Gate Error Probability Research Articles

Markov Chains and Probabilistic Computation—A General Framework for Multiplexed Nanoelectronic Systems

In emerging nanotechnologies, reliable computation will have to be carried out with unreliable components being integral parts of computing systems. One promising scheme for designing these systems is von Neumann's multiplexing technique. Using bifurcation theory and its associated geometrical representation, we have studied a NAND-multiplexing system recently proposed. The behavior of the system is characterized by the stationary distribution of a Markov chain, which is uni- or bi-modal, when the error probability of NAND gates is larger or smaller than the threshold value, respectively. The two modes and the median of the stationary distribution are the keys to the characterization of the system reliability. Examples of potential future nanochips are used to illustrate how the NAND-multiplexing technique can lead to high system reliability in spite of large gate error probability while keeping the cost of redundancy moderate. In nanoelectronic systems, while permanent defects can be taken care of by reconfiguration, probabilistic computation schemes can incorporate another level of redundancy so that high tolerance of transient errors may be achieved. The Markov chain model is shown to be a powerful tool for the analysis of multiplexed nanoelectronic systems.

UNCERTAINTY PRINCIPLE FOR QUANTUM INSTRUMENTS AND COMPUTING

The notion of quantum instruments is formalized as statistical equivalence classes of all the possible quantum measurements and mathematically characterized as normalized completely positive map valued measures under naturally acceptable axioms. Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative generalization of the Wigner–Araki–Yanase theorem on the precision limit of measurements under conservation laws. Applying this, a rigorous lower bound is obtained for the gate error probability of physical implementations of Hadamard gates on a standard qubit of a spin 1/2 system by interactions with control fields or ancilla systems obeying the angular momentum conservation law.

Parallel information and computation with restitution for noise-tolerant nanoscale logicnetworks

Nanoelectronic devices are anticipated to become exceedingly noisy as they are scaledtowards thermodynamic limits. Hence the development of nanoscale classical informationsystems will require optimal schemes for reliable information processing in the presence ofnoise. We present a novel, highly noise-tolerant computer architecture based on the work ofvon Neumann that may enable the construction of reliable nanocomputers comprised ofnoisy gates. The fundamental principles of this technique of parallel restitution are parallelprocessing by redundant logic gates, parallelism in the interconnects between gate resourcesand intermittent signal restitution performed in parallel. The results of our mathematicalmodel, verified by Monte Carlo simulations, show that nanoprocessors consisting of gates incorporating this technique can be made 90% reliable over 10 years ofcontinuous operation with a gate error probability per actuation of and a redundancy of . This compares very favourably with corresponding results utilizing modular redundantarchitectures of with , and with no noise tolerance. Arbitrary reliability is possible within a noise limit of , with massive redundancy. We show parallel restitution to be a general paradigmapplicable to different kinds of information processing, including neural communication.Significantly, we show how our treatment of para-restituted computation as a statisticalensemble coupled to a heat bath allows consideration of the computation entropy of logicgates, and tentatively sketch a thermodynamic theory of noisy computation that might setfundamental physical limits on scaling classical computation to the nanoscale. Ourpreliminary work indicates that classical computation may be confined to the macroscaleby noise, quantum computation possibly being the only information processing possible atthe extreme nanoscale.