Speedup of the quantum adiabatic algorithm using delocalization catalysis
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Abstract
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to antiferromagnetic Heisenberg spin models. The algorithm is catalyzed in such a way that the evolution approximates such models in the middle of its course, and the model is in a delocalized phase. We show numerically that we can speed up the standard algorithm for finding the ground state of the random-field Ising model using this idea. We can also show that the speedup is due to gap amplification, even though the underlying model is not frustration-free. Our method is verified by experimental results from IBM quantum computer. Even though only relatively small systems can be investigated, the evidence suggests that the scaling of the method with system size is favorable. The cost of the catalytic method compared to the standard algorithm is only a constant factor.