Multiangle QAOA Does Not Always Need All Its Angles
Multiangle QAOA Does Not Always Need All Its Angles
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DOI：
10.1109/sec54971.2022.00062
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Kaiyan Shi;Rebekah Herrman;Ruslan Shaydulin;Shouvanik Chakrabarti;Marco Pistoia;Jeffrey Larson
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文献类型：
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作者：
Kaiyan Shi;Rebekah Herrman;Ruslan Shaydulin;Shouvanik Chakrabarti;Marco Pistoia;Jeffrey Larson
在量子电路中引入额外的可调参数是一种在不增加硬件要求的情况下提高性能的有效方法。最近引入的量子近似优化算法的多角度扩展（ma-QAOA）通过允许哈密顿量中的每一项的参数独立地变化，与QAOA相比显著地提高了解的质量。然而，先前的结果表明，相当多的冗余参数，删除将降低参数优化的成本。在这项工作中，我们数值显示的问题的对称性和参数冗余之间的连接，通过证明对称性可以用来减少使用的参数的数量，而不会降低解决方案的质量。我们研究了所有7，565个具有非平凡对称群的连通非同构8节点图的最大割，并通过数值计算表明，在这些图中的67.4%中，对称性可以用来减少参数的数量而不会减少目标，参数的平均比率减少了28.1%。此外，我们表明，在35.9%的图，这种减少可以通过简单地使用最大的对称性。对于减少参数数量导致目标减少的图，可以使用最大对称性以目标仅减少6.1%的代价将参数计数减少37.1%。我们展示了对称性的核心作用，表明一个随机的参数减少策略导致更差的性能。
Introducing additional tunable parameters to quantum circuits is a powerful way of improving per-formance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm (ma-QAOA) signifi-cantly improves the solution quality compared with QAOA by allowing the parameters for each term in the Hamilto-nian 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.