Reassessing the Foundations of Quantum Computation: From Theoretical Artifacts to Physical Realities

Abstract: This analysis argues that Shor’s algorithm, while mathematically elegant, functions as a theoretical artifact defined under physically unrealizable conditions—perfect coherence, infinite precision, and unbounded resources—rendering it a mathematical trap that has misdirected the field toward infeasible engineering goals. In contrast, Landauer’s principle—that “information is physical”—provides a necessary foundation for evaluating computation within thermodynamic and material constraints. Empirical evidence reveals a fundamental scaling phase transition: beyond current scales, quantum error correction fails to suppress errors due to correlated failures, operator imprecision, and material defects, causing system reliability to degrade. The resulting divergence in resource requirements makes commercial-scale quantum computing physically infeasible. A constructive path forward requires abandoning idealized models of exponential speedup and developing computational paradigms intrinsically grounded in physical law. Keywords: Quantum computing; Shor’s algorithm; Landauer’s principle; Quantum error correction; Computational scalability; Fault-tolerant quantum computing; Physical limits of computation; Decoherence; Two-level systems; Operator imprecision; Phase transition in quantum systems; Quantum hardware; Information theory; Thermodynamics of computation; Quantum supremacy