Quantum Simulation Programming via Typing

Abstract: Quantum simulations are designed to model quantum systems, and many compilation frameworks have been developed for executing such simulations on quantum computers. Most compilers leverage the capabilities of digital and analog quantum computers by representing quantum particle systems with Pauli strings or digital quantum circuits, making it challenging for users in physics, chemistry, and biology to program simulations effectively. QBLUE is proposed as the first programming language for describing the behaviors of quantum systems in terms of second quantization Hamiltonians. Within QBLUE, a novel type system is proposed to clearly define states across different quantum systems and treat quantum computers as quantum particle systems of specific types. The type system is compatible with the compilation of quantum simulations expressed in QBLUE for digital and analog quantum computers. With QBLUE, users can specify the desired quantum particle system and model the system on quantum computers.