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Invariance of complexity measures for networks with unreliable gates
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A new probabilistic failure model for networks of gates is formulated and supports the proofs of both the positive and negative results appearing in the literature.Abstract:
A new probabilistic failure model for networks of gates is formulated. Although this model has not been used previously, it supports the proofs of both the positive and negative results appearing in the literature. Furthermore, with respect to this new model, the complexity measures of both size and depth are affected by at most constant multiplicative factors when the set of functions that can be computed by gates is changed from one finite and complete basis to another, or when the bound on the failure probability of the gates is changed (within the limits allowed by the basis), or when the bound on the error probability of the network is changed (within the limits allowed by the basis and the failure probability of the gates).read more
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Journal ArticleDOI
Good quantum error-correcting codes exist
A. R. Calderbank,Peter W. Shor +1 more
TL;DR: The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.
Proceedings ArticleDOI
Fault-tolerant quantum computation
TL;DR: For any quantum computation with t gates, a polynomial size quantum circuit that tolerates O(1/log/sup c/t) amounts of inaccuracy and decoherence per gate, for some constant c, was shown in this article.
Posted Content
Fault-tolerant quantum computation
TL;DR: For any quantum computation with t gates, it is shown how to build a polynomial size quantum circuit that tolerates O(1/log/sup c/t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O( 1/t).
Journal ArticleDOI
Coding for interactive communication
TL;DR: A deterministic method for simulating noiseless-channel protocols on noisy channels, with only a constant slowdown is described, an analog for general, interactive protocols of Shannon's coding theorem, which deals only with data transmission, i.e., one-way protocols.
Syntactic Measures of Complexity
TL;DR: This dissertation aims to clarify the role of language in the development of Complexity and investigates the role that language plays in the design of models and their application to complex systems.
References
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Proceedings ArticleDOI
On networks of noisy gates
TL;DR: It is shown that many Boolean functions (including, in a certain sense, "almost all" Boolean functions) have the property that the number of noisy gates needed to compute them differs from the numberof noiseless gates by at most a constant factor.
Journal ArticleDOI
Reliable computation with cellular automata
TL;DR: A one-dimensional array of cellular automata on which arbitrarily large computations can be implemented reliably, even though each automaton at each step makes an error with some constant probability, leads to the refutation of the positive probability conjecture.
Journal ArticleDOI
Reliable computation by formulas in the presence of noise
TL;DR: It is shown that if formulas are used to compute Boolean functions in the presence of randomly occurring failures then: there is a limit strictly less than 1/2 to the failure probability per gate that can be tolerated, and formulas that tolerate failures must be deeper than those that do not.
Journal ArticleDOI
Complexity in Electronic Switching Circuits
TL;DR: The complexity of an electronic switching circuit is defined in a sufficiently general way so that most definitions which are presently used may be included and theoretical bounds are compared with those obtained from a few known circuiit designs.