Alignment between Initial State and Mixer Improves QAOA Performance for Constrained Optimization

TL;DR

This paper shows that initializing QAOA in the ground state of the mixing Hamiltonian enhances its performance on constrained optimization problems, supported by numerical simulations and experiments on a trapped-ion quantum processor.

Contribution

It demonstrates that aligning the initial state with the adiabatic ground state improves QAOA effectiveness, validated through simulations and real quantum hardware experiments.

Findings

Optimal initial state is the ground state of the mixing Hamiltonian.

QAOA with this initialization outperforms other states in constrained portfolio optimization.

Successful implementation of QAOA on a 32-qubit trapped-ion quantum processor.

Abstract

Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low ($p\leq 3$) and high ($p = 100$) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.