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Simplified Factoring Algorithms for Validating Small-Scale Quantum Information Processing Technologies

Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification scheme based on compiled versions of Shor's factoring algorithm that may be extended to large circuits in the future. The general version Shor's algorithm has been experimentally elusive due to bottlenecks associated with the modular exponentiation operation. Experiments to date have only been able to execute compiled versions of the latter operation. We provide some new compiled circuits for experimentalists to use in the near future. We also demonstrate that an additional layer of compilation can be added using classical operations, that will reduce the number of qubits and gates needed in a given compiled circuit.