A Verified Compiler for Quantum Simulation

2025-09-22

AI Summary

Existing quantum simulation compilers predominantly rely on low-level Pauli representations, suffering from limited programmability and lacking formal correctness guarantees. This paper introduces QBlue, a higher-order quantum simulation compilation framework that achieves the first end-to-end formally verified compilation of second-quantized Hamiltonian simulations. QBlue adopts creation and annihilation operators as primitive language constructs and introduces a static type system to enforce particle-number conservation and Hermiticity constraints, while supporting joint generation of digital and analog quantum circuits. Leveraging the Rocq proof framework, we mechanize the full semantic verification across the entire compilation pipeline—from source programs to target circuits. Experimental evaluation demonstrates that QBlue significantly enhances modeling expressivity and compilation reliability, providing rigorous mathematical correctness guarantees for quantum simulation software.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Hamiltonian simulation is a central application of quantum computing, with significant potential in modeling physical systems and solving complex optimization problems. Existing compilers for such simulations typically focus on low-level representations based on Pauli operators, limiting programmability and offering no formal guarantees of correctness across the compilation pipeline. We introduce QBlue, a high-level, formally verified framework for compiling Hamiltonian simulations. QBlue is based on the formalism of second quantization, which provides a natural and expressive way to describe quantum particle systems using creation and annihilation operators. To ensure safety and correctness, QBlue includes a type system that tracks particle types and enforces Hermitian structure. The framework supports compilation to both digital and analog quantum circuits and captures multiple layers of semantics, from static constraints to dynamic evolution. All components of QBlue, including its language design, type system, and compilation correctness, are fully mechanized in the Rocq proof framework, making it the first end-to-end verified compiler for second-quantized Hamiltonian simulation.

Problem

• Existing quantum simulation compilers lack formal correctness guarantees
• Low-level Pauli operator representations limit programmability and expressiveness
• Need for verified compilation from high-level Hamiltonian descriptions to circuits

Innovation

• High-level formalism using second quantization
• Type system enforcing Hermitian structure correctness
• End-to-end verification in Rocq proof framework