Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem

Abstract

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It has been observed that the optimal parameters obtained from one instance of a COP can be transferred to another instance, resulting in generally good solutions for the latter. In this work, we propose a refinement scheme in which only a subset of QAOA layers is optimized following parameter transfer, with a focus on the Max-Cut problem. Our motivation is to reduce the complexity of the loss landscape when optimizing all the layers of high-depth QAOA circuits, as well as to reduce the optimization time. We investigate the potential hierarchical roles of different layers and analyze how the approximation ratio scales with increasing problem size. Our findings indicate that the selective layer optimization scheme offers a favorable trade-off between solution quality and computational time, and can be more beneficial than full optimization at a lower optimization time.

11 pages, 9 figures. Revised version

References in corpus (20)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• A variational eigenvalue solver on a quantum processor
• Ising formulations of many NP problems
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
• A Review on Quantum Approximate Optimization Algorithm and its Variants
• Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
• The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• $XY$-mixers: analytical and numerical results for QAOA
• Quantum Annealing: An Overview
• Quantum annealing initialization of the quantum approximate optimization algorithm
• Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem
• Parameter Concentration in Quantum Approximate Optimization
• Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut
• Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm
• Transfer learning of optimal QAOA parameters in combinatorial optimization
• Symmetry-informed transferability of optimal parameters in the Quantum Approximate Optimization Algorithm