A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
Complexity of Finding Short Resolution Proofs
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Random Benchmark Circuits with Controlled Attributes
EDTC '97 Proceedings of the 1997 European conference on Design and Test
Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Parallelizing quantum circuits
Theoretical Computer Science
Universal sets of quantum information processing primitives and their optimal use
General Theory of Information Transfer and Combinatorics
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This paper introduces a simple but nontrivial set of local transformation rules for designing Control-NOT(CNOT)-based combinatorial circuits. We also provide a proof that the rule set is complete, namely, for any two equivalent circuits, S1 and S2, there is a sequence of transformations, each of them in the rule set, which changes S1 to S2. Two applications of the rule set are also presented. One is to simulate Resolution with only polynomial overhead by the rule set. Therefore we can conclude that the rule set is reasonably powerful. The other is to reduce the cost of CNOT-based circuits by using the transformations in the rule set. This implies that the rule set might be used for the practical circuit design.