Comparative Study between Quantum and Classical Methods: Few Observations from Portfolio Optimization Problem

Classical computers have a limitation in solving NP-hard (nondeterministic polynomial) problems, which cannot be solved in polynomial time. However, the Quantum Computing paradigm is inherently capable of solving such types of problems. One of the major milestones inclined to a quantum -ready era is a relative comparison of execution speed and overall efficiency of current classical versus quantum models. In our approach, we are initiating the foremost step towards addressing the above milestone by performing a comparative study between quantum optimization techniques (available on both gate-model as well as quantum annealers) versus classical by solving a finance domain problem, that is, portfolio optimization using Markowitz mean-variance optimization. Historical market data from Jan’2011 till Dec’2016 of 48 NSE stocks were considered to build the portfolio by optimizing the mean-variance based on Harry Markowitz’s Modern Portfolio Theory. We approach this first classically and then on gate-model based quantum computer using Qiskit SDK, followed by D-wave solvers to build efficient portfolio and compare which among these frameworks are mature enough in this NISQ era to solve portfolio optimization problem related to the finance domain. Our results are comparable and from our experimentation performed on D-wave annealers and gate-model simulators, we observed that implementations using quantum methods were faster than the corresponding implementation of classical methods.