We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment, and prove that any other true equation can be derived from these. This is the first such completeness result for a finitely-generated, universal fragment of quantum circuits, with no parameterized gates and no need for ancillas.

翻译：本文针对由实数 Clifford 门与双量子比特受控 Hadamard 门生成的量子电路片段，提出了一套完备的等式理论。具体而言，我们给出了该片段电路中一组简洁的等式关系，并证明任何其他成立的等式均可由这些等式推导得出。这是首次针对有限生成、通用且无需参数化门或辅助量子比特的量子电路片段所获得的完备性结果。