Fault-tolerant hardware developer Alice & Bob, in collaboration with researchers from Inria, CEA, and the University of Edinburgh, has released a comprehensive physical-layer resource estimation demonstrating that Shor’s algorithm could factor an RSA-2048 integer using 22,593 physical cat qubits in 3.14 days. Detailed in a preprint published via the International Association for Cryptologic Research (IACR ePrint 2026/2665) titled Shor’s algorithm compiled on cat qubits: 22 593 qubits for RSA-2048 in 3.14 days, the study provides a complete schedule down to physical routing, magic-state factory floor plans, and adder operations, lowering the physical qubit footprint by roughly a factor of 40 compared to leading transmon-based estimates.
Asymmetric Noise Suppression, LDPC-Cat Codes, and Physical Microarchitecture
Conventional transmon-based fault-tolerant architectures running two-dimensional surface codes must correct bit-flip (σx) and phase-flip (σz) errors simultaneously, incurring massive physical-to-logical scaling ratios typically demanding hundreds of thousands to millions of physical qubits. Alice & Bob’s architecture relies on autonomous two-photon stabilization to suppress bit-flip errors at the physical hardware layer exponentially with photon number, leaving phase flips as the dominant noise channel to be addressed by outer error-correcting codes. Building on this bias, the authors replaced one-dimensional repetition codes with two-dimensional low-density parity-check (LDPC) cat codes, cutting required physical qubits by more than half compared to their 2023 baseline (49,649 qubits). The compiled microarchitecture pairs specialized parity-CNOT gates and multi-target CNOT extensions with an adapted, continuous-flow adder derived from recent algorithmic optimizations by Craig Gidney.
| Alice & Bob Compiled Cryptanalytic Benchmarks on Cat-Qubit Hardware | ||
|---|---|---|
| Cryptographic Target | Hardware Trade-Off Profile | Compiled Physical Resources & Runtime |
| RSA-2048 (Factoring) | Balanced Configuration | 22,593 physical cat qubits; 3.14 days execution time. |
| RSA-2048 (Factoring) | Accelerated (Parallel Factories) | 610,530 physical cat qubits; 1.25 hours execution time. |
| RSA-2048 (Factoring) | Hardware-Constrained Footprint | 21,188 physical cat qubits; 8.08 days execution time. |
| ECDLP-256 (Bitcoin / secp256k1) | Elliptic Curve Discrete Log | ≤ 29,588 physical cat qubits; 61.8 minutes execution time. |
| FFDLP-512 (Intermediate Scale) | Finite Field Discrete Log | 6,656 physical cat qubits; 21.2 minutes execution time. |
Hardware Assumptions, Blockchain Implications, and Cryptographic Deadlines
The headline footprint assumes an error-correction cycle time of 1 μs, a classical reaction time of 10 μs, circuit-level phase-flip noise probability of 10−3, and an effectively infinite bit-flip lifetime (macroscopically suppressed to roughly 100 years). If hardware parameters permit residual bit-flip events at a rate of once per hour, the authors demonstrate that adding a distance-3 bit-flip concatenation layer increases the required machine size to approximately 45,000 cat qubits. Applied to the elliptic-curve discrete logarithm problem (ECDLP-256) on the secp256k1 curve securing Bitcoin, the compilation yields a runtime of 61.8 minutes using 29,588 qubits. While an hour-long execution remains well outside Bitcoin’s 10-minute block-mining window—preventing real-time hijacking of active mempool transactions—it places dormant or reused public-key addresses at risk once machines of this scale are realized.
The accelerated convergence of algorithmic efficiency and bosonic error correction reinforces transition mandates enforced by the U.S. National Institute of Standards and Technology (NIST) and the UK National Cyber Security Centre (NCSC), which direct critical infrastructure to complete migration to post-quantum standards by 2035.
The technical paper is accessible on the IACR Cryptology ePrint Archive here, with company commentary detailed in Alice & Bob’s Engineering Breakdown here and official Newsroom Release here.
October 30, 2026