Quantum Formalism and Quantum Computing: What Can They Actually Solve in Economics and Finance?

This note separates two things often labelled “quantum finance”: the quantum formalism, which applies quantum-mechanical mathematics on classical computers and is judged by empirical fit, and quantum computers, which are judged by whether they complete tasks classical machines cannot. Classifying the evidence into four types (unconditional; beyond-classical under complexity assumptions; empirical claims on specific problems; asymptotic speedups requiring fault tolerance), it finds that, among the public evidence identified and verified here (cut-off 17 October 2026), no economic or financial task has demonstrated broadly accepted practical quantum advantage against strong classical baselines and end-to-end costs. The strongest unconditional results concern information resources rather than computational speed; the formalism has already produced methods usable on classical hardware and testable empirical results; the most mature provable speedup directly relevant to finance is the quadratic speedup of amplitude estimation, which requires fault-tolerant hardware; and because published estimates place the logical-qubit threshold for elliptic-curve discrete logarithms below that for derivative-pricing advantage, cryptographic infrastructure is a channel through which material impact may arrive earlier — a scenario, not a timing prediction, since the two workloads differ in gate counts, runtimes and fault-tolerance assumptions. The note is a structured synthesis of published evidence and reports no new experiments or measurements.