Quantum Resource Requirements for Breaking Elliptic Curve Cryptography: How NISQ-Era Innovations Accelerate the Path to Fault-Tolerant Attacks

We present a comprehensive synthesis of how innovations developed during the Noisy Intermediate-Scale Quantum (NISQ) era are reducing the resource requirements for future fault-tolerant quantum attacks on elliptic curve cryptography (ECC). While pure Shor’s algorithm requires NL = 2, 330 logical qubits and ∼ 1.29 × 1011 Toffoli gates for NIST P-256—well beyond current NISQ capabilities—we demonstrate that NISQ-era innovations could reduce future fault-tolerant quantum computer (FTQC) requirements by factors of 1.5–2.3×. A critical engineering challenge remains: the memory-to-computation gap. Google’s Willow processor achieves exponential error suppression for quantum memory, offering a 2.14× improvement for each increase in code distance. Yet, by October 2025, new demonstrations on this platform show that technological progress is rapidly narrowing this gap. IBM’s roadmap projects 200 logical qubits by 2029 and scaling to 2,000 qubits by 2033+, targets now validated by DARPA’s Quantum Benchmarking Initiative, which establishes 2033 as a formal government milestone for utility-scale fault-tolerant quantum computing. Our analysis reveals projections with varying probabilities of technological success, grounded in convergent external validation from multiple independent authoritative sources: Conservative (high probability): NL ∈ [1, 800, 2, 200] with timeline 2033–2035; Realistic (moderate probability): NL ∈ [1, 200, 1, 600] with timeline 2031–2033; Optimistic (lower probability): NL ∈ [900, 1, 100] with timeline 2029–2031. These projections are directly validated by the convergence of three independent industry and government roadmaps, providing robust external validation for our timeline projections.