A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A new universal and fault-tolerant quantum basis
Information Processing Letters
Quantum computation and quantum information
Quantum computation and quantum information
Classical and Quantum Computation
Classical and Quantum Computation
Quantum and classical tradeoffs
Theoretical Computer Science
An algebraic approach for quantum computation
Journal of Computing Sciences in Colleges
Invited Talk: Embedding Classical into Quantum Computation
Mathematical Methods in Computer Science
Asymptotically optimal circuits for arbitrary n-qubit diagonal comutations
Quantum Information & Computation
Quantum computing and polynomial equations over the finite field Z2
Quantum Information & Computation
Quantum universality by state distillation
Quantum Information & Computation
Achieving perfect completeness in classical-witness quantum merlin-arthur proof systems
Quantum Information & Computation
Stronger methods of making quantum interactive proofs perfectly complete
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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What additional gates are needed for a set of classical universal gates to do universal quantum computation? We prove that any single-qubit real gate suffices, except those that preserve the computational basis. The Gottesman-Knill Theorem implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its like) are universal for quantum computing. Previously only a generic gate, namely a rotation by an angle incommensurate with π, is known to be sufficient in both problems, if only one single-qubit gate is added.