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Let us now consider the gates in the classical FFT circuit after the recursive calls to F F TM/2 : the wires pair up j with M/2 + j, and ignoring for now the phase that is applied to the contents of the (M/2 + j)th wire, we must add and subtract these two quantities to obtain the jth and the (M/2 + j)th outputs, respectively How would a quantum circuit achieve the result of these M classical gates Simple: just perform the Hadamard gate on the rst qubit! Recall from the preceding discussion (Section 1051) that for every possible con guration of the remaining m 1 qubits x, this pairs up the strings 0x and 1x Translating from binary, this means we are pairing up x and M/2+x.

dbvacctmgr@aos>-- forced to change it to a password dbvacctmgr@aos>-- they can control at next login dbvacctmgr@aos>ALTER USER alan_analyst PASSWORD EXPIRE; User altered. dbvacctmgr@aos>CONNECT jean_oper_dba Enter password: Connected. jean_oper_dba@aos>-- provide the ability to connect to the database GRANT CREATE SESSION TO alan_analyst; Grant succeeded. jean_oper_dba@aos>-- this won't work, the role is now protected GRANT sh_data_analyst_0101 TO alan_analyst; jean_oper_dba@aos>GRANT sh_data_analyst_0101 TO alan_analyst * ERROR at line 1: ORA-00604: error occurred at recursive SQL level 1 ORA-47401: Realm violation for grant role privilege on sh_data_analyst_0101. ORA-06512: at "DVSYS.AUTHORIZE_EVENT", line 55 ORA-06512: at line 31 jean_oper_dba@aos>-- we have to login as the Sales History Security jean_oper_dba@aos>-- administrator to perform the grant jean_oper_dba@aos>CONNECT sam_sec_mgr Enter password: Connected. sam_sec_mgr@aos>GRANT sh_data_analyst_0101 TO alan_analyst; Grant succeeded. sam_sec_mgr@aos>-- now connect as the data analyst sam_sec_mgr@aos>-- and see how it works sam_sec_mgr@aos>CONNECT alan_analyst Enter password: ERROR: ORA-28001: the password has expired Changing password for alan_analyst New password: Retype new password: Password changed Connected. alan_analyst@aos>-- the account can query the COSTS table alan_analyst@aos> SELECT * FROM sh.costs WHERE ROWNUM < 6; PROD_ID TIME_ID PROMO_ID CHANNEL_ID UNIT_COST UNIT_PRICE ---------- --------- ---------- ---------- ---------- ---------13 20-JAN-98 999 2 793.14 1205.99 13 30-JAN-98 999 3 783.03 1232.16 13 21-FEB-98 999 3 813.07 1237.31 13 25-FEB-98 999 3 798.69 1232.99 14 19-JAN-98 999 2 886.45 1108.99 5 rows selected. alan_analyst@aos>-- demonstrate the account cannot delete alan_analyst@aos>-- data in the COSTS table alan_analyst@aos>DELETE sh.costs WHERE prod_id = 22; DELETE sh.costs WHERE prod_id = 22

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Moreover the result of the Hadamard gate is that for each such pair, the amplitudes are replaced by the sum and difference (normalized by 1/ 2) , respectively So far the QFT requires almost no gates at all! The phase that must be applied to the (M/2 + j)th wire for each j requires a little more work Notice that the phase of j must be applied only if the rst qubit is 1 Now if j is j represented by the m 1 bits j1 jm 1 , then j = m 1 2 l Thus the phase j can be l=1 l applied by applying for the lth wire (for each l) a phase of 2 if the lth qubit is a 1 and the rst qubit is a 1 This task can be accomplished by another two-qubit quantum gate the conditional phase gate.

YEASTS (UNICELLULAR)

It leaves the two qubits unchanged unless they are both 1, in which case it applies a speci ed phase factor The QFT circuit is now speci ed The number of quantum gates is given by the formula S(m) = S(m 1)+O(m), which works out to S(m) = O(m 2 ) The QFT on inputs of size M = 2m thus requires O(m2 ) = O(log2 M ) quantum operations 302.

Access the Device Manager by clicking the System icon and then choosing the Device Manager Tab in the Control Panel on Windows 9x systems. Windows 2000/XP systems use the Computer Management icon and then selecting the Device Manager. The Device Manager allows you to manage devices on your computer by disabling devices, refreshing drivers, or reallocating resources on your system. Device Manager is one of the primary methods of troubleshooting problems involving hardware.

To allow the user to select multiple items in a choose from list dialog box, add the with multiple selections allowed parameter. You don t need to set this to true or false; if you add this parameter to your code, it s true, and if you omit the parameter, it s false. Here s an example:

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