Dimensionality reduction for adiabatic quantum optimizers: Beyond symmetry exploitation

Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the minimum energy gap encountered during the dynamics. Unfortunately, the direct calculation of the gap is strongly limited by the exponential growth in dimensionality of quantum systems. Although many special-purpose methods have been devised to reduce the effective dimensionality of the Hilbert space, they are strongly limited to particular classes of problems with evident symmetries. Here, we propose and implement a reduction method that does not rely on any explicit symmetry and which requires, under certain but quite general conditions, only a polynomial amount of classical resources. As a concrete example, we analyze the well known Grover problem in presence of local disorder. In particular we show that adiabatic quantum optimization, even when affected by random noise, is still potentially faster than any classical algorithm.