Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor*

Quantum computers hold promise as accelerators for certain classically-intractable problems – necessitating a hybrid quantum-classical system. Understanding how these two computing paradigms work in tandem is necessary to identify where hybrid systems could provide an advantage. In the context of quantum optimization, we study such systems and investigate the tradeoff between quantum resources, such as circuit depth, and solution accuracy. We use the variational quantum factoring (VQF) algorithm as a prototypical hybrid workflow and execute experimental demonstrations using a superconducting quantum processor. We factor 1,099,551,473,989 (3 qubits), 3,127 (4 qubits), and 6,557 (5 qubits) with up to 8 layers of the QAOA ansatz and analyze the success probability at each layer. Our results demonstrate how the success probability trends with the number of layers and reveal that coherent noise is a dominant source of error affecting the algorithm's performance. This suggests that VQF could form an “application benchmark" to measure the performance of quantum computers.