Achieving Pareto-Optimality in Quantum Circuit Compilation via a Multi-Objective Heuristic Optimization Approach

High Performance Computing-Quantum Computing (HPCQC) integration presents a promising yet challenging opportunity, particularly in the area of quantum circuit compilation and optimization, requiring further advancements in the field of Quantum Computing (QC). To address this, we introduce the Munich Quantum Compiler, a key component of the Munich Quantum Software Stack (MQSS). This compiler employs a heuristic-based approach to select a Pareto-optimal subset of optimizations in the form of LLVM passes for quantum circuits described in an LLVM-compliant Intermediate Representation (IR).