Quantum Computing at the Threshold of Utility: A Critical Review of Hardware Platforms, Algorithms, Cryptographic Implications and Commercial Readiness (2024–2026)

Quantum information processing has moved, within the space of roughly two years, from a discipline defined by extrapolation to one defined by measurement. This review consolidates and critically appraises the technical and commercial state of the field as it stood in mid-2026. Four developments frame the analysis: the demonstration of verifiable computational advantage on superconducting hardware through observable-based echo protocols in April 2026; the extension of advantage claims into the simulation of heterogeneous quantum materials in July 2026; the operation of surface-code memories below the fault-tolerance threshold; and the completion of the first tranche of standardised post-quantum cryptographic primitives. Against these advances the review sets an equally important body of negative evidence — systematic benchmark studies in which classically tractable formulations of putative quantum use cases were solved to proven optimality in seconds, and the withdrawal of at least one major financial institution from quantum research after resource estimation placed its target problem beyond any plausible machine. The paper surveys six physical qubit modalities, evaluates them against criteria that extend well past raw qubit count, examines the principal algorithmic families and their known limitations, assesses the software and cloud-access ecosystem, analyses the cryptographic migration timeline in policy and engineering terms, and reviews error-correction progress from repetition codes through quantum low-density parity-check constructions. The central conclusion is that the field has entered a period in which scientific advantage is demonstrable but economic advantage is not, and that the interval between the two will be governed less by qubit counts than by logical error rates, compilation overheads, and the availability of trained personnel.