Predicting practical speedups offered by future quantum computers has become a major focus of the quantum community. Typically, such predictions involve numerical simulations supported by lengthy manual analyses and are carried out for one specific algorithm at a time. In this work, we present Traq, a principled approach towards estimating the quantum speedup of classical programs fully automatically. It consists of a classical language that includes high-level primitives amenable to quantum speedups, a compilation to low-level quantum programs, and a source-level cost analysis with provable guarantees. Our cost analysis upper bounds the complexity of the resulting quantum program and is sensitive to the input data of the program (in addition to providing worst-case costs). Traq is implemented as a Haskell package with an extensive evaluation.

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