Optimization and design for multi-valued quantum comparator circuits
Tingyan Zhang, Yi Li, Shih-Wen Lu, Jingwen Ai, Ming-Qiang Bai, Zhiwen Mo, Wenbo Du, Pengheng Jiang, Jiawei Liu · Journal of Physics A Mathematical and Theoretical · 2025
Abstract Multi-valued quantum systems have more significant advantages in computational performance than binary quantum system, since the circuit design is more compact and efficient in multi-valued quantum systems. Hence, synthesizing multi-valued logic circuits is a better choice for future quantum computing technology. A subcircuit in the Grover’s algorithm is called an oracle, which inputs a set of quantum qudits and gives an output according to the search conditions. Greater-than/less-than/equality comparators are widely used in search conditions. In this paper, the ternary Toffoli gate proposed by Monfared and Haghparast is extended to multi-valued under certain conditions, and the existing optimal quaternary n-qudit comparator is optimized using the multi-valued Toffoli gate. In addition, we design universal multi-valued equality/greater-than/less-than comparators and complementary component, which constitute a comprehensive multi-valued n-qudit comparator. Compared to existing comparator circuits, these comparator circuits are more efficient in terms of quantum cost, garbage output, hardware complexity, and constant input.