A Quantum Model for Constrained Markowitz Modern Portfolio Using Slack Variables to Process Mixed-Binary Optimization under QAOA
This work addresses a key bottleneck in applying quantum algorithms to constrained optimization problems in finance, offering a novel method that could enhance quantum computing's utility in this domain, though it is incremental as it builds on existing QAOA frameworks.
The paper tackled the challenge of encoding inequality constraints in quantum financial optimization by introducing a quantum model for Markowitz portfolio optimization that uses slack variables and ancilla qubits to transform the problem into a QUBO formulation for QAOA. The result showed that this method consistently finds optimal portfolios in simulations where standard penalty-based QAOA fails, and it posits a fundamental quantum limit on portfolio risk and return precision.
Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables directly into the problem Hamiltonian. The method maps each slack variable to a dedicated ancilla qubit, transforming the problem into a Quadratic Unconstrained Binary Optimization (QUBO) formulation suitable for the Quantum Approximate Optimization Algorithm (QAOA). This process internalizes the constraints within the quantum state, altering the problem's energy landscape to facilitate optimization. The model is empirically validated through simulation, showing it consistently finds the optimal portfolio where a standard penalty-based QAOA fails. This work demonstrates that modifying the Hamiltonian architecture via a slack-ancilla scheme provides a robust and effective pathway for solving constrained optimization problems on quantum computers. A fundamental quantum limit on the simultaneous precision of portfolio risk and return is also posited.