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Abstract A leading approach to algorithm design aims to minimize the number of operations in an algorithm’s compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer’s potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize themore » resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm’s number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.« less

Here we consider a model of heat engine operating in the microscopic regime: the two-stroke engine. It produces work and exchanges heat in two discrete strokes that are separated in time. The working body of the engine consists of two d-level systems initialized in thermal states at two distinct temperatures. Additionally, an auxiliary nonequilibrium system called catalyst may be incorporated with the working body of the engine, provided the state of the catalyst remains unchanged after the completion of a thermodynamic cycle. This ensures that the work produced by the engine arises solely from the temperature difference. Upon establishing themore » rigorous thermodynamic framework, we characterize twofold improvement stemming from the inclusion of a catalyst. Firstly, we prove that in the noncatalytic scenario, the optimal efficiency of the two-stroke heat engine with a working body composed of two-level systems is given by the Otto efficiency, which can be surpassed by incorporating a catalyst with the working body. Secondly, we show that incorporating a catalyst allows the engine to operate in frequency and temperature regimes that are not accessible for noncatalytic two-stroke engines. We conclude with a general conjecture about the advantage brought by a catalyst: including the catalyst with the working body always allows to improve efficiency over the noncatalytic scenario for any microscopic two-stroke heat engines. We prove this conjecture for two-stroke engines where the working body is composed of two d-level systems initialized in thermal states at two distinct temperatures, as long as the final joint state leading to optimal efficiency in the noncatalytic scenario is not a product state, or at least one of the d-level system is not thermal.« less