6 research outputs found

    Deviation-tolerant computation in concurrent failure-prone hardware

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    Quantitative Robustness Analysis of Quantum Programs (Extended Version)

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    Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called \epsilon-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

    Static typing for a faulty lambda calculus

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    A transient hardware fault occurs when an energetic particle strikes a transistor, causing it to change state. These faults do not cause permanent damage, but may result in incorrect program execution by altering signal transfers or stored values. While the likelihood that such transient faults will cause any significant damage may seem remote, over the last several years transient faults have caused costly failures in high-end machines at America Online, eBay, and the Los Alamos Neutron Science Center, among others [6, 44, 15]. Because susceptibility to transient faults is proportional to the size and density of transistors, the problem of transient faults will become increasingly important in the coming decades. This paper defines the first formal, type-theoretic framework for studying reliable computation in the presence of transient faults. More specifically, it defines 位zap, a lambda calculus that exhibits intermittent data faults. In order to detect and recover from these faults, 位zap programs replicate intermediate computations and use majority voting, thereby modeling software-based fault tolerance techniques studied extensively, but informally [10, 20, 30, 31, 32
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