Variational quantum machine learning is an extensively studied application of
near-term quantum computers. The success of variational quantum learning models
crucially depends on finding a suitable parametrization of the model that
encodes an inductive bias relevant to the learning task. However, precious
little is known about guiding principles for the construction of suitable
parametrizations. In this work, we holistically explore when and how symmetries
of the learning problem can be exploited to construct quantum learning models
with outcomes invariant under the symmetry of the learning task. Building on
tools from representation theory, we show how a standard gateset can be
transformed into an equivariant gateset that respects the symmetries of the
problem at hand through a process of gate symmetrization. We benchmark the
proposed methods on two toy problems that feature a non-trivial symmetry and
observe a substantial increase in generalization performance. As our tools can
also be applied in a straightforward way to other variational problems with
symmetric structure, we show how equivariant gatesets can be used in
variational quantum eigensolvers.

本研究探讨了如何利用问题的对称性构建量子学习模型，并提出了一种通过门对称化将标准门集转换为等变门集的方法，在具有对称性结构的变分问题中得到了应用。