Quantum Computational Finance: Quantum Algorithm for Portfolio Optimization

We present a quantum algorithm for portfolio optimization. We discuss the market data input of asset prices, the processing of such data via quantum operations, and the output of financially relevant results. Given quantum access to a historical record of asset 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 \(\textrm{poly}(\log (N))\) $\text{poly}(log(N))$ , where N is the number of assets. Direct classical algorithms for determining the risk-return curve and other properties of the optimal portfolio take time \(\textrm{poly}(N)\) $\text{poly}(N)$ and we discuss potential quantum speedups in light of efficient classical sampling approaches.