Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not efficiently computable on classical devices. However, there is no straightforward method to engineer the optimal quantum kernel for each specific use case. While recent literature has focused on exploiting the potential offered by the presence of symmetries in the data to guide the construction of quantum kernels, we adopt here a different approach, which employs optimization techniques, similar to those used in neural architecture search and AutoML, to automatically find an optimal kernel in a heuristic manner. The algorithm we present constructs a quantum circuit implementing the similarity measure as a combinatorial object, which is evaluated based on a cost function and is then iteratively modified using a meta-heuristic optimization technique. The cost function can encode many criteria ensuring favorable statistical properties of the candidate solution, such as the rank of the Dynamical Lie Algebra. Importantly, our approach is independent of the optimization technique employed. The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach, showing the potential of our technique to deliver superior results with reduced effort.

翻译：量子计算可通过使核机器利用量子核来表示数据间的相似度量，从而赋能机器学习模型。量子核能够捕获经典设备无法高效计算的数据关系，但目前尚无直接方法为每个特定用例设计最优量子核。尽管近期文献集中于利用数据中的对称性来指导量子核构建，我们在此采用不同方法，运用类似神经架构搜索和AutoML中的优化技术，以启发式方式自动寻找最优核。本文提出的算法将实现相似度量的量子电路构建为组合对象，基于代价函数评估后通过元启发式优化技术迭代修改。代价函数可编码多项确保候选解良好统计特性的准则，如动力学李代数秩。重要的是，本方法独立于所采用的优化技术。在高能物理问题上的测试结果表明，在最佳情形下，我们的方法能与人工设计方法匹配甚至提升测试精度，展现了该技术以更少投入获得更优结果的潜力。