@article {2809, title = {Behavior of Analog Quantum Algorithms}, year = {2021}, month = {7/2/2021}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/2107.01218}, author = {Lucas T. Brady and Lucas Kocia and Przemyslaw Bienias and Aniruddha Bapat and Yaroslav Kharkov and Alexey V. Gorshkov} } @article {2321, title = {Bang-bang control as a design principle for classical and quantum optimization algorithms}, journal = {Quantum Information \& Computation }, volume = {19}, year = {2019}, month = {8/1/2019}, pages = {424-446}, abstract = {

Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, we argue that the type of control strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.

}, url = {https://arxiv.org/abs/1812.02746}, author = {Aniruddha Bapat and Stephen Jordan} }