Shortcuts to the quantum approximate optimization algorithm

Abstract

The quantum approximate optimization algorithm (QAOA) is a quantum-classical hybrid algorithm intending to find the ground state of a target Hamiltonian. Theoretically, QAOA can obtain the approximate solution if the quantum circuit is deep enough. Actually, the performance of QAOA decreases practically if the quantum circuit is deep since near-term devices are not noise free, and the errors caused by noise accumulate as the quantum circuit increases. In order to reduce the depth of quantum circuits, we propose an ansatz dubbed as ``Shortcuts to QAOA'' (S-QAOA), S-QAOA provides shortcuts to the ground state of the target Hamiltonian by including more two-body interactions and releasing the parameter freedoms. To be specific, besides the existing $ZZ$ interaction in the QAOA ansatz, other two-body interactions are introduced in the S-QAOA ansatz such that the approximate solutions could be obtained with smaller circuit depth. Considering the Max-Cut problem and the Sherrington-Kirkpatrick model, numerically computation shows the $YY$ interaction has the best performance. The reason for this might arise from the counterdiabatic effect generated by $YY$ interaction. On top of this, we release the freedom of parameters of two-body interactions, which a priori do not necessarily have to be fully identical, and numerical results show that it is worth paying the extra cost of having more parameter freedom since one has a greater improvement on success rate.