev Factoring More Practical

This project sits at the bleeding edge of quantum algorithm research. Regev's 2023 factoring algorithm was a major breakthrough, offering a way to factor integers with fewer qubits than Shor's, but at the cost of significantly higher circuit depth. This project combines two disparate techniques—Craig Gidney's 'Spooky Pebbling' (which uses measurements to save space) and parallel pebble game theory (Blocki et al.)—to mitigate that depth penalty. The defensibility is high (8) because the barrier to entry is extreme domain expertise in both quantum complexity theory and reversible circuit synthesis. While the project is only 4 days old with 0 stars, the 3 forks suggest immediate peer interest within the small, specialized quantum research community. Frontier AI labs (OpenAI/Anthropic) have zero interest in this niche, and while 'Quantum Frontier' labs like Google or IBM are active here, this work is more likely to be integrated into their standard libraries (like Cirq) than competed against. The moat is purely intellectual; the math required to optimize these circuits is non-trivial and represents a significant step toward making quantum factoring viable on NISQ or early fault-tolerant hardware.