Question: 6. Parallelizing phase-queries 3 marks Let Us denote the unitary operation that maps |0) > 10) and (1) >eidl1). Note that Uke = UK. However,

6. Parallelizing phase-queries 3 marks Let Us
6. Parallelizing phase-queries 3 marks Let Us denote the unitary operation that maps |0) > 10) and (1) >eidl1). Note that Uke = UK. However, if a black-box process for implementing U. takes time t then implementing Uke in this serial way takes time kt. (a) What is the result of applying UQUQ. . .OU. = Ugk to |00. ..0) + -|11 ...1) = $ 210) 8k + 41 1) Bk ? (b) Show that it is possible to parallelize the implementation of Uk. in such a way that all k of the U. gates are applied in parallel (on different qubits). You may perform standard quantum gates on the qubits before and after the application of the k parallel phase gates

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