



01816nas a2200193   4500008004100000245007600041210006900117260001400186300001500200490000600215520125400221100001901475700001901494700001801513700002001531700001901551700001501570856003701585       2018                        eng d00aQuantitative Robustness Analysis of Quantum Programs (Extended Version)0 aQuantitative Robustness Analysis of Quantum Programs Extended Ve  c2018/12/1  aArticle 310 v33 a<p>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 ε-robustness, which characterizes possible &quot;distance&quot; 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.</p>1 aHung, Shih-Han1 aHietala, Kesha1 aZhu, Shaopeng1 aYing, Mingsheng1 aHicks, Michael1 aWu, Xiaodi  uhttps://arxiv.org/abs/1811.03585