Quantum unary approach to option pricing

TL;DR

This paper introduces a quantum unary approach for European option pricing that simplifies circuit design and potentially offers advantages for near-term quantum devices, using amplitude estimation and unary representation.

Contribution

The paper presents a novel unary quantum algorithm for option pricing, improving circuit simplicity and error mitigation compared to binary methods.

Findings

Unary representation simplifies quantum circuit structure and depth.

Quantum superposition in unary representation bypasses classical Monte Carlo.

Unary approach may outperform binary algorithms on near-term quantum devices.

Abstract

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude distribution corresponding to the asset value at maturity is generated using a low depth circuit; second, the computation of the expected return is computed with simple controlled gates; and third, standard Amplitude Estimation is used to gain quantum advantage. On the positive side, unary representation remarkably simplifies the structure and depth of the quantum circuit. Amplitude distributions uses quantum superposition to bypass the role of classical Monte Carlo simulation. The unary representation also provides a post-selection consistency check that allows for a substantial mitigation in the error of the computation. On the negative side, unary representation requires linearly many qubits to represent a target probability distribution, as compared to the logarithmic scaling of binary algorithms. We compare the performance of both unary vs. binary option pricing algorithms using error maps, and find that unary representation may bring a relevant advantage in practice for near-term devices.