Title: Exploring ab initio machine synthesis of quantum circuits

Abstract: Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Here we explore methods for the ab initio creation of circuits within a machine, either a classical computer or a hybrid quantum-classical device. We consider a range of techniques including: methods for introducing new gate structures, optimisation of parameterised circuits and choices of cost functions, and efficient removal of low-value gates exploiting the quantum geometric tensor and other heuristics. Using these principles we tackle the tasks of automatic encoding of unitary processes and translation (recompilation) of a circuit from one form to another. Using emulated quantum computers with various noise-free gate sets we provide simple examples involving up to 10 qubits, corresponding to 20 qubits in the augmented space we use. Further applications of specific relevance to chemistry modelling are considered in a sister paper, 'Exploiting subspace constraints and ab initio variational methods for quantum chemistry'.