The complexity of elementary algebra and geometry
Journal of Computer and System Sciences
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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A logic for reasoning about quantum circuits and protocols is proposed. It incorporates the basic features of quantum theory-probability, unitary dynamics, tensor products and measurement. The underlying language could be used for verification and synthesis of quantum circuits. Important algorithms like the quantum search algorithm of Grover are discussed. The logic also forms the foundation on which more elaborate formal systems for reasoning about quantum protocols could be based. A sound and complete axiomatization is presented. Algorithms for circuit verification, circuit equivalence (exact and approximate) are outlined. Some related complexity issues are also discussed.