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

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.

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• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Neural Predictor based Quantum Architecture Search
• Quantum transport and localization in 1d and 2d tight-binding lattices
• Scalable Method for Eliminating Residual $ZZ$ Interaction between Superconducting Qubits
• Two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
• Digitized Adiabatic Quantum Factorization
• Suppressing Coherent Two-Qubit Errors via Dynamical Decoupling
• Squeezing and quantum approximate optimization
• Variational quantum iterative power algorithms for global optimization
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Noise tailoring for Robust Amplitude Estimation