������

Authors

Linus Jern, Valter Uotila, Cong Yu, and Bo Zhao

Abstract

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.

The study was covered in Quantum Zeitgeist:

Authors

Valter Uotila, Julia Ripatti, and Bo Zhao

Abstract

Portfolio optimization is one of the most studied optimization problems at the intersection of quantum computing and finance. In this work, we develop the first quantum formulation for a portfolio optimization problem with higher-order moments, skewness and kurtosis. Including higher-order moments leads to more detailed modeling of portfolio return distributions. Portfolio optimization with higher-order moments has been studied in classical portfolio optimization approaches but with limited exploration within quantum formulations. In the context of quantum optimization, higher-order moments generate higher-order terms in the cost Hamiltonian. Thus, instead of obtaining a quadratic unconstrained binary optimization problem, we obtain a higher-order unconstrained binary optimization (HUBO) problem, which has a natural formulation as a parametrized circuit. Additionally, we employ realistic integer variable encoding and a capital-based budget constraint. We consider the classical continuous variable solution with integer programming-based discretization to be the computationally efficient classical baseline for the problem. Our extensive experimental evaluation of 100 portfolio optimization problems shows that the solutions to the HUBO formulation often correspond to better portfolio allocations than the classical baseline. This is a promising result for those who want to perform computationally challenging portfolio optimization on quantum hardware, as portfolio optimization with higher moments is classically complex. Moreover, the experimental evaluation studies QAOA's performance with higher-order terms in this practically relevant problem.