Quantum Intermediate Representation (QIR) is an LLVM-based intermediate representation developed by Microsoft for quantum program compilers. QIR is designed to offer a universal solution for quantum program compilers, decoupled from both front-end languages and back-end hardware, thereby eliminating the need for redundant development of intermediate representations and compilers. However, the lack of a formal definition and reliance on natural language descriptions in the current state of QIR result in interpretational ambiguity and a dearth of rigor in implementing quantum functions. In this paper, we present formal definitions for QIR's data types and instruction sets to establish correctness and safety assurances for operations and intermediate code conversions within QIR. To demonstrate the effectiveness of our approach, we provide examples of unsafe QIR codes where errors can be identified with our method.

As quantum programming evolves, more and more quantum programming languages are being developed. As a result, debugging and testing quantum programs have become increasingly important. While bug fixing in classical programs has come a long way, there is a lack of research in quantum programs. To this end, this paper presents a comprehensive study on bug fixing in quantum programs. We collect and investigate 96 real-world bugs and their fixes from four popular quantum programming languages (Qiskit, Cirq, Q#, and ProjectQ). Our study shows that a high proportion of bugs in quantum programs are quantum-specific bugs (over 80%), which requires further research in the bug fixing domain. We also summarize and extend the bug patterns in quantum programs and subdivide the most critical part, math-related bugs, to make it more applicable to the study of quantum programs. Our findings summarize the characteristics of bugs in quantum programs and provide a basis for studying testing and debugging quantum programs.