Low-depth quantum architectures for factoring

Abstract

Quantum computing is a new field which combines computer science and quantum physics. Its most famous result, Shor's factoring algorithm, would enable us to one day compromise the widely-used RSA cryptosystem if we are able to design efficient quantum architectures. Studying the depth of these architectures would allow us to solve this human problem within a human lifetime. Toward that end, we contribute two hybrid factoring architectures in poly-logarithmic and sub-logarithmic depths, which are both exponential improvements over previous known works. We also present an improved procedure for generating quantum Fourier states useful for quantum compiling. Finally, we invent a new circuit resource called coherence which upper bounds the error-correcting effort needed in a future quantum computer. We use this to characterize a better time-space tradeoff for factoring as well as to provide configurable-depth factoring architectures.