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STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the Power of Quantum Computation
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
SIAM Journal on Computing
Information Processing Letters
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Theoretical Computer Science
A Foundation of Programming a Multi-tape Quantum Turing Machine
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Complexity Limitations on Quantum Computation
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Fault-tolerant quantum computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Random polynomial time is equal to slightly-random polynomial time
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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In this paper we explore the power of quantum computers with restricted amplitudes. Adleman, DeMarrais and Huang showed that quantum Turing machines (QTMs) with the amplitudes from A = {0, 卤 3/5, 卤 4/5, 卤 1} are equivalent to ones with the polynomial-time computable amplitudes as machines implementing bounded-error polynomial time algorithms. We show that QTMs with the amplitudes from A is polynomial-time equivalent to deterministic Turing machines as machines implementing exact algorithms. Extending this result, it is shown that exact computers with rational biased 'quantum coins' are equivalent to classical computers. We also show that from the viewpoint of zero-error algorithms A is not more useful than B = {0, 卤 1/驴2, 卤 1} but sufficient for the factoring problem as the set of amplitudes taken by QTMs.