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3A-4s Synthesis of Quantum Logic Circuits Vivek V. Shende1 vshende@eecs.umich.edu 1 Dept. Stephen S. Bullock2 stephen.bullock@nist.gov Igor L. Markov1 imarkov@eecs.umich.edu 2 Mathematical of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109-2212, USA and Computational Sciences Division, Natl. Inst. of Standards and Technology, Gaithersburg, MD 20899-8910, USA Abstract The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits to the attention of the EDA community [10, 17, 4, 16, 9]. We discuss ef cient circuits to initialize quantum registers and implement generic quantum computations. Our techniques yield circuits that are twice as small as the best previously published technique. Moreover, a theoretical lower bound shows that our new circuits can be improved by at most a factor of two. Further, the circuits grow by at most a factor of nine under severe architectural restrictions. commercially available from MagiQ Technologies in the U.S. and IdQuantique in Europe. Quantum bit data states differ from classical states in two important ways. First, a single quantum bit may take on a continuum of values z1 |0 + z2 |1 for z1 , z2 complex numbers.
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