Towards Quantum Software for Quantum Simulation

TL;DR

The paper addresses the lack of a scalable software stack for quantum simulation by arguing for a modular, model-driven engineering framework that spans from high-level physical theories to hardware-specific implementations. It proposes a vision of a cross-platform quantum simulation stack that unifies digital and analogue approaches, illustrated through a 1D $U(1)$ lattice gauge theory and its mapping to a Bose–Hubbard hardware model using parity encoding. The authors outline essential abstractions, including domain-specific representations, hardware-independent intermediate representations, automated code generation, and transformations between abstraction levels, while discussing alternative simulation realizations and the need for benchmarking and noise-aware toolchains. This work aims to enable automated, reusable, and scalable quantum simulations across platforms, driving toward practical quantum advantage in physics-driven computation.

Abstract

Quantum simulation is a leading candidate for demonstrating practical quantum advantage over classical computation, as it is believed to provide exponentially more compute power than any classical system. It offers new means of studying the behaviour of complex physical systems, for which conventionally software-intensive simulation codes based on numerical high-performance computing are used. Instead, quantum simulations map properties and characteristics of subject systems, for instance chemical molecules, onto quantum devices that then mimic the system under study. Currently, the use of these techniques is largely limited to fundamental science, as the overall approach remains tailored for specific problems: We lack infrastructure and modelling abstractions that are provided by the software engineering community for other computational domains. In this paper, we identify critical gaps in the quantum simulation software stack-particularly the absence of general-purpose frameworks for model specification, Hamiltonian construction, and hardware-aware mappings. We advocate for a modular model-driven engineering (MDE) approach that supports different types of quantum simulation (digital and analogue), and facilitates automation, performance evaluation, and reusability. Through an example from high-energy physics, we outline a vision for a quantum simulation framework capable of supporting scalable, cross-platform simulation workflows.

Figures (2)

• Figure 1: Continuous vs. discrete (Trotterised) time evolution. Left: The continuous dynamic of a physical systems is described by the Hamiltonian $\hat{H}_\text{sys}$ starting at an initial state at time $0$, which then evolves under the corresponding unitary $\hat{U}_\text{sys}$ to a target state at time $t$. Right: Continuous time evolution is discretised (Trotterised) into local one- and two-qubit gates that can be executed on universal, gate-based quantum hardware, yet in the general case results in a time evolution under an approximated Hamiltonian $\hat{H}_\approx$.
• Figure 2: Envisioned quantum simulation framework illustrated for one-dimensional qed (left), and suggested software abstraction layers (right).