A Complete Equational Theory for Real-Clifford+CH Quantum Circuits

Key Points

• Any valid equation can be derived from a simple set of equalities, confirming completeness for this quantum circuit fragment.
• The developed equational theory applies to circuits using real Clifford gates along with the controlled-Hadamard gate, ensuring universality.
• This is the first completeness result without the use of parameterized gates or ancillas, simplifying quantum computations.
• The findings support further exploration in understanding the foundational aspects of quantum circuit design and optimization.

Abstract