  Quantum approximate optimization algorithm (QAOA) has attracted much
attention as an algorithm that has the potential to efficiently solve
combinatorial optimization problems. Among them, a fermionic QAOA (FQAOA) for
solving constrained optimization problems has been developed [Yoshioka, Sasada,
Nakano, and Fujii, Phys. Rev. Research vol. 5, 023071, 2023]. In this
algorithm, the constraints are essentially imposed as fermion number
conservation at arbitrary approximation level. We take the portfolio
optimization problem as an application example and propose a new driver
Hamiltonian on an one-dimensional cyclic lattice. Our FQAOA with the new driver
Hamiltonian reduce the number of gate operations in quantum circuits.
Experiments on a trapped-ion quantum computer using 16 qubits on Amazon Braket
demonstrates that the proposed driver Hamiltonian effectively suppresses noise
effects compared to the previous FQAOA.
