Adiabatic quantum optimization in presence of discrete noise: Reducing the problem dimensionality

TL;DR

This paper introduces a general reduction method for adiabatic quantum optimization that handles discrete noise and defects, enabling analysis of performance in realistic, noisy conditions and showing potential quantum advantage.

Contribution

The authors develop a symmetry-independent reduction technique requiring polynomial classical resources, facilitating the study of noisy adiabatic quantum optimization performance.

Findings

Quantum optimization remains potentially faster than classical algorithms despite noise.

The reduction method applies to problems with discrete local defects.

Adiabatic quantum algorithms can outperform classical ones even with imperfections.

Abstract

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 the dimensionality of the Hilbert space associated to the quantum system. Although many special-purpose methods have been devised to reduce the effective dimensionality, they are strongly limited to particular classes of problems with evident symmetries. Moreover, little is known about the computational power of adiabatic quantum optimizers in real-world conditions. Here, we propose and implement a general purposes reduction method that does not rely on any explicit symmetry and which requires, under certain general conditions, only a polynomial amount of classical resources. Thanks to this method, we are able to analyze the performance of "non-ideal" quantum adiabatic optimizers to solve the well-known Grover problem, namely the search of target entries in an unsorted database, in the presence of discrete local defects. In this case, we show that adiabatic quantum optimization, even if affected by random noise, is still potentially faster than any classical algorithm.