Quantum computing simulators form the classical software foundation on which virtually all quantum algorithm research depends. We present Broken Quantum, the first comprehensive formal security audit of the open-source quantum computing simulator ecosystem. Applying COBALT QAI -- a four-module static analysis engine backed by the Z3 SMT solver -- we analyze 45 open-source quantum simulation frameworks from 22 organizations spanning 12 countries. We identify 547 security findings (40 CRITICAL, 492 HIGH, 15 MEDIUM) across four vulnerability classes: CWE-125/190 (C++ memory corruption), CWE-400 (Python resource exhaustion), CWE-502/94 (unsafe deserialization and code injection), and CWE-77/22 (QASM injection -- a novel, quantum-specific attack vector with no classical analog). All 13 vulnerability patterns are formally verified via Z3 satisfiability proofs (13/13 SAT). The 32-qubit boundary emerges as a consistent formal threshold in both C++ and Python vulnerability chains. Supply chain analysis identifies the first documented case of vulnerability transfer from a commercial quantum framework into US national laboratory infrastructure (IBM Qiskit Aer to XACC/Oak Ridge National Laboratory). Nine frameworks score 100/100 under all four scanners; Qiskit Aer,Cirq, tequila, PennyLane, and 5 others score 0/100.