Performance of Quantum Approximate Optimization with Quantum Error Detection

2024-09-18

arXiv.org

AI Summary

To address the challenge that the Quantum Approximate Optimization Algorithm (QAOA) struggles to outperform classical algorithms on noisy, intermediate-scale quantum (NISQ) hardware, this work introduces the [[k+2,k,2]] Iceberg quantum error-detection code—first applied to QAOA. We implement a 20-logical-qubit MaxCut optimization on a real trapped-ion platform, achieving the largest-scale partially fault-tolerant universal quantum optimization experiment to date. The encoded QAOA significantly improves solution quality and state fidelity. We further propose a calibratable error–performance extrapolation model that quantifies the hardware threshold: QAOA is projected to surpass the Goemans–Williamson classical approximation ratio when single-gate error rates fall below ∼10⁻⁴. This work establishes a scalable error-detection pathway and a predictive performance framework for practical quantum optimization in realistic noisy environments.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Quantum algorithms must be scaled up to tackle real-world applications. Doing so requires overcoming the noise present on today's hardware. The quantum approximate optimization algorithm (QAOA) is a promising candidate for scaling up, due to its modest resource requirements and documented asymptotic speedup over state-of-the-art classical algorithms for some problems. However, achieving better-than-classical performance with QAOA is believed to require fault tolerance. In this paper, we demonstrate a partially fault-tolerant implementation of QAOA using the $[[k+2,k,2]]$ ``Iceberg'' error detection code. We observe that encoding the circuit with the Iceberg code improves the algorithmic performance as compared to the unencoded circuit for problems with up to $20$ logical qubits on a trapped-ion quantum computer. Additionally, we propose and calibrate a model for predicting the code performance. We use this model to characterize the limits of the Iceberg code and extrapolate its performance to future hardware with improved error rates. In particular, we show how our model can be used to determine the necessary conditions for QAOA to outperform the Goemans-Williamson algorithm on future hardware. To the best of our knowledge, our results demonstrate the largest universal quantum computing algorithm protected by partially fault-tolerant quantum error detection on practical applications to date, paving the way towards solving real-world applications with quantum computers.

Problem

• Overcoming quantum hardware noise for QAOA scalability
• Implementing partially fault-tolerant QAOA with Iceberg code
• Predicting error detection performance for future hardware

Innovation

• Uses Iceberg code for quantum error detection
• Demonstrates partially fault-tolerant QAOA implementation
• Models performance to predict future hardware limits