Automated near-term quantum algorithm discovery for molecular ground states

Abstract

Designing quantum algorithms is a complex and counterintuitive task, making it an ideal candidate for AI-driven algorithm discovery. To this end, we employ the Hive, an AI platform for program synthesis, which utilises large language models to drive a highly distributed evolutionary process for discovering new algorithms. We focus on the ground state problem in quantum chemistry, and discover efficient quantum heuristic algorithms that solve it for molecules LiH, H2O, and F2 while exhibiting significant reductions in quantum resources relative to state-of-the-art near-term quantum algorithms. Further, we perform an interpretability study on the discovered algorithms and identify the key functions responsible for the efficiency gains. Finally, we benchmark the Hive-discovered circuits on the Quantinuum System Model H2 quantum computer and identify minimum system requirements for chemical precision. We envision that this novel approach to quantum algorithm discovery applies to other domains beyond chemistry, as well as to designing quantum algorithms for fault-tolerant quantum computers.

Figures (9)

• Figure 1: Overview of AI algorithm discovery frameworks. The system samples high-performing programs from a programs database that serve as the basis for improvements proposed by an LLM. New programs are evaluated in a sandbox to generate a quantifiable performance score, and both the program and its score are stored in the programs database to use in future iterations.
• Figure 2: VQE-style quantum algorithms. This family of quantum algorithms is defined by two components: a parametrised quantum circuit and a classical optimisation step. The aim is to find the ground state of a molecule, so we seek a trial state that yields the lowest eigenvalue of the molecule's Hamiltonian. We first define the Hamiltonian of a molecule in a chosen basis and at a given geometry, the initial state, typically the Hartree–Fock state, and an operator pool $\{O_i(\theta_i)\}$. These parameterised operators are used by the classical optimisation step to generate an ansatz and update its parameters. The trial state is evaluated, and based on the results, the classical step updates the ansatz and its parameters iteratively in a feedback loop.
• Figure 3: Quantum algorithm discovery workflow. An application of the workflow shown in Fig. \ref{['fig:EvoAI4Algo']} to the quantum algorithm skeleton shown in Fig. \ref{['fig:vqeskeleton']}. The Hive is provided with a problem skeleton and information about the molecule at hand, which contains basic code to construct and evaluate quantum operators implemented by InQuanto. It is also given a generic prompt that contains a basic description of the molecular ground-state problem in quantum chemistry. The candidate algorithms are evaluated on a backend, a quantum computer, or a classical simulator or emulator, which returns the energy value that serves as the main objective for the Hive to optimise.
• Figure 4: Energy precision of bond dissociation curves obtained with the Hive algorithms and ADAPT baselines as a function of bond length.a--c, Bond dissociation curves (top panels) and energy errors relative to FCI (bottom panels) for LiH (a), H$_2$O (b), and F$_2$ (c). Hive results are shown as red circles, ADAPT-VQE and QEB-ADAPT-VQE are shown as blue squares and green pentagons, respectively. Hollow markers indicate the specific bond lengths used in the evolution of the Hive ansatz, while solid markers represent test points evaluated using the evolved algorithms. The dashed grey line in the error plots marks the chemical precision threshold (1.6e-3). Bond length for LiH denotes the Li--H distance; for H$_2$O, the O--H bond length (with both O--H bonds stretched symmetrically); and for F$_2$, the F--F distance.
• Figure 5: Quantum resource overhead of the Hive algorithms and ADAPT baselines for different molecules. Scaling of variational parameters (top row), total circuit evaluations (exact statevector energy evaluations, middle row), and two-qubit gate counts (after compilation to the Quantinuum H2 native gate set, bottom row) for LiH (a), H$_2$O (b), and F$_2$ (c). Hive results are shown as red circles, ADAPT-VQE and QEB-ADAPT-VQE are shown as blue squares and green pentagons, respectively. Points where algorithms failed to converge to energy error below chemical precision $E-E_{\mathrm{FCI}}\le 1.6\,\mathrm{mHa}$ are omitted from the plots. Bond lengths follow the definitions in Fig. \ref{['fig:precision']}.