PUSHO, a pulse-level variational quantum algorithm for Rydberg atom platforms

Abstract

The manipulation of neutral atoms by light is at the heart of countless scientific discoveries in the field of quantum physics in the last three decades. The level of control that has been achieved at the single particle level within arrays of optical traps, while preserving the fundamental properties of quantum matter (coherence, entanglement, superposition), makes these technologies prime candidates to implement disruptive computation paradigms. The current quantum processing units (QPU) are nothing close to universal computers but can already target specific combinatorial problems, on which many industrial issues can be mapped. Problems, whose classical complexity scales exponentially with their size, such as finding the Maximum Independent Set (MIS) of a Unit-Disk (UD) graph or approximating the solution of a Quadratic Unconstrained Binary Optimisation (QUBO) can be mapped to Rydberg platforms. It enables to solve them by approximating their cost function with the Hamiltonian of the atomic array. Then the atoms are optimally driven with implementable laser pulses shaped by Bayesian Optimisation (BO) to a solution state which minimises the previous cost. Initially, BO performs well with fewer iterations than others classical algorithms and additionally can maintain this level with noisier estimations, especially when the number of shots is limited for instance. Pulse Shaping Optimisation (PUSHO) provides a straightforward but powerful Variational Quantum Algorithm (VQA), taking advantage of our ability to precisely control the shape of the driving fields.