[Paper Review] Quantum approximate optimization via learning-based adaptive optimization

Lixue Cheng, Yuqin Chen+2 more|arXiv (Cornell University)|Mar 27, 2023

Quantum Computing Algorithms and Architecture56 references8 citations

TL;DR

The authors introduce DARBO, a double adaptive-region Bayesian optimizer for QAOA, achieving faster, more accurate, and more stable optimization than baselines, demonstrated in simulations and a 5-qubit hardware proof-of-concept with error mitigation.

ABSTRACT

Combinatorial optimization problems are ubiquitous and computationally hard to solve in general. Quantum approximate optimization algorithm (QAOA), one of the most representative quantum-classical hybrid algorithms, is designed to solve combinatorial optimization problems by transforming the discrete optimization problem into a classical optimization problem over continuous circuit parameters. QAOA objective landscape is notorious for pervasive local minima, and its viability significantly relies on the efficacy of the classical optimizer. In this work, we design double adaptive-region Bayesian optimization (DARBO) for QAOA. Our numerical results demonstrate that the algorithm greatly outperforms conventional optimizers in terms of speed, accuracy, and stability. We also address the issues of measurement efficiency and the suppression of quantum noise by conducting the full optimization loop on a superconducting quantum processor as a proof of concept. This work helps to unlock the full power of QAOA and paves the way toward achieving quantum advantage in practical classical tasks.

Motivation & Objective

• Motivate solving NP-hard combinatorial optimization problems with quantum approaches like QAOA.
• Address optimization landscape challenges in QAOA, including local minima and barren plateaus, and improve training efficiency.
• Propose and validate a gradient-free, learning-based optimizer (DARBO) leveraging Gaussian processes and adaptive regions.
• Demonstrate end-to-end QAOA optimization on real hardware with quantum error mitigation to showcase practical viability.

Proposed method

• Introduce Double Adaptive-Region Bayesian Optimization (DARBO) as a gradient-free classical optimizer for QAOA.
• Use a Gaussian process surrogate model with a Matérn5/2 kernel to model the QAOA objective.
• Incorporate two adaptive regions: an adaptive trust region for local surrogate accuracy and an adaptive search region to constrain candidate queries.
• Employ an upper confidence bound (UCB) acquisition function to select the next query point within the adaptive regions.
• Show robustness to measurement shot noise and quantum noise, and integrate quantum error mitigation (QEM) in the end-to-end workflow.
• Evaluate end-to-end performance via analytical simulation, numerical simulation with finite shots, and real hardware experiments with five qubits and QEM.

Experimental results

Research questions

• RQ1 Can DARBO improve efficiency, stability, and accuracy of QAOA optimization compared with standard optimizers (e.g., Adam, COBYLA, SPSA) under various depths (p) and problem instances?
• RQ2 How does measurement noise and quantum noise affect QAOA optimization, and can Bayesian, noise-aware strategies (like DARBO with EM-QAOA) mitigate these effects?
• RQ3 What is the impact of end-to-end hardware implementation with quantum error mitigation on QAOA performance and optimizer behavior?
• RQ4 Is the two-adaptive-region approach scalable to broader variational quantum algorithms beyond QAOA?

Key findings

• DARBO outperforms common optimizers in efficiency, stability, and accuracy across analytically exact and noisy simulations.
• For MAX-CUT on n=16 w3R graphs, final 1-r gaps under DARBO are smaller than those of Adam and COBYLA across depths p from 2 to 10 in exact simulations.
• In numerical simulations with finite measurement shots, DARBO achieves significantly smaller approximation gaps than Adam, COBYLA, and SPSA, with robustness improving as shot number increases.
• On real hardware with QEM, DARBO improves objective values and final success ratios compared to raw measurements, and deeper QAOA (p=2) offers a better trade-off between expressiveness and noise.
• The combination of EM-QAOA and DARBO demonstrates practical viability and improved end-to-end performance, suggesting potential quantum advantage as hardware scales.