Quantum Algorithms for Trading: A Survey of Speedups, Thresholds, and Dequantization

Abstract

Quantum algorithms for trading span computational tasks with different input models and standards of evidence. This structured critical review describes its search scope, selection criteria and limitations, and distinguishes reported findings from author assessments. Amplitude estimation estimates bounded expectations to additive error ϵ with O(ϵ−1) oracle queries rather than the O(ϵ−2) samples of plain classical Monte Carlo at fixed confidence. This query advantage does not establish an end-to-end runtime advantage: state preparation, arithmetic, error correction and classical competitors must also be costed. Published resource estimates for benchmark exotics require thousands of logical qubits and demanding logical operation rates. An illustrative sensitivity analysis shows how the crossover depends on classical throughput, oracle depth and the comparison window; its numbers are scenarios, not calibrated hardware forecasts. Portfolio and trading-trajectory formulations have device demonstrations, but a 250-instance benchmark of discretized minimum-variance allocation finds classical mixed-integer programming and a tailored heuristic superior on the tested formulation. Specific low-rank quantum machine learning algorithms have been dequantized under analogous sampling-access assumptions. Separately, a controlled study of quantum kernels for Chinese equity returns finds no significant advantage and demonstrates sensitivity to evaluation design; this does not settle other learning tasks. Entanglement-assisted coordination offers advantages in specified nonlocal games without computational-complexity assumptions, while its financial implementation and economics remain open. We distinguish computational performance from economic value and identify input/output costs, structured algorithms, reproducible benchmarking and explicit financial evaluation as priorities.