A qubit-efficient boolean quantum oracle for value-at-risk estimation in NISQ devices

Abstract

Value-at-risk (VaR) is a broadly used measure for evaluating financial tail risk, but its estimation depends on assessing threshold exceeding probabilities over complex loss distributions. Probability estimation tasks using quantum algorithms works based on amplitude estimation that has a potential to offer quadratic speedup; however, their implementation on noisy intermediate-scale quantum devices is obstructed by the qubit and circuit depth requirements of arithmetic-heavy comparator oracles. This work proposes a qubit-efficient Boolean quantum oracle for threshold-based risk screening motivated by VaR analysis that has the ability to directly flag loss scenarios that violate a predefined threshold condition without utilizing high depth quantum adders or quantum subtractors. The proposed oracle employs a risk ancilla together with a reusable work qubit and utilizes a shallow circuit depth, making it a feasible candidate for near-term quantum hardware. In this work we analyze the resource scaling of the proposed oracle and benchmark it against arithmetic-based approaches under noisy simulations. This work further shows how the proposed oracle can be integrated within a hybrid quantum–classical variational optimization framework to restrain high-risk configurations.