Energy Bounds for Fault-Tolerant Nanoscale Designs
Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Fault tolerance in cellular automata at high fault rates
Journal of Computer and System Sciences
Analysis of defect tolerance in molecular crossbar electronics
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Upper bounds on the noise threshold for fault-tolerant quantum computing
Quantum Information & Computation
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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The information carried by a signal decays when the signal is corrupted by random noise. This occurs when a message is transmitted over a noisy channel, as well as when a noisy component performs computation. We first study this signal decay in the context of communication and obtain a tight bound on the rate at which information decreases as a signal crosses a noisy channel. We then use this information theoretic result to obtain depth lower bounds in the noisy circuit model of computation defined by von Neumann. In this model, each component fails (produces 1 instead of 0 or vice-versa) independently with a fixed probability, and yet the output of the circuit is required to be correct with high probability. Von Neumann showed how to construct circuits in this model that reliably compute a function and are no more than a constant factor deeper than noiseless circuits for the function. We provide a lower bound on the multiplicative increase in circuit depth necessary for reliable computation, and an upper bound on the maximum level of noise at which reliable computation is possible