Ion-native variational ansatz for quantum approximate optimization

Abstract

Variational quantum algorithms involve training parameterized quantum circuits using a classi-cal co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm. Realization of this algorithm on any modern quantum processor requires either embedding a problem instance into a Hamiltonian or emulating the corresponding propagator by a gate sequence. For a vast range of problem instances this is impossible due to current circuit depth and hardware limitations. Hence we adapt the variational approach—using ion native Hamiltonians—to create ansatze families that can prepare the ground states of more general problem Hamiltonians. We analytically determine symmetry protected classes that make certain problem instances inaccessible unless this symmetry is broken. We exhaustively search over six qubits and consider upto twenty circuit layers, demonstrating that symmetry can be broken to solve all problem instances of the Sherrington-Kirkpatrick Hamiltonian. Going further, we numerically demonstrate training convergence and level-wise improvement for up to twenty qubits. Specifically these findings widen the class problem instances which might be solved by ion based quantum processors. Generally these results serve as a test-bed for quantum approximate optimization approaches based on system native Hamiltonians and symmetry protection.