Southwest Quantum Information and Technology

Behavior of Analog Quantum Algorithms

Presenting Author: Lucas Brady, National Institute of Standards and Technology, Maryland
Contributing Author(s): Lucas Kocia, Przemyslaw Bienias, Aniruddha Bapat, Yaroslav Kharkov, Alexey Gorshkov

Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are promising candidates for near-term quantum applications, but they often require fine tuning via the annealing schedule or variational parameters. In this work, we explore connections between these analog algorithms, as well as limits in which they become approximations of the optimal procedure. Notably, we explore how the optimal procedure approaches a smooth adiabatic procedure but with a superposed oscillatory pattern that can be explained in terms of the interactions between the ground state and first excited state that effect the coherent error cancellation of diabatic transitions. Furthermore, we provide numeric and analytic evidence that QAOA emulates this optimal procedure with the length of each QAOA layer equal to the period of the oscillatory pattern. Additionally, the ratios of the QAOA bangs are determined by the smooth, non-oscillatory part of the optimal procedure. We provide arguments for these phenomena in terms of the product formula expansion of the optimal procedure. With these arguments, we conclude that different analog algorithms can emulate the optimal protocol under different limits and approximations. Finally, we present a new algorithm for better approximating the optimal protocol using the analytic and nu

Read this article online: https://arxiv.org/abs/2107.01218

(Session 5 : Thursday from 12:00pm-2:00 pm)