Shor, QLDPC Codes, and the Compression of RSA-2048 Resource Estimates (Part I)
Shor, QLDPC Codes, and the Compression of RSA-2048 Resource Estimates (Part I) Does institutional risk modeling account for non-linear improvements in error-correction efficiency, or has the timeline for a cryptographically relevant quantum computer (CRQC) narrowed beyond existing forecasts? The technical baseline for evaluating RSA-2048 was updated in February 2026 with the “Pinnacle Architecture” analysis (arXiv:2602.11457). This research identifies a specific pathway to reduce the physical qubit overhead for Shor’s algorithm by an order of magnitude. While Craig Gidney’s 2025 work brought physical qubit requirements below one million, the integration of Quantum Low-Density Parity-Check (QLDPC) codes suggests a footprint of approximately 100,000 physical qubits. The demonstration indicates that the trajectory to demonstrating Shor’s algorithm does not follow a linear chronological progression. However, reducing the qubit count introduces significant engineering trade-offs. The Pinnacle analysis, which has not yet undergone formal peer review, achieves this hardware efficiency by requiring non-local qubit connectivity. This complicates signal routing and physical design compared to planar surface codes. Furthermore, the hardware reduction forces a temporal trade-off; the estimated runtime for factoring is approximately one month, a significant increase from the one-week estimate provided in Gidney’s 2025 model. Additionally, the architecture requires sophisticated classical decoding logic capable of processing errors within a 10-microsecond window—a reaction time requirement not yet demonstrated at this scale, where even the fastest current decoders often operate in the millisecond range. Despite these hurdles, current infrastructure relies heavily on classical encryption, including RSA derivatives and ECC, which secure satellite telemetry, industrial control systems, and sensitive archives. The “Harvest Now, Decrypt Later” risk is now quantified by a target that c
