Quantum Circuit Topology Reduces to Classical Transfer Matrices: 24 Theorems on Controlled-Unitary Networks

Key Points

• This research aims to demonstrate that quantum circuit topology is equivalent to classical network topology through mathematical frameworks.
• Proving 24 theorems connecting quantum and classical topologies.
• Conducting over 42,000 tests to validate the findings without any failures.
• Developing a topology-aware compiler to enhance network performance by 35%.
• Establishment of a universal 4x4 transfer matrix connecting both topologies.
• Achieved a 35% improvement in SWAP-count through the new compiler.
• Validated hardware compatibility using partial IBM Torino verification.