Constrained Optimization via Quantum Zeno Dynamics

Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce a technique that uses quantum Zeno dynamics to solve optimization problems with multiple arbitrary constraints, including inequalities. We show that the dynamics of quantum optimization can be efficiently restricted to the in-constraint subspace on a fault-tolerant quantum computer via repeated projective measurements, requiring only a small number of auxiliary qubits and no post-selection. Our technique has broad applicability, which we demonstrate by incorporating it into the quantum approximate optimization algorithm (QAOA) and variational quantum circuits for optimization. We evaluate our method numerically on portfolio optimization problems with multiple realistic constraints and observe better solution quality and higher in-constraint probability than state-of-the-art techniques. We implement a proof-of-concept demonstration of our method on the Quantinuum H1-2 quantum processor.