02137nas a2200169 4500008004100000245004200041210004200083260001300125520166200138100002101800700001701821700002401838700002101862700002201883700002501905856003701930 2021 eng d00aBehavior of Analog Quantum Algorithms0 aBehavior of Analog Quantum Algorithms c7/2/20213 a
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 numeric insights from the rest of the paper. In practice, numerically, we find that this algorithm outperforms standard QAOA and naive quantum annealing procedures.
1 aBrady, Lucas, T.1 aKocia, Lucas1 aBienias, Przemyslaw1 aBapat, Aniruddha1 aKharkov, Yaroslav1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2107.01218