Quantum computational finance: quantum algorithm for portfolio optimization

TL;DR

This paper introduces a quantum algorithm for portfolio optimization that can efficiently process large financial data sets, potentially offering exponential speedups over classical methods in determining optimal investment strategies.

Contribution

The paper presents a novel quantum algorithm capable of efficiently computing the risk-return tradeoff and sampling from optimal portfolios, leveraging quantum data access and processing.

Findings

Quantum algorithm attains poly(log N) runtime for portfolio optimization.

Potential exponential speedup over classical algorithms.

Discussion of quantum advantages in financial data analysis.

Abstract

We present a quantum algorithm for portfolio optimization. We discuss the market data input, the processing of such data via quantum operations, and the output of financially relevant results. Given quantum access to the historical record of returns, the algorithm determines the optimal risk-return tradeoff curve and allows one to sample from the optimal portfolio. The algorithm can in principle attain a run time of ${\rm poly}(\log(N))$, where $N$ is the size of the historical return dataset. Direct classical algorithms for determining the risk-return curve and other properties of the optimal portfolio take time ${\rm poly}(N)$ and we discuss potential quantum speedups in light of the recent works on efficient classical sampling approaches.