%0 Journal Article
%T Checking Equivalence of Quantum Circuits and States
%A George F. Viamontes
%A Igor L. Markov
%A John P. Hayes
%J Computer Science
%D 2007
%I arXiv
%X Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as determining if two states or circuits are functionally equivalent. While differences in classical states are easy to detect, quantum states, which are represented by complex-valued vectors, exhibit subtle differences leading to several notions of equivalence. This provides flexibility in optimizing quantum circuits, but leads to difficult new equivalence-checking issues for simulation and synthesis. We identify several different equivalence-checking problems and present algorithms for practical benchmarks, including quantum communication and search circuits, which are shown to be very fast and robust for hundreds of qubits.
%U http://arxiv.org/abs/0705.0017v2