Multi-Angle QAOA Does Not Always Need All Its Angles

Abstract

Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm (ma-QAOA) significantly improves the solution quality compared with QAOA by allowing the parameters for each term in the Hamiltonian to vary independently. Prior results suggest, however, considerable redundancy in parameters, the removal of which would reduce the cost of parameter optimization. In this work we show numerically the connection between the problem symmetries and the parameter redundancy by demonstrating that symmetries can be used to reduce the number of parameters used by ma-QAOA without decreasing the solution quality. We study Max-Cut on all 7,565 connected, non-isomorphic 8-node graphs with a nontrivial symmetry group and show numerically that in 67.4% of these graphs, symmetry can be used to reduce the number of parameters with no decrease in the objective, with the average ratio of parameters reduced by 28.1%. Moreover, we show that in 35.9% of the graphs this reduction can be achieved by simply using the largest symmetry. For the graphs where reducing the number of parameters leads to a decrease in the objective, the largest symmetry can be used to reduce the parameter count by 37.1% at the cost of only a 6.1% decrease in the objective. We demonstrate the central role of symmetries by showing that a random parameter reduction strategy leads to much worse performance.

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Cited by in corpus (7)

• A Review on Quantum Approximate Optimization Algorithm and its Variants
• Performance Analysis of Multi-Angle QAOA for p > 1
• Analyzing the quantum approximate optimization algorithm: ansätze, symmetries, and Lie algebras
• Efficient Sparse State Preparation via Quantum Walks
• Constraint-Aware Quantum Optimization via Hamming Weight Operators
• A Cyclic Layerwise QAOA Training
• Decoded Quantum Interferometry Under Noise