Lyapunov control-inspired protocol for quantum approximate optimization

It is widely hoped that quantum devices will be able to solve practical problems in the near future. One potential path for realizing this is via the quantum approximate optimization algorithm, which seeks an approximate solution to an optimization problem by encoding it in the ground state of an Ising problem Hamiltonian. A classical processor is then used to optimize a set of coefficients parameterizing a relatively-shallow quantum circuit in order to drive the qubits to the problem Hamiltonian’s ground state. However, the success of this approach hinges on the performance of the classical optimizer, which depends on numerous factors. In this talk, we introduce an alternate strategy based on Lyapunov control that offers a deterministic, constructive protocol for assigning values to the quantum circuit parameters, such that the problem Hamiltonian's expectation value decreases layer-by-layer. The parameter values are assigned sequentially as a function per layer of measurement information, eliminating the need for any classical optimization. Numerical analyses are presented that investigate the utility of this Lyapunov control-inspired protocol towards the MaxCut problem.

Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525.