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I am working on a circuit for a Grover problem and during that I am trying to minimize the used QuBits.

The problem is shown in the attached image. In this case the circuit is more or less efficient but with a growing number of input bits (the x register) the ccx grows more complex (cccx, ccccx, ...) and inefficient but more importantly more qubits in y register are needed (one more for each comparison).

My primary goal is to reduce the used y-QuBits. Can someone think of such a circuit or is it already optimal (I really dont think so).

enter image description here

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Instead of saving the information of a single comparison into a y qubit, you can use a controlled adder. Instead of $n$ y qubits you would only need $\log_2 n$.

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  • $\begingroup$ Thanks for your answer. Could you clarify what you mean by a controleld adder? A link to a paper or further information would be great. $\endgroup$
    – Idefixus
    Commented May 3, 2020 at 13:09
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    $\begingroup$ @Idefixus maybe this : arxiv.org/pdf/quant-ph/0206028 but there are plenty of adders online. Pick one and perform every operation of the adder implementation as a controlled operation so that you only increment when you state is a solution $\endgroup$
    – draks ...
    Commented May 3, 2020 at 16:06

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