ELEMENTARY GATES FOR FAULT-TOLERANT QUANTUM COMPUTING

摘要

A novel proof on the universality of the fault-tolerant Shor 's basis is provided. Such a set of elementary quantum gates is necessary for the approximation of the generic unitary operators, on any number of qubits. The basis considered here contains the following quantum gates: Hadamard, phase, CNOT and Toffoli. Since the proof is made by construction, a couple of circuits necessary for implementing some elementary unitary operators on one qubit are also provided.