Qaoa

In this paper, we explore the impact of noise on quantum computing, particularly focusing on the challenges when sampling bit strings from noisy quantum computers as well as the implications for optimization and machine learning applications. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the Conditional Value at Risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on a real quantum computer involving up to 127 qubits. The results show a strong alignment with theoretical predictions. ...

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA Ansatz is not optimal, there is no systematic approach for finding better Ansätze. We address this problem by developing an iterative version of QAOA that is problem tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity. ...