| 摘要 |
<P>PROBLEM TO BE SOLVED: To perform quantum computation without using an auxiliary bit in linear size and linear depth. <P>SOLUTION: CNOT arithmetic operation to Q<SB>2n+1</SB>and Q<SB>k+2</SB>(k=1,..., 2n-2) is performed and Toffoli arithmetic operation to Q<SB>1</SB>, Q<SB>2</SB>, and Q<SB>2n+1</SB>is performed. Then, MAJ arithmetic operation to Q<SB>2p+1</SB>, Q<SB>2p+2</SB>, and Q<SB>2n+1</SB>and Toffoli arithmetic operation to Q<SB>2p+1</SB>, Q<SB>2p+2</SB>, and Q<SB>1</SB>are repeated in order in which p is increased by 1 from p=1 to p=n-2. After the repetition, MAJ arithmetic operation to the Q<SB>2n-1</SB>, Q<SB>2n</SB>, and Q<SB>2n+1</SB>is performed. Also, CNOT arithmetic operation to Q<SB>1</SB>and Q<SB>2p+4</SB>and Toffoli arithmetic operation to Q<SB>2p+1</SB>, Q<SB>2p+2</SB>and Q<SB>1</SB>are repeated in order in which q is decreased by 1 from q=n-2 to q=1. Then, NOT arithmetic operation to Q<SB>2</SB>is performed and Toffoli arithmetic operation to Q<SB>1</SB>, Q<SB>2</SB>, and Q<SB>2r+4</SB>(r=1, ..., n-2) is performed. Then, NOT arithmetic operation to Q<SB>2</SB>and Toffoli arithmetic operation to Q<SB>1</SB>, Q<SB>2</SB>, and Q<SB>4</SB>are performed, and after that operation, CNOT arithmetic operation to Q<SB>2t</SB>and Q<SB>2t-1</SB>(t=1, ..., n) is performed. <P>COPYRIGHT: (C)2007,JPO&INPIT |
