Preserving symmetries in NISQ algorithms

Many classical optimization problems display local or global symmetries. In the Quantum Alternating Operator Ansatz (QAOA), these symmetries can be used to design mixers which restrict the evolution of the system to a subspace which is exponentially smaller than the full Hilbert space [1,2]. However, in realistic scenarios, errors can break the symmetry and yield invalid solutions to the optimization problem. In this talk, we show an analysis of the probability of staying in the correct subspace under the influence of realistic noise models. Moreover, for the example of 3-coloring, we show that it is possible to exploit the natural redundancy of the qubit encoding to bring back the evolution into the correct subspace.
[1] From QAOA to QAOA, Hadfield, Wang, O'Gorman, Rieffel, Venturelli, Biswas, Algorithms, 2019.
[2] XY-mixers: analytical and numerical results for QAOA, Wang, Rubin, Dominy, Rieffel, arXiv:1904.09314