NISQ-HHL: Portfolio Optimization for Near-Term Quantum Hardware

Portfolio optimization is an essential use case in finance, but its computational complexity forces financial institutions to resort to approximated solutions, which are still time consuming. Thus, the scientific community is looking at how Quantum Computing can be used for efficient and accurate portfolio optimization.

Portfolio optimization can be formulated as a quadratic program, with the cost function enforcing risk minimization for a targeted return. Of particular interest is the mean-variance portfolio optimization problem. Using the method of Lagrange multipliers, the program can be converted into a system of linear equations and potentially benefit from the exponential speedup provided by the HHL quantum algorithm. However, multiple components in HHL are unsuitable for execution on Noisy Intermediate Scale Quantum (NISQ) hardware.

This work introduces NISQ-HHL, the first hybrid formulation of HHL suitable for the end-to-end execution of small-scale portfolio-optimization problems on NISQ devices. NISQ-HHL extends the hybrid HHL variant with newly available quantum-hardware features: mid-circuit measurement, Quantum Conditional Logic (QCL), and qubit reset and reuse. To best of our knowledge, NISQ-HHL is the first algorithm incorporating a QCL-enhanced version of Phase Estimation that was executed on real hardware.  In addition, NISQ-HHL includes a novel method for choosing the optimal evolution time for the Hamiltonian simulation. Although this work focuses on portfolio optimization, the techniques it proposes to make HHL more scalable are generally applicable to any problem that can be solved via HHL in the NISQ era.

We empirically demonstrate the effectiveness of NISQ-HHL by presenting the experimental results we obtained on a real quantum device, the trapped-ion Honeywell System Model H1.