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

TL;DR

This paper demonstrates the implementation of a variational quantum factoring algorithm on a superconducting quantum processor, analyzing how quantum resources and noise affect factoring success, and identifying optimal circuit configurations.

Contribution

It provides experimental insights into the performance of VQF on real hardware, including noise effects and optimal circuit depth for factoring specific integers.

Findings

Factored integers 1099551473989, 3127, 6557 with 3-5 qubits.

Identified optimal circuit layers for success probability.

Noise, especially residual ZZ-coupling, significantly impacts performance.

Abstract

In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms could provide a quantum advantage. In this work, we study a QAOA-based quantum optimization algorithm by implementing the Variational Quantum Factoring (VQF) algorithm. We execute experimental demonstrations using a superconducting quantum processor and investigate the trade-off between quantum resources (number of qubits and circuit depth) and the probability that a given biprime is successfully factored. In our experiments, the integers 1099551473989, 3127, and 6557 are factored with 3, 4, and 5 qubits, respectively, using a QAOA ansatz with up to 8 layers and we are able to identify the optimal number of circuit layers for a given instance to maximize success probability. Furthermore, we demonstrate the impact of different noise sources on the performance of QAOA and reveal the coherent error caused by the residual ZZ-coupling between qubits as a dominant source of error in the superconducting quantum processor.