# Benchmarking Quantum Solvers in Noisy Digital Simulations for Financial Portfolio Optimization

## TL;DR

This paper compares quantum algorithms QITE and QAOA for portfolio optimization, analyzing their performance and robustness on noisy quantum hardware, highlighting trade-offs between scalability and noise tolerance.

## Contribution

It provides the first systematic benchmarking of QITE and QAOA on a practical financial problem under realistic noisy quantum conditions.

## Key findings

- QAOA converges well in noiseless settings.
- QITE is more robust to noise but computationally intensive.
- QAOA scales better and remains effective with noise mitigation.

## Abstract

In this work, we benchmark two prominent quantum algorithms: Quantum Imaginary-Time Evolution (QITE) and the Quantum Approximate Optimization Algorithm (QAOA) for obtaining the ground state of Ising-type Hamiltonians. Specifically, we apply them to the Markowitz portfolio optimization problem in quantitative finance, on both digital quantum computers and local quantum simulators with controllable two-qubit errors (noise). In noiseless settings, we find that QAOA achieves excellent convergence to the optimal results. Under noisy conditions, the QITE method exhibits greater robustness and stability, though it incurs substantially more classical numerical cost. In contrast, we demonstrate that QAOA offers better scalability and can still yield robust results if the noise can be effectively mitigated. Our findings provide valuable insights into the trade-offs between scalability and noise tolerance and demonstrate the practical potential of quantum algorithms for solving real-world optimization problems on near-term quantum devices.