Twirlator: A Pipeline for Analyzing Subgroup Symmetry Effects in Quantum Machine Learning Ansatzes

Leveraging data symmetries has been a key driver of performance gains in geometric deep learning and geometric and equivariant quantum machine learning. While symmetrization appears to be a promising method, its practical overhead, such as additional gates, reduced expressibility, and other factors, is not well understood in quantum machine learning. In this work, we develop an automated pipeline to measure various characteristics of quantum machine learning ansatzes with respect to symmetries that can appear in the learning task. We define the degree of symmetry in the learning problem as the size of the subgroup it admits. Subgroups define partial symmetries, which have not been extensively studied in previous research, which has focused on symmetries defined by whole groups. Symmetrizing the 19 common ansatzes with respect to these varying-sized subgroup representations, we compute three classes of metrics that describe how the common ansatz structures behave under varying amounts of symmetries. The first metric is based on the norm of the difference between the original and symmetrized generators, while the second metric counts depth, size, and other characteristics from the symmetrized circuits. The third class of metrics includes expressibility and entangling capability. The results demonstrate varying gate overhead across the studied ansatzes and confirm that increased symmetry reduces expressibility of the circuits. In most cases, increased symmetry increases entanglement capability. These results help select sufficiently expressible and computationally efficient ansatze patterns for geometric quantum machine learning applications.

Fine-Tuning Large Language Models on Quantum Optimization Problems for Circuit Generation

Large language models (LLM) have achieved remarkable outcomes in addressing complex problems, including math, coding, and analyzing large amounts of scientific reports. Yet few works have explored the potential of LLM in quantum computing. The most challenging problem is how to leverage LLMs to automatically generate quantum circuits at a large scale. In this paper, we address such a challenge by fine-tuning LLMs and injecting the domain-specific knowledge of quantum computing. In particular, we investigate the mechanisms to generate training data sets and construct the end-to-end pipeline to fine-tune pre-trained LLMs that produce parameterized quantum circuits for optimization problems. We have prepared 14,000 quantum circuits covering a substantial part of the quantum optimization landscape: 12 optimization problem instances and their optimized QAOA, VQE, and adaptive VQE circuits. The fine-tuned LLMs can construct syntactically correct parametrized quantum circuits in the most recent OpenQASM 3.0. We have evaluated the quality of the parameters by comparing them to the optimized expectation values and distributions. Our evaluation shows that the fine-tuned LLM outperforms state-of-the-art models and that the parameters are better than random. The LLM-generated parametrized circuits and initial parameters can be used as a starting point for further optimization, \emph{e.g.,} templates in quantum machine learning and the benchmark for compilers and hardware.

SQL2Circuits: Estimating Metrics for SQL Queries with A Quantum Natural Language Processing Method

Quantum computing has developed significantly in recent years. Developing algorithms to estimate various metrics for SQL queries has been an important research question in database research since the estimations affect query optimization and database performance. This work represents a quantum natural language processing (QNLP) -inspired approach for constructing a quantum machine learning model which can classify SQL queries with respect to their execution times and cardinalities. From the quantum machine learning perspective, we compare our model and results to the previous research in QNLP and conclude that our model reaches similar accuracy as the QNLP model in the classification tasks. This indicates that the QNLP model is a promising method even when applied to problems that are not in QNLP. We study the developed quantum machine learning model by calculating its expressibility and entangling capability histograms. The results show that the model has favorable properties to be expressible but also not too complex to be executed on quantum hardware.