Valter Uotila

Valter Uotila

Recent advances in quantum computing have led to progress in exploring quantum applications across diverse fields, including databases and data management. This work presents a quantum machine learning model that tackles the challenge of estimating metrics, such as cardinalities, execution times, and costs, for SQL queries in relational databases. Precise estimations are crucial for the query optimizer to optimize query processing in relational databases efficiently. Our proposed quantum machine learning model consists of a novel query encoding mechanism, which maps SQL queries into high-dimensional Hilbert spaces using grammatical representations of the queries. The encoding mechanism translates SQL queries into parameterized quantum circuits, forming the core of the quantum machine learning model. The parameters in this model are tuned using standard quantum machine learning techniques. This encoding was first developed in quantum natural language processing (QNLP), and this work demonstrates its natural application in database optimization. Because the encoding mechanism is mathematically robust, the quantum machine learning model is also explainable, allowing us to draw a one-to-one correspondence between the elements in SQL queries and the model's parameters. The method is also scalable because it consists of multiple circuits, and we train and evaluate the model with hundreds of queries. Compared to previous research, our model achieves high accuracy, supporting the results obtained in the original QNLP research. We extend the previous QNLP work by adding 4-class and 8-class classification tasks and comparing the cardinality estimation results with those from state-of-the-art databases. We theoretically analyze the quantum machine learning model by calculating its expressibility and entangling capabilities.

Valter Uotila, Väinö Mehtola, Ilmo Salmenperä et al.

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.

Linus Jern, Valter Uotila, Cong Yu et al.

Large language models (LLMs) have achieved remarkable outcomes in complex problems, including math, coding, and analyzing large amounts of scientific reports. Yet, few works have explored the potential of LLMs in quantum computing. The most challenging problem is to leverage LLMs to automatically generate quantum circuits at a large scale. Fundamentally, the existing pre-trained LLMs lack the knowledge of quantum circuits. In this paper, we address this challenge by fine-tuning LLMs and injecting the domain-specific knowledge of quantum computing. We describe Agent-Q, an LLM fine-tuning system to generate and optimize quantum circuits. In particular, Agent-Q implements the mechanisms to generate training data sets and constructs an end-to-end pipeline to fine-tune pre-trained LLMs to generate parameterized quantum circuits for various optimization problems. Agent-Q provides 14,000 quantum circuits covering a large spectrum of the quantum optimization landscape: 12 optimization problem instances and their optimized QAOA, VQE, and adaptive VQE circuits. Based thereon, Agent-Q fine-tunes LLMs and constructs syntactically correct parametrized quantum circuits in OpenQASM 3.0. We have evaluated the quality of the LLM-generated circuits and parameters by comparing them to the optimized expectation values and distributions. Experimental results show superior performance of Agent-Q, compared to several state-of-the-art LLMs and better parameters than random. Agent-Q can be integrated into an agentic workflow, and the generated parametrized circuits with initial parameters can be used as a starting point for further optimization, e.g., as templates in quantum machine learning and as benchmarks for compilers and hardware.

Cong Yu, Valter Uotila, Shilong Deng et al.

Designing and optimizing task-specific quantum circuits are crucial to leverage the advantage of quantum computing. Recent large language model (LLM)-based quantum circuit generation has emerged as a promising automatic solution. However, the fundamental challenges remain unaddressed: (i) parameterized quantum gates require precise numerical values for optimal performance, which also depend on multiple aspects, including the number of quantum gates, their parameters, and the layout/depth of the circuits. (ii) LLMs often generate low-quality or incorrect quantum circuits due to the lack of quantum domain-specific knowledge. We propose QUASAR, an agentic reinforcement learning (RL) framework for quantum circuits generation and optimization based on tool-augmented LLMs. To align the LLM with quantum-specific knowledge and improve the generated quantum circuits, QUASAR designs (i) a quantum circuit verification approach with external quantum simulators and (ii) a sophisticated hierarchical reward mechanism in RL training. Extensive evaluation shows improvements in both syntax and semantic performance of the generated quantum circuits. When augmenting a 4B LLM, QUASAR has achieved the validity of 99.31% in Pass@1 and 100% in Pass@10, outperforming industrial LLMs of GPT-4o, GPT-5 and DeepSeek-V3 and several supervised-fine-tuning (SFT)-only and RL-only baselines.