Elementary Gates for Quantum Computation

(quant-ph/9503007) 36] R. Landauer, \Is quantum mechanics useful?", Proc. Roy. Soc. Lond., (to be published). 37] The only non-trivial one-bit classical invertible operation is 0 1 1 0. 41] Corresponding with the deenition in the previous section, the top two wires contain the input bits x 1 and x 2 , and the third wire contains the input y). 42] The angle-halving of this deenition conforms to the usual relation between operations in SO(3) and SU(2). for the use of SO(3) language (rigid body rotations) to describe SU(2) operations. 43] D. P. DiVincenzo and J. Smolin, \Results on two-bit gate design for quantum comput-ers", 28] A. Barenco, \A universal two-bit gate for quantum computation", preprint (1994). 29] S. Lloyd, \Almost any quantum logic gate is universal", preprint (1994). of the Fredkin gate using a series of one-and two-body operators", Report IASSNS-HEP-95/15, (1995). (quant-ph/9503005) 32] D. Coppersmith, \An approximate Fourier transform useful in quantum factoring",