Differential Optimization of Quantum Circuits Dominated by Clifford Gates

Finding a good initialization for variational quantum algorithms is believed to be crucial for successful training for near-term applications. However, the methodology for finding quality initializations is yet unclear. In this work, we propose to use the classical differential architecture search method to optimize quantum circuits dominated by Clifford gates, which we call the Clifford+kT ansatz. The optimal solution found within this ansatz can be viewed as a promising initialization for universal variational quantum circuits. In the regime of a small number of T-gates k, we numerically demonstrate that such optimization with differential architecture search is scalable. We illustrate the effectiveness of our methods for variational quantum eigensolver (VQE) using a molecular Hamiltonian of many qubits. We also compare differential architecture search with simulated annealing and numerically show the effect of adding T-gates to the ansatz. Last but not the least, we establish that our initialization strategy indeed helps with the training of variational algorithms on near-term quantum devices.