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Checking equivalence of quantum circuits and states

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3 Author(s)
Viamontes, G.F. ; Lockheed Martin ATI., Cherry Hill ; Markov, I.L. ; Hayes, J.P.

Among the post-CMOS technologies currently under investigation, quantum computing (QC) holds a special place. QC offers not only extremely small size and low power, but also 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.

Published in:

Computer-Aided Design, 2007. ICCAD 2007. IEEE/ACM International Conference on

Date of Conference:

4-8 Nov. 2007