Abstract
The development of quantum computers represents a breakthrough in the
evolution of computing. Their graceful processing capacity will help to
solve some problems impossible until now because the algorithms that
calculate their solution require too much amount of memory or processing
time. In portfolio theory, the investment portfolio optimization
problem is one of those problems whose complexity grows exponentially
with the number of assets. In this work we analyze the Variational
Quantum Eigensolver algorithm, applied to solve the portfolio
optimization problem, running on simulators and real quantum computers
from IBM. We compare the results with three other classical algorithms
for the same problem, running one equivalent condition. By backtesting
classical and quantum computing algorithms, we can get a sense of how
these algorithms might perform in the real world. This work explores the
backtesting of quantum and classical computing algorithms for portfolio
optimization and compares the results. The benefits and drawbacks of
backtesting are discussed, as well as some of the challenges involved in
using real quantum computers of more than 100 qubits. Results show
quantum algorithms can be competitive with classical ones, with the
advantage of being able to handle a large number of assets in a
reasonable time on a future larger quantum computer.