Constrained optimization via quantum Zeno dynamics

The paper presents an approach for solving optimization problems with multiple arbitrary constraints on quantum computers by combining quantum Zeno dynamics with common quantum optimization algorithms like QAOA. The number of Zeno measurements required is shown to be independent of the problem size in QAOA. 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.

Automated summary

This paper presents an approach that combines quantum Zeno dynamics with common quantum optimization algorithms (such as QAOA) to solve optimization problems with multiple arbitrary constraints on quantum computers. The authors introduce a technique that uses quantum Zeno dynamics to efficiently restrict the dynamics of quantum optimization to the in-constraint subspace on a fault-tolerant quantum computer, requiring only a small number of auxiliary qubits and no post-selection. They demonstrate the broad applicability of their technique by incorporating it into the quantum approximate optimization algorithm (QAOA) and variational quantum circuits for optimization. Numerical evaluations and a proof-of-concept demonstration on a quantum processor show the superiority of their method compared to state-of-the-art techniques in solving portfolio optimization problems with multiple realistic constraints.