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We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n , we show that there exists a constant ϵ ≈ 0.034 such that the quantum routing time is at most ( 1 − ϵ ) n , whereas any swap-based protocol needs at least time n − 1 . This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2 n / 3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k ≤ n qubits and give algorithms with quantum routing time at most n / 3 + O ( k 2 ) on paths and at most 2 r / 3 + O ( k 2 ) on general graphs with radius r . 

Card-not-present credit card fraud costs businesses billions of dollars a year. In this paper, we present Boxer, a mobile SDK and server that enables apps to combat card-not-present fraud by scanning cards and verifying that they are genuine. Boxer analyzes the images from these scans, looking for telltale signs of attacks, and introduces a novel abstraction on top of modern security hardware for complementary protection. Currently, 323 apps have integrated Boxer, and tens of them have deployed it to production, including some large, popular, and international apps, resulting in Boxer scanning over 10 million real cards already. Our evaluation of Boxer from one of these deployments shows ten cases of real attacks that our novel hardware-based abstraction detects. Additionally, from the same deployment, without letting in any fraud, Boxer’s card scanning recovers 89% of the good users whom the app would have blocked. In another evaluation of Boxer, we run our image analysis models against images from real users and show an accuracy of 96% and 100% on the two models that we use.